AFuzzySoftModelforHazePollutionManagementin NorthernThailand · occurred: Mae Hong Son, Chiang Mai,...

Research ArticleA Fuzzy Soft Model for Haze Pollution Management inNorthern Thailand

Parkpoom Phetpradap 12

1Department of Mathematics Faculty of Science Chiang Mai University Chiang Mai 50200 ailand2Centre of Excellence in Mathematics CHE Si Ayutthaya Rd Bangkok 10400 ailand

Correspondence should be addressed to Parkpoom Phetpradap parkpoomphetpradapcmuacth

Received 27 June 2019 Revised 18 January 2020 Accepted 23 January 2020 Published 11 March 2020

Academic Editor Jose A Sanz

Copyright copy 2020 Parkpoom Phetpradap )is is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

In this article we propose fuzzy soft models for decisionmaking in the haze pollutionmanagement)emain aims of this researchare (i) to provide a haze warning system based on real-time atmospheric data and (ii) to identify themost hazardous location of thestudy area PM10 is used as the severity index of the problem )e efficiency of the model is justified by the prediction accuracyratio based on the real data from 1st January 2016 to 31st May 2016)e fuzzy soft theory is modified in order to makemodels moresuitable for the problems )e results show that our fuzzy models improve the prediction accuracy ratio compared to theprediction based on PM10 density only )is work illustrates a fuzzy analysis that has the capability to simulate the unknownrelations between a set of atmospheric and environmental parameters )e study area covers eight provinces in the northernregion of)ailand where the problem severely occurs every year during the dry season Seven principle parameters are consideredin the model which are PM10 density air pressure relative humidity wind speed rainfall temperature and topography

1 Introduction

Pollution problems are inevitably a global concern of the 21stcentury Over the past decade polluted haze has become amajor problem in the northern region of )ailand andsurrounded countries InMarch 2019 the problem reached acrisis when the daily average PM25 and PM10 (particulatematter of 25 microns and 10 microns in diameter orsmaller) density rates were well beyond the national stan-dard of 25 μgm3 and 50 μgm3 for several days according tolocal environmental data sources such as Pollution ControlDepartment [1] Climate Change Data Centre of ChiangMaiUniversity [2] and Smoke Haze Integrated Research Unit[3] )is situation has occurred every year on dry seasonfrom January to May and generally reached its peak inMarch During this period a large amount of particulatematters are released into the atmosphere including carbonmonoxide carbon dioxide volatile organic compounds andcarcinogenic polycyclic aromatic hydrocarbons [4] )emain emission source is biomass open burning such as

forest fires solid waste burning and agricultural residuefield burning [5 6]

)is problem has a significant effect on human healthlocal traveling industry and the economy as a whole espe-cially in Chiang Mai province a popular tourist destination

)e public health ministry of )ailand has reported anincrease in bronchial asthma and respiratory diseases inpeople living in these areas In addition these fine particlescontain carcinogenic polycyclic aromatic hydrocarbons thatcan induce lung cancer [7] )e smoke haze episodes alsoreduce visibility and cause a variety of environmental effectswhich eventually leads to decline in various economicsectors such as tourism transportation and agriculture)aigovernment has launched various policies to get the smokehaze problem under control However the problem stillcontinues to grow even with the enforcement of outdoorburning ban issued by )ai government during February toApril period

Apparently the atmospheric parameters and topographyplay the key parts of the problem )e air pollutants are

HindawiAdvances in Fuzzy SystemsVolume 2020 Article ID 6968705 13 pageshttpsdoiorg10115520206968705

trapped near ground level due to the meteorological con-ditions (eg stagnant air) and the basin-like topographysurrounded by high mountain ranges results in restrictedpollution dispersion Moreover low rainfall in dry seasonalso adds on to the severity of the haze problem For thisreason the leaching of smoke or dust particles in the air islow [6] )ese conditions caused the air pollutants to flowout difficultly and the particle cannot be easily escaped fromthe area Notably there are some technologies that mitigatethe pollution problem However the costs of devices areconsiderably expensive

Undoubtedly an efficient warning system would becomea major help in the haze problem management )e systemwill significantly improve public safety and mitigate damagecaused )e Goddard Earth Observing System Model Ver-sion 5 (GEOS-5) is currently one of the widely used pollutionprediction models developed by NASArsquos research team

In this article the potential use of fuzzy soft set theory inreal-time haze warning is investigated)e main aims of thisresearch are (i) to provide a haze warning system based onreal-time atmospheric data and (ii) to identify the mosthazardous location of the study area )e benefits are tocreate the awareness for people in the affected area and tosuggest the location to establish pollutionmitigation devicesMolodtsov [8ndash10] initiated the concept of soft set theory as anew mathematical tool for dealing with uncertainties Softset theory has rich potential for applications in several di-rections a few of which had been shown by Molodtsov [8])e idea of applying fuzzy soft set theory in atmosphericmodels is already considered concerning the applications toair pollution management [11ndash14] and water management[15ndash20] However it is believed that air pollution modelsmay be different for each region due to many several factors[21 22] )erefore existing models still need to be restudiedUp to our knowledge there are only a few prediction modelsin the region of study since the main concerns are on the siteof environmental science )e prediction results fromGEOS-5 model are popular choices to be used as bench-marks for environmental scientist )e regional-developedmodels include a logistic regression model [23] and Geo-graphic Information System- (GIS-) based model [24])erefore our model would offer an alternative predictionmodel for the haze pollution problem

)e study location covered eight provinces in thenorthern part of )ailand where haze problem has severelyoccurred Mae Hong Son Chiang Mai Lamphun ChiangRai Phayao Lampang Phrae and Nan)e density of PM10is used as severity index of the haze pollution level Addi-tionally seven principle parameters are considered in themodel six are atmospheric parametersmdashPM10 air pressurerelative humidity wind speed rainfall and temper-aturemdashand the other one is the topographic parameter Allatmospheric data are obtained from the Pollution ControlDepartment [1])e obtained data period is from 1st January2016 to 31st May 2016

)e rest of this article is organized as follows In Section2 we explain the methodology and present some examplesIn Section 3 we describe the setup of the model whichincludes the study location the data and the parameters

)en we present our decision-making results and discussionin Section 4 Finally the conclusion is given in Section 5

2 Methodology

21 Fuzzy Soft eory In this section we provide usefulnotations of soft sets and fuzzy soft sets LetU L1 L2 Lm1113864 1113865 be an initial universal set and let E

P1 P2 Pn1113864 1113865 be a set of parameters

Definition 1 (see [8]) Let P(U) denote the power set of U

and A sub E A pair (F A) is called a soft set over U where F

is a mapping given by F A⟶ P(U)

Example 1 Let the initial universe U L1 L2 L81113864 1113865 bethe eight selected provinces in the northern region of)ailand Mae Hong Son Chiang Mai Lamphun ChiangRai Phayao Lampang Phrae and Nan Moreover let E

P1 P2 P3 P41113864 1113865 be atmospheric parameters PM10 densityair pressure relative humidity and wind speed respectively)en an example of possible soft set is

F P1( 1113857 L1 L2 L31113864 1113865

F P2( 1113857 L2 L4 L7 L81113864 1113865

F P3( 1113857 L1 L5 L6 L81113864 1113865

F P4( 1113857 L4 L71113864 1113865

(1)

Note that each approximation has two parts predicate p

and approximate value set For example the predicate isPM10 density and the approximate value set is L1 L2 L31113864 1113865

for F(P1) Additionally the summary information of thissoft set is represented in Table 1

Definition 2 (see [25]) Let Ψ(U) denote the set of all fuzzysets of U and let Ai sub E A pair (Fi Ai) is called a fuzzy softset over U where Fi is a mapping given byFi Ai ⟶Ψ(U)

Example 2 We consider the same setup as in Example 1 Anexample of a fuzzy soft set is

F P1( 1113857 L1

071113874 1113875

L2

091113874 1113875

L3

11113874 1113875

L4

041113874 1113875

L5

021113874 1113875

L6

031113874 1113875

L7

041113874 1113875

L8

051113874 11138751113882 1113883

F P2( 1113857 L1

051113874 1113875

L2

081113874 1113875

L3

011113874 1113875

L4

11113874 1113875

L5

021113874 1113875L50

L6

031113874 1113875

L7

061113874 1113875

L8

11113874 11138751113882 1113883

F P3( 1113857 L1

081113874 1113875

L2

021113874 1113875

L3

011113874 1113875

L4

01113874 1113875

L5

091113874 1113875

L6

071113874 1113875

L7

021113874 1113875

L8

081113874 11138751113882 1113883

F P4( 1113857 L1

021113874 1113875

L2

041113874 1113875

L3

041113874 1113875

L4

071113874 1113875

L5

11113874 1113875

L6

051113874 1113875

L7

061113874 1113875

L8

041113874 11138751113882 1113883

(2)

Table 2 provides the summary information of this fuzzysoft set

Definition 3 For a given fuzzy soft set with a universal set U

and parameter set P we denote lij as the membership valueof Li in F(Pj)

2 Advances in Fuzzy Systems

Definition 4 (see [25]) For a given fuzzy soft set the choicevalue of Li is defined by

ci 1113944

n

j1lij (3)

Definition 5 (see [25]) For a given fuzzy soft set thecomparison table is the n times n table in which the entry eij isthe number of parameters for which the membership valueof Li exceeds or equals the membership value of Lj Both rowand column of the table are labelled by the elements of theuniversal set

Remark 1

(1) Each main diagonal element of a comparison table isalways equal to n

(2) 0le eij le n for all i j

Definition 6 (see [25])

(i) Impact indicator of Li is the sum of all values on row i

on the comparison table)is can be calculated by thefollowing formula

Ii 1113944n

j1eij (4)

(ii) Divider indicator of Lj is the sum of all values oncolumn j on the comparison table )is can becalculated by the following formula

Di 1113944n

i1eij (5)

(iii) )e score value of Li is defined as

ci Ii minus Di (6)

Both values can be used as evaluations in a decisionmaking However according to Kong et al [26] it is possiblethat these values may lead to different decision results)erefore they introduced grey relational grade a newevaluation indicator that combines both information ofscore values and choice values to make the decision makingmore robust )e calculation algorithm of grey relationalgrade is briefly presented

Algorithm 1 (see [26]) Decision making based on greyrelational grade

(1) Input the choice value sequence (c1 c2 cm) andthe score sequence (s1 s2 sm) where ci and si

are the choice value and the score value of Lirespectively

(2) Calculate grey relational generating values

ciprime

ci minus mini

ci1113864 1113865

maxi

ci1113864 1113865 minus mini

ci1113864 1113865

siprime

si minus mini

si1113864 1113865

maxi

si1113864 1113865 minus mini

s

(7)

(3) Calculate grey difference information

cmaxprime maxi

ciprime1113864 1113865

Δciprime cmaxprime minus ci

prime1113868111386811138681113868

1113868111386811138681113868

smaxprime maxi

siprime1113864 1113865

Δsiprime smaxprime minus si

prime1113868111386811138681113868

1113868111386811138681113868

Δmax maxiΔciprimeΔsiprime1113864 1113865

Δmin miniΔciprimeΔsiprime1113864 1113865

(8)

(4) Calculate grey relative coefficients

cc ci( 1113857 Δmin + 05Δmax

Δciprime + 05Δmax

cs si( 1113857 Δmin + 05Δmax

Δsiprime + 05Δmax

(9)

Table 1 Tabular presentation of the soft set in Example 1

Label PM10 density Air pressure Humidity Wind speedL1 1 0 1 0L2 1 1 0 0L3 1 0 0 0L4 0 1 0 1L5 0 0 1 0L6 0 0 1 0L7 0 1 0 1L8 0 1 1 0

Table 2 Tabular presentation of the fuzzy soft set in Example 2


Advances in Fuzzy Systems 3

(5) Calculate grey relational grade

c Li( 1113857 05cc ci( 1113857 + 05cs si( 1113857 (10)

(6) )e decision is Lk if c(Lk) maxi c(Li)1113864 1113865 Optimalchoices may have more than one if there are morethan one element corresponding to the maximum

Decision making based on score values and choice valuesrelies on the assumption that the parameters are equallyimportant However in some decision-making problemssome parameters can be more important than the others)erefore we propose new definitions of choice values andscore values based on weight information Note that idea ofweighted score value is briefly discussed in Maji et al [9]

Define a weight w (w1 w2 wn) as weight se-quence of parameters where wi is the weight associated withthe parameter Pi

Definition 7 For a given fuzzy soft set and a weight w theweighted choice value of Li is defined by

cwi 1113944n

j1wjlij (11)

Definition 8 For a given fuzzy soft set and a weight w theweighted comparison table is the n times n table in which theentry eij is calculated by the following formula

eij 1113944n

i1wj1 lik ge ljk1113872 1113873 (12)

where 1(middot) is an indicator function defined by

1(A) 1 if the statementA is true

0 otherwise1113896 (13)

In other words this is the weighted sum of parameterswhich the membership value of Li exceeds or equals themembership value of Lj Both row and column of the tableare labelled by the elements of the universal set

Remark 2

(1) Each main diagonal element of a weighted com-parison table is always equal to the sum 1113936kwk

(2) 0le eij le1113936kwk for all i j

Definition 9

(i) A weighted impact indicator is the impact indicatorthat is calculated based on the weighted comparisontable associated with the weight w

(ii) A weighted divider indicator is the divider indicatorthat is calculated based on the weighted comparisontable associated with the weight w

(iii) )e weighted score values of Li are the score valuesthat are calculated based on the weighted impact

indicator and weighted divider indicator associatedwith the weight w

Apparently if w (1 1 1 1) the weighted choicevalues and the weight score values are equal to the choicevalues and the score values defined in Definitions 4 and 6

Example 3 In a decision-making problem withU L1 L2 L81113864 1113865 E P1 P2 P81113864 1113865 define theweight w (3 2 1 2 2 1 1 2) Suppose that a fuzzy softset is

F P1( 1113857 L1

071113874 1113875

L2

091113874 1113875

L3

11113874 1113875

L4

041113874 1113875

L5

021113874 1113875

L6

031113874 1113875

L7

041113874 1113875

L8

051113874 11138751113882 1113883

F P2( 1113857 L1

051113874 1113875

L2

081113874 1113875

L3

011113874 1113875

L4

11113874 1113875

L5

01113874 1113875

L6

031113874 1113875

L7

061113874 1113875

L8

11113874 11138751113882 1113883

F P3( 1113857 L1

081113874 1113875

L2

021113874 1113875

L3

011113874 1113875

L4

01113874 1113875

L5

091113874 1113875

L6

071113874 1113875

L7

021113874 1113875

L8

081113874 11138751113882 1113883

F P4( 1113857 L1

021113874 1113875

L2

041113874 1113875

L3

041113874 1113875

L4

071113874 1113875

L5

11113874 1113875

L6

051113874 1113875

L7

061113874 1113875

L8

041113874 11138751113882 1113883

F P5( 1113857 L1

041113874 1113875

L2

021113874 1113875

L3

081113874 1113875

L4

091113874 1113875

L5

021113874 1113875

L6

041113874 1113875

L7

071113874 1113875

L8

071113874 11138751113882 1113883

F P6( 1113857 L1

051113874 1113875

L2

011113874 1113875

L3

011113874 1113875

L4

031113874 1113875

L5

051113874 1113875

L6

071113874 1113875

L7

11113874 1113875

L8

051113874 11138751113882 1113883

F P7( 1113857 L1

051113874 1113875

L2

051113874 1113875

L3

041113874 1113875

L4

081113874 1113875

L5

021113874 1113875

L6

041113874 1113875

L7

021113874 1113875

L8

071113874 11138751113882 1113883

F P8( 1113857 L1

0751113874 1113875

L2

11113874 1113875

L3

11113874 1113875

L4

0751113874 1113875

L5

0751113874 1113875

L6

051113874 1113875

L7

0751113874 1113875

L8

0751113874 11138751113882 1113883

(14)

Our aim is to choose the optimum choice according tothe weight w By Definition 7 the weighted choice valuesequence is (76 83 82 9 43 61 79 87) Next wecalculate weighted score value By Definition 8 the weightedcomparison table is shown in Table 3 )en by Definition 9the weighted impact indicator the weighted dividerindicator and the weighted score values are shown inTable 4 )e weighted score value sequence is(minus 1 13 18 31 minus 60 minus 29 9 19) Finally we make a deci-sion based on grey relational grade )e calculation of Al-gorithm 1 is shown in Table 5 )erefore L4 is the optimalchoice

22 Particle Swarm Optimization )e particle swarm op-timization (PSO) algorithm is a metaheuristic algorithmbased on the concept of swarm intelligence )e algorithmwas proposed in 1995 by Kennedy and Eberhart [27] PSO ismetaheuristic as it makes few or no assumptions about theproblem being optimized and can search very large spaces ofcandidate solutions Also PSO does not use the gradient ofthe problem being optimized which means PSO does notrequire that the optimization problem be differentiable as isrequired by classic optimization methods such as gradientdescent and quasi-Newton methods Also it is capable ofsolving complex mathematics problems existing in engi-neering [28]


)is method is now available to use in computerpackages such as Matlab or R

3 Model Construction

31 eStudyArea Our study area is in the northern regionof )ailand the haze pollution affected area )e regionapproximately 94000 km2 in size and six million in pop-ulation consists of nine provinces Mae Hong Son ChiangMai Lamphun Chiang Rai Phayao Lampang Phrae Nanand Uttaradit For this case study Uttaradit was excludedsince its haze problem was not severe )e study area isgeographically characterised by several mountain rangeswhich continue from the Shan Hills in bordering Myanmarto Laos and the river valleys which cut through them )ebasins of rivers Ping Wang Yom and Nan run from northto south )e basins cut across the mountains of two greatranges the )anon )ong Chai Range in the west and the

Phi Pan Nam in the east All studied provinces lie betweenthese basins )e elevations are generally moderate a littleabove 2000 metres (6600 ft) for the highest summit Table 6provides the geographic information summary of eachprovince )e latitudes and longitudes shown are the lo-cations of meteorology stations where atmospheric data arecollected )e basin sizes are divided into five categories nobasin wide normal moderate and narrow and we set theairflow difficulty level of each category to be 0 1 2 3 and 4respectively)e narrow basin implies that the flow of the airis more difficult )e location map of study area is shown inFigure 1

32 eData )e hourly atmospheric data of PM10 density(μgm3 at 3m from ground) air pressure (mmHg at 2m)relative humidity (RH at 2m) wind speed (ms at 30m)rainfall (mm at 3m) and temperature (degC at 2m) from 1stJanuary 2016 to 31st May 2016 were obtained with autho-rization from the Pollution Control Department [1] About3 of data was missing from the record )e missing datawere replaced by the same data at the preceding timeFigure 2 represents the daily fluctuation of PM10 density ofthe eight selected locations during the study period Table 7represents the summary statistics of PM10 density of theeight selected locations

33 e Parameters Based on environmental researchstudies [30ndash33] the climate and the topography of the studyarea play significant roles in the pollution problem)erefore the parameter set consists of seven parameters inthis application which are PM10 density air pressurerelative humidity wind speed rainfall temperature andairflow difficulty level )e first six parameters are atmo-spheric parameters while the last parameter is topographicparameter Additionally the effects of each atmosphericcomponents on the PM10 density the severity index can becategorized into two types positive and negative A positiveatmospheric component is the component such that in-creasing in its value will lead to the increase of the PM10density while a negative atmospheric component is thecomponent such that increasing in its value will lead to thedecrease of the PM10 density )e parameter information issummarised in Table 8

4 Results and Discussion

41HazeWarning System )e first aim of this research is tocreate a warning system based on real-time atmosphericdata )e system predicts whether the PM10 density willexceed the crisis level or not in the following 4 hours Notethat the length of warning period can be adjusted In thisarticle we choose the period of 4 hours since the period oftime is reasonable enough to do some safety mitigation suchas buying protection masks completing necessary outdooractivities or evacuating to public designated safe zones )ewarnings will be set to be announced at 12 am 4 am 8pm 4 pm 8 pm and 12 pm each day )e PM10 crisis

Table 5 )e calculation of grey relational grade based on theweighted choice value sequence and the weighted score value se-quence in Example 3

cwiprime swi

prime Δcwi Δswi ccw(ci) csw

(s) cw(Li)

L1 0702 0648 0298 0352 0627 0587 0607L2 0851 0802 0149 0198 0770 0717 0744L3 0830 0857 0170 0143 0746 0778 0762L4 1 1 0 0 1 1 1L5 0 0 1 1 0333 0333 0333L6 0383 0341 0617 0659 0448 0431 0439L7 0766 0758 0234 0242 0681 0674 0678L8 0936 0868 0064 0132 0887 0791 0839

Table 3 )e weighted comparison table in Example 3

L1 L2 L3 L4 L5 L6 L7 L8

L1 14 5 5 7 13 11 7 6L2 10 14 9 6 12 8 9 7L3 9 10 14 6 12 8 8 9L4 9 8 8 14 12 12 12 9L5 4 4 2 4 14 3 4 3L6 5 6 7 2 11 14 2 4L7 9 6 6 7 13 12 14 7L8 9 9 7 7 11 12 9 14

Table 4 )e weighted impact indicator the weighted dividerindicator and the weighted score values of each choice in Example3

Iwi Dwi swi

L1 68 69 minus 1L2 75 62 13L3 76 58 18L4 84 53 31L5 38 98 minus 60L6 51 80 minus 29L7 74 65 9L8 78 59 19


Table 6 Geographic information summary of the study area

Label Province Latitude Longitude Approximate height above sea level (m) Basin size Airflow difficulty levelL1 Mae Hong Son 19137805 97975261 330 Moderate 3L2 Chiang Mai 18837539 98971612 310 Narrow 4L3 Lamphun 18657448 99020208 290 Narrow 4L4 Chiang Rai 19932397 99799329 410 Moderate 3L5 Phayao 19211871 100209360 400 Moderate 3L6 Lampang 18278623 99506985 235 Normal 2L7 Phrae 19714564 100180450 155 Moderate 3L8 Nan 18814173 100781905 250 Normal 2

Figure 1)e study area eight selected provinces in the northern region of)ailand)e figure is obtained from Samphutthanon et al [29]

000

5000

10000

15000

20000

25000

30000

1 January 2016 1 February 2016 1 March 2016 1 April 2016 1 May 2016Date

PM10 density rate in the study area

Mae Hong Son (L1)Chiang Mai (L2)Lamphun (L3)

Phayao (L5)Lampang (L6)

Chiang Rai (L4) Phrae (L7)Nan (L8)

PM10

den

sity

(μg

m3 )

Figure 2 PM10 density rate of the eight selected locations from 1st January 2016 to 31st May 2016


level is set at 120 μgm3 based on )ailand national ambientair quality standard [34]

411 Warning System Based on PM10 Density )e trivialwarning system is a warning that relies on the information ofthe PM10 density only )at is a warning is signaled whenthe PM10 density at current time exceeds a certain thresholdvalue )e warning system is generated by Algorithm 2

Algorithm 2 Haze warning system based on PM10 density

(1) At the warning time input PM10 density data ofeach location )e inputted data are the average ofhourly data of the components in the preceding 4hours

(2) A warning is signaled if the PM10 density of thelocation exceeds the threshold value α

)e efficiency of the algorithm is evaluated by the ac-curacy ratio compared to the real data )e prediction iscounted as accurate if the warning is signaled and the PM10density in the next 4 hours exceeds 120 μgm3 or the warningis not signaled and the PM10 density in the next 4 hours doesnot exceed 120 μgm3 We test the algorithm withα 84 96 108 114 and 118 which are respectively 7080 90 95 and 98 of the crisis level )e accuracyratios of each threshold values are shown in Table 9)e plotbetween the average accuracy ratio of all eight locations andthe threshold values is shown in Figure 3 It can be seen thatthe best threshold value for these data is 118 (98 of thecrisis level) with 9099 accuracy ratio

412 Warning System Based on Fuzzy Soft Set with WeightedInformation To improve the efficiency of the warning

system the fuzzy soft set with weighted information can becomprised Note that the fuzzy soft set without weights is notsuitable for this model )is is due to the fact that theimportance of the parameters is not the same For instancePM10 density parameter is the most important parameterthan the other parameters for the reason that no hazeproblem will occur if the PM10 density amount is low Itshould be noted that the membership values of the atmo-spheric parameters change in every warning based on thereal-time data while the topographic parameter remains thesame throughout the time period Additionally when theweighted information is w (1 0 0) this warningsystem turns out to be the warning system based on PM10density defined in Section 411

)e choice values are used in decision making For thissystem a warning is signaled when the weighted choicevalues at current time exceed a certain threshold value

Our proposed decision making for the warning systemwith weighted information is as follows

Table 7 )e summary statistics of PM10 density of the eight selected locations from 1st January 2016 to 31st May 2016

Location Min Median Max Average SDL1 425 6175 38500 7618 5786L2 200 6625 25650 6998 3744L3 100 6975 22550 7111 3652L4 300 6638 37300 7559 5501L5 150 6750 28000 7324 4731L6 350 7950 20675 7814 3892L7 825 7750 23075 7784 3835L8 375 6475 25250 6958 4221All locations 100 6900 38500 7401 4498

Table 8 Parameter information summary of the haze pollution problem

Label Parameters Parameter types Effects (for atmospheric parameters)P1 PM10 density Atmospheric PositiveP2 Air pressure Atmospheric PositiveP3 Relative humidity Atmospheric PositiveP4 Wind speed Atmospheric NegativeP5 Rainfall Atmospheric NegativeP6 Temperature Atmospheric NegativeP7 Airflow difficulty level Topographic NA

Table 9 )e accuracy ratio of the haze warning system byAlgorithm 3

Location)e threshold value α out of 120 μgm3

70 80 90 95 98L1 8046 8584 8946 9034 9089L2 7936 8639 9012 9221 9286L3 7629 8639 9166 9232 9297L4 7859 8507 8902 8891 9188L5 7849 8529 8902 9012 8979L6 6729 7651 8496 8639 8727L7 6981 8211 8804 9012 9122L8 7706 8332 8814 9078 9100Average 7592 8386 8880 9015 9099


Algorithm 3 Haze warning system based on weightedchoice values

(1) At the warning time input the atmospheric data ofeach location PM10 density air pressure relativehumidity wind speed rain and temperature )einputted data are the average of hourly data of thecomponents in the preceding 4 hours Additionallyinput the weight information w (w1 w2 w7)

(2) Calculate the membership values of the parametersof the fuzzy soft set

(i) For PM10 density parameter the membershipvalues are calculated from

μF(x)

x

120 xlt 120

1 xge 120

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(15)

where x is the inputted PM10 density data(ii) For the other positive atmospheric parameters the

membership values are calculated from

μF(x) x minus m

M minus m (16)

where x is the inputted atmospheric componentdata and m and M are the minimum value and themaximum value of the atmospheric componentduring January to May 2016 respectively

(iii) For negative atmospheric parameters the mem-bership values are calculated from

μF(x) M minus x

M minus m (17)

where x m and M are defined in (ii)(iv) For the topographic parameters the membership

values are 0 025 05 075 and 1 when the airflowdifficulty levels are 0 1 2 3 and 4 respectively

(3) Calculate the weighted choice values according tothe weight information w of each location

(4) A warning is signaled if the choice values of thelocation exceed the threshold value α where0le αle 1

)e flowchart of Algorithm 3 is given in Figure 4Clearly the accuracy ratio of the model depends on the

weight information and the threshold value )e calculationexamples when weighted information is w1 (1 1 11

1 1 1)w2 (5 2 1 2 2 1 2)w3 (10 2 1 2 2 1 2)w4

(15 2 1 2 2 1 2) and w5 (20 2 1 2 2 1 2) are shown inTable 10 In these examples the threshold value is set to be90 of the possible maximum values which depend on theweight information

Since the aim of this problem is to find the weight in-formation and the threshold value that give the best accuracyratio this problem coincides with the optimization problem

max Average accuracy ratio

subject to

w1 w2 w7 are integers

0lew1 le 30

0lew2 w3 w7 le 10

α 0 001 002 099 1

(18)

By employing the particle swarm optimization methodin Matlab programme the optimum average accuracy ratiois 9212 with the optimum weight (17 0 0 2 3 0 0) andthe optimum threshold α 098 )is optimum result isshown in Table 11

42 Identification of the Most Hazardous Location )esecond aim of this research is to identify the location with themost serious haze pollution problem based on real-time at-mospheric data)e location is identified at the same time as thewarning)e effective prediction will benefit the community inthe affected area and assist the authority to provide safety aidsand prepare helping devices such as mobile air purifier

421 Identification of the Most Hazardous Location Based onPM10 Density Similar to Section 411 the simple decision

8700875088008850890089509000905091009150

108 110 112 114 116 118 120 122

Aver

age a

ccur

acy

ratio

()

reshold values

e average accuracy ratio for each threshold values

Figure 3 )e plot between the average accuracy ratio of the eight selected locations and the threshold values


making is to choose a location based on the information ofPM10 density only )at is the location with the highestvalue of PM10 density at current time is chosen as the mosthazardous location in the following 4 hours

)e algorithm of the decision making is as follows

Algorithm 4 Identification of the most hazardous locationbased on PM10 density


(2) )e decision is Lk the location with the maximumvalue of PM10 density at current time Optimalchoices may have more than one if there are morethan one element corresponding to the maximum

)e efficiency of the algorithm is evaluated by the ac-curacy ratio compared to the real data )e prediction iscounted as accurate if the most severe location in the next 4hours is correctly identified By making decision based onAlgorithm 4 the average accuracy ratio from eight locationsis 5115 and Cohenrsquos kappa index of agreement is 04312

422 Identification of the Most Hazardous Location Based onFuzzy Soft Set with Weighted Information )e fuzzy soft setwith weighted information can be comprised in order toimprove the efficiency of the decision makings With asimilar reason to Section 412 the fuzzy soft set with weightis more suitable Note that the membership values of theatmospheric parameters change in every decision makingbased on the real-time data while the topographic parameterremains the same throughout the time period Additionallywhen the weighted information is w (1 0 0) thisdecisionmaking turns out to be the warning system based onPM10 density defined in Section 421 It should be em-phasized that the membership calculation of PM10 densityparameter is different from Algorithm 3 )is is because weneed to make a comparison of location

Finally the evaluation of decision making must bechosen Note that it can be evaluated based on choice valuesscore values or grey relation grade In our result we will useall three evaluations in order to choose which evaluationgives the best result

Our proposed algorithm for decision making of the mosthazardous location based on weighted choice values is asfollows

Algorithm 5 Identification of the most hazardous locationbased on weighted choice values

(1) At the warning time input the atmospheric data ofeach location PM10 density air pressure relative

Input atmospheric data

No warning signal

No

Calculate weighted choicevalues

Calculate membership values ofparameters

Is the weight choicevalue more than the

threshold

Yes Warning signal

Figure 4 Flowchart of Algorithm 3

Table 10 )e accuracy ratio of the haze warning system by Al-gorithm 3 with weight information )e threshold value of eachweight is set to be 90 of the possible maximum

LocationWeight information

w1 () w2 () w3 () w4 () w5 ()

L 1 8375 8913 9034 9045 9034L 2 9133 9133 9133 9133 9297L 3 9122 9122 9122 9385 9297L 4 8518 8518 8551 8858 8880L 5 8452 8452 8452 8452 8540L 6 8573 8573 8573 8573 8573L 7 8749 8749 8749 8749 8979L 8 8924 8924 8924 8924 8913Average 8731 8798 8817 8890 8939

Table 11 )e optimum average accuracy ratio of the haze warningsystem based on Algorithm 3

Location )reshold value α 098w (17 0 0 2 3 0 0) ()

L 1 9211L 2 9408L 3 9397L 4 9365L 5 9156L 6 8816L 7 9123L 8 9222Average 9212


humidity wind speed rain and temperature )einputted data are the average of hourly data of thecomponents in the preceding 4 hours Additionallyinput the weight information w (w1 w2 w7)


(i) For positive atmospheric parameters the mem-bership values are calculated from

μF(x) x minus m

M minus m (19)

where x is the inputted atmospheric component dataand m and M are the minimum value and themaximum value of the atmospheric componentduring January to May 2016 respectively

(ii) For negative atmospheric parameters the mem-bership values are calculated from

μF(x) M minus x

M minus m (20)

where x m and M are defined in (i)(iii) For the topographic parameters the membership


(3) Calculate the weighted choice values cw(4) )e decision is Lk if cw(Lk) maxi cw(Li)1113864 1113865 Opti-

mal choices may have more than one if there aremore than one element corresponding to themaximum

)e flowchart of Algorithm 5 is given in Figure 5

Remark 3 If the decision making is based on weighted scorevalues sw or grey relational grades cw then Step 3 and Step 4of Algorithm 5 will be changed accordingly

Clearly the accuracy ratio of the model depends on theweight information Table 12 displays the accuracy ratio ofthe location identification by Algorithm 5 where the decisionmakings are based on choice values score values and greyrelational grades )e weighted information are w1

(1 1 1 1 1 1 1) w2 (5 2 1 2 2 1 2) w3 (10 2 1

2 2 1 2) w4 (15 2 1 2 2 1 2) and w5 (20 2

1 2 2 1 2)Since our desire of this problem is to find the weight

information that gives the best accuracy ratio this is similarto the optimization problem


subject to


0lew1 le 30

0lew2 w3 w7 le 10

(21)

By employing the particle swarm optimization methodin Matlab programme the optimum average accuracy ratiobased on weighted choice values weighted score values and

grey relational grades is 5658 5713 and 5702 re-spectively )e summary of the optimum result is shown inTable 13 Cohenrsquos kappa of the decision making based onweighted choice values weighted score values and greyrelational grades is 04457 04521 and 04489 respectively

43 Discussion

431 Haze Warning System By introducing the fuzzy softmodel with weighted information the prediction accuracyratio of the warning system is improved slightly from 9099to 9212 compared to the simple warning system that onlyconsiders the PM10 density Moreover it is clear that thefuzzy soft models with weighted information provide betterprediction than the original (equal weight) fuzzy soft modelTable 14 shows the parametersrsquo weights that provide the bestaccuracy ratio Note that the principal parameters are PM10density rainfall and wind speed respectively while theother parameters have no weight )is suggests that a simplejudgment on the warning can be done by observing onlyPM10 density wind speed and rainfall )e problem isexpected to be severe if PM10 density is high with no windand no rain )is agrees with the principle study in envi-ronmental science research

432 Identification of the Most Hazardous Location Byselecting the most severe location based on the informationfrom PM10 density only the accuracy ratio is 5112However this ratio is improved to 5713 when the loca-tions are chosen by the fuzzy weight model )e decisionmaking is decided by weighted score values Table 15 showsthe parametersrsquo weights that provide the best accuracy ratio

Based on the optimal parametersrsquo weights this wouldimply the following

(1) PM10 density is clearly the main factor in the de-cision making

(2) )is result shows that topography plays a role in thehaze pollution problem for this region of study


Calculate membership values of parameters

Calculate weighted choice values or weightedscore values or grey relational grade

The most hazardous locations is chosen based onthe evaluation basis



(3) Temperature wind speed and rainfall are factors inthe model Unfortunately these atmospheric pa-rameters are uncontrollable

(4) Air pressure and relative humidity have less or noimpact for the prediction model

)is study analysis agrees with principle study in en-vironmental science research It should be emphasized thatthe only parameter that can be controlled is PM10 density)e activities that contribute to PM10 such as outdoor burnor car emissions should be disregarded

433 Other Discussion By the results from Sections 41 and42 it should be pointed out that a simple warning systemand location identification based on the information ofPM10 density is reasonable enough By adding the pa-rameters the efficiency of the model is improved veryslightly )is emphasizes the fact that environmentalmodeling is complicated However since the calculation ofour algorithm is not expensive Algorithms 3 and 5 shouldstill be in use to improve the decision-making problem

For further works our suggestions are to add the fol-lowing parameters

Atmospheric parameters PM25 density SO2 ozoneand wind directionTopographic parameters height above sea level of thelocation location of surrounded mountains and heightof surrounded mountainsOthers parameters population

5 Conclusions

In this article we propose a fuzzy soft model to benefit in thehaze pollution management in northern)ailand )e mainaims of this research are to provide a haze warning systembased on real-time atmospheric data and to identify the mosthazardous location of the study area )e study area coverseight provinces in the northern)ailand where the problemseverely occurs every year )e parameters of the fuzzy softset include both atmospheric parameters and topographicparameter )e membership values of atmospheric pa-rameters are calculated based on the real-time data )e

Table 12 )e accuracy ratio of the location identification by Algorithm 5 with weight information

Decision basedWeight information

w1 () w2 () w3 () w4 () w5 ()

Average accuracy ratioChoice values 2118 2580 3337 4040 4555Score values 2656 4215 4896 5049 5181

Grey relational grades 2613 3743 4599 4984 5104

Table 13 )e best accuracy ratio

Decision based Accuracy ratio () Optimal weightChoice values 5658 (20 0 0 2 4 1 1)

Score values 5713 (18 1 0 2 2 3 3)

Grey relational grades 5702 (23 1 0 2 2 3 2)

Table 14 Parameters and optimum weights for the haze warning system

Label Parameters Weight Effects (for atmospheric parameters)P1 PM10 density 17 PositiveP2 Air pressure 0 PositiveP3 Relative humidity 0 PositiveP4 Wind speed 2 NegativeP5 Rainfall 3 NegativeP6 Temperature 0 NegativeP7 Airflow difficulty level 0 NA

Table 15 Parameters and optimum weights for the identification of the most hazardous location



efficiency of the model is tested with the real data from 1stJanuary 2016 to 31st May 2016 )e results show that ourfuzzy models improve the prediction accuracy ratio com-pared to the prediction based on PM10 density only )eoptimum results and optimum weights are chosen based onparticle swarm optimization )e meaning of optimumweights also agrees with the principle study in environ-mental science research Another benefit of our model is thatthe topographic parameter which is normally being dis-regarded from many models is included Moreover ourmodel would offer an alternative prediction model for thehaze pollution problem in northern )ailand

)e fuzzy soft set approach in the application to hazepollution management furnishes very promising prospectand possibilities We strongly believe that the efficiency ofthe model can be improved when appropriate parametersare added )e calculation formula for the membershipvalues and the severity index can also be adjusted )e ef-ficient model will clearly improve the health safety and raisethe life quality of the sufferers

Data Availability

)e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

)e author declares that there are no conflicts of interest

Acknowledgments

)e author would like to thank Department of Environ-mental Science Faculty of Science Chiang Mai University)ailand and Pollution Control Department Ministry ofNatural Resource and Environment )ailand for providingthe atmospheric data )is research was supported by theCentre of Excellence in Mathematics CHE and Chiang MaiUniversity

References

[1] Pollution Control Department (PCD) Website httpwwwpcdgoth

[2] Climate Change Data Centre of ChiangMai University (CMUCCDC) Website httpwwwcmuccdcorg

[3] Smoke Haze Integrated Research Unit (SHIRU) Websitehttpwwwshiru-cmuorg

[4] S Phoothiwut and S Junyapoon ldquoSize distribution of at-mospheric particulates and particulate-bound polycyclic ar-omatic hydrocarbons and characteristics of PAHs during hazeperiod in Lampang Province Northern )ailandrdquo AirQuality Atmosphere ampHealth vol 6 no 2 pp 397ndash405 2013

[5] S Chantara S Sillapapiromsuk and W Wiriya ldquoAtmo-spheric pollutants in Chiang Mai ()ailand) over a five-yearperiod (2005ndash2009) their possible sources and relation to airmass movementrdquo Atmospheric Environment vol 60pp 88ndash98 2012

[6] W Wiriya T Prapamontol and S Chantara ldquoPM10-boundpolycyclic aromatic hydrocarbons in Chiang Mai ()ailand)seasonal variations source identification health risk

assessment and their relationship to air-mass movementrdquoAtmospheric Research vol 124 pp 109ndash122 2013

[7] P Pengchai S Chantara K Sopajaree S WangkarnU Tengcharoenkul and M Rayanakorn ldquoSeasonal variationrisk assessment and source estimation of PM10 and PM10-bound PAHs in the ambient air of Chiang Mai and Lamphun)ailandrdquo Environmental Monitoring and Assessmentvol 154 no 1ndash4 pp 197ndash218 2009

[8] D Molodtsov ldquoSoft set theory-first resultsrdquo Computers ampMathematics with Applications vol 37 no 4-5 pp 19ndash311999

[9] P K Maji R Biswas and A R Roy ldquoFuzzy soft setsrdquo eJournal of Fuzzy Mathematics vol 9 no 3 pp 589ndash602 2001

[10] N Cagman S Enginoglu and F Citak ldquoFuzzy soft set theoryand its applicationsrdquo Iranian Journal of Fuzzy System vol 8pp 137ndash147 2011

[11] B Fisher ldquoFuzzy environmental decision-making applica-tions to air pollutionrdquo Atmospheric Environment vol 37no 14 pp 1865ndash1877 2003

[12] A K Gorai K Kanchan A Upadhyay and P Goyal ldquoDesignof fuzzy synthetic evaluation model for air quality assess-mentrdquo Environment Systems and Decisions vol 34 no 3pp 456ndash469 2014

[13] A Khan ldquoUse of fuzzy set theory in environmental engi-neering applications a reviewrdquo International Journal of En-gineering Research and Applications vol 7 no 6 pp 1ndash62017

[14] H Yang Z Zhu C Li and R Li ldquoA novel combined fore-casting system for air pollutants concentration based on fuzzytheory and optimization of aggregation weightrdquo Applied SoftComputing vol 87 Article ID 105972 2020

[15] S L Chen ldquo)e application of comprehensive fuzzy judge-ment in the interpretation of water-flooded reservoirsrdquo eJournal of Fuzzy Mathematics vol 9 no 3 pp 739ndash743 2001

[16] S J Kalayathankal and G S Singh ldquoA fuzzy soft flood alarmmodelrdquo Mathematics and Computers in Simulation vol 80Article ID 887893 2010

[17] S J Kalayathankal G S Singh and P B VinodkumarldquoMADMmodels using ordered ideal intuitionistic fuzzy setsrdquoAdvances in Fuzzy Mathematics vol 4 no 2 pp 101ndash1062009

[18] P C Nayak K P Sudheer and K S Ramasastri ldquoFuzzycomputing based rainfall-runoff model for real time floodforecastingrdquo Hydrological Processes vol 19 no 4pp 955ndash968 2005

[19] E Toth A Brath and A Montanari ldquoComparison of short-term rainfall prediction models for real-time flood forecast-ingrdquo Journal of Hydrology vol 239 no 1ndash4 pp 132ndash1472000

[20] S J Kalayathankal G S Singh S Joseph et al ldquoOrdered idealintuitionistic fuzzy model of flood alarmrdquo Iranian Journal ofFuzzy Systems vol 9 no 3 pp 47ndash60 2012

[21] J Tan J Fu G Carmichael et al ldquoWhy models performdifferently on particulate matter over East Asia A multi-model intercomparison study for MICS-Asia IIIrdquo Atmo-spheric Chemistry and Physics Discussions 2019 in review

[22] R Bhakta P S Khillare and D S Jyethi ldquoAtmosphericparticulate matter variations and comparison of two fore-casting models for two Indian megacitiesrdquo Aerosol Scienceand Engineering vol 3 no 2 pp 54ndash62 2019

[23] B Pimpunchat and S Junyapoon ldquoModeling haze problemsin the north of )ailand using logistic regressionrdquo Journal ofMathematical and Fundamental Sciences vol 46 no 2pp 183ndash193 2014


[24] B Mitmark and W Jinsart ldquoA GIS model for PM10 exposurefrom biomass burning in the north of )ailandrdquo AppliedEnvironmental Research vol 39 no 2 pp 77ndash87 2017

[25] A R Roy and P K Maji ldquoA fuzzy soft set theoretic approachto decision making problemsrdquo Journal of Computational andApplied Mathematics vol 203 no 2 pp 412ndash418 2007

[26] Z Kong L Wang and ZWu ldquoApplication of fuzzy soft set indecision making problems based on grey theoryrdquo Journal ofComputational and Applied Mathematics vol 236 no 6pp 1521ndash1530 2011

[27] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquoProceedings of the International Conference on Neural Net-works vol 4 1995

[28] A Meneses M Machado and R Schirru ldquoParticle swarmoptimization applied to the nuclear reload problem of apressurized water reactorrdquo Progress in Nuclear Energy vol 51no 3 pp 319ndash326 2009

[29] R Samphutthanon N K Tripathi S Ninsawat et al ldquoSpatio-temporal distribution and hotspots of hand foot and mouthdisease (HFMD) in northern)ailandrdquo International Journalof Environmental Research and Public Health vol 11 no 1pp 312ndash336 2013

[30] L Wang N Zhang Z Liu et al ldquo)e influence of climatefactors meteorological conditions and boundary-layerstructure on severe haze pollution in the beijing-tianjin-hebeiregion during January 2013rdquo Advances in Meteorologyvol 2014 Article ID 685971 14 pages 2014

[31] S Zhou S Peng M Wang et al ldquo)e characteristics andcontributing factors of air pollution in nanjing a case studybased on an unmanned aerial vehicle experiment andmultipledatasetsrdquo Atmosphere vol 9 no 9 p 343 2018

[32] N Pasukphun ldquoEnvironmental health burden of openburning in northern )ailand a reviewrdquo PSRU Journal ofScience and Technology vol 3 no 3 pp 11ndash28 2018

[33] WMankan ldquo)e causing factors of the smog phenomenon inLampang basinrdquo Burapha Science Journal vol 22 no 3pp 226ndash239 2017

[34] L Pardthaisong P Sin-ampol C Suwanprasit andA Charoenpanyanet ldquoHaze pollution in Chiang Mai )ai-land a road to resiliencerdquo Procedia Engineering vol 212pp 85ndash92 2018


trapped near ground level due to the meteorological con-ditions (eg stagnant air) and the basin-like topographysurrounded by high mountain ranges results in restrictedpollution dispersion Moreover low rainfall in dry seasonalso adds on to the severity of the haze problem For thisreason the leaching of smoke or dust particles in the air islow [6] )ese conditions caused the air pollutants to flowout difficultly and the particle cannot be easily escaped fromthe area Notably there are some technologies that mitigatethe pollution problem However the costs of devices areconsiderably expensive

Undoubtedly an efficient warning system would becomea major help in the haze problem management )e systemwill significantly improve public safety and mitigate damagecaused )e Goddard Earth Observing System Model Ver-sion 5 (GEOS-5) is currently one of the widely used pollutionprediction models developed by NASArsquos research team

In this article the potential use of fuzzy soft set theory inreal-time haze warning is investigated)e main aims of thisresearch are (i) to provide a haze warning system based onreal-time atmospheric data and (ii) to identify the mosthazardous location of the study area )e benefits are tocreate the awareness for people in the affected area and tosuggest the location to establish pollutionmitigation devicesMolodtsov [8ndash10] initiated the concept of soft set theory as anew mathematical tool for dealing with uncertainties Softset theory has rich potential for applications in several di-rections a few of which had been shown by Molodtsov [8])e idea of applying fuzzy soft set theory in atmosphericmodels is already considered concerning the applications toair pollution management [11ndash14] and water management[15ndash20] However it is believed that air pollution modelsmay be different for each region due to many several factors[21 22] )erefore existing models still need to be restudiedUp to our knowledge there are only a few prediction modelsin the region of study since the main concerns are on the siteof environmental science )e prediction results fromGEOS-5 model are popular choices to be used as bench-marks for environmental scientist )e regional-developedmodels include a logistic regression model [23] and Geo-graphic Information System- (GIS-) based model [24])erefore our model would offer an alternative predictionmodel for the haze pollution problem

)e study location covered eight provinces in thenorthern part of )ailand where haze problem has severelyoccurred Mae Hong Son Chiang Mai Lamphun ChiangRai Phayao Lampang Phrae and Nan)e density of PM10is used as severity index of the haze pollution level Addi-tionally seven principle parameters are considered in themodel six are atmospheric parametersmdashPM10 air pressurerelative humidity wind speed rainfall and temper-aturemdashand the other one is the topographic parameter Allatmospheric data are obtained from the Pollution ControlDepartment [1])e obtained data period is from 1st January2016 to 31st May 2016

)e rest of this article is organized as follows In Section2 we explain the methodology and present some examplesIn Section 3 we describe the setup of the model whichincludes the study location the data and the parameters

)en we present our decision-making results and discussionin Section 4 Finally the conclusion is given in Section 5

2 Methodology

21 Fuzzy Soft eory In this section we provide usefulnotations of soft sets and fuzzy soft sets LetU L1 L2 Lm1113864 1113865 be an initial universal set and let E

P1 P2 Pn1113864 1113865 be a set of parameters

Definition 1 (see [8]) Let P(U) denote the power set of U

and A sub E A pair (F A) is called a soft set over U where F

is a mapping given by F A⟶ P(U)

Example 1 Let the initial universe U L1 L2 L81113864 1113865 bethe eight selected provinces in the northern region of)ailand Mae Hong Son Chiang Mai Lamphun ChiangRai Phayao Lampang Phrae and Nan Moreover let E

P1 P2 P3 P41113864 1113865 be atmospheric parameters PM10 densityair pressure relative humidity and wind speed respectively)en an example of possible soft set is

F P1( 1113857 L1 L2 L31113864 1113865

F P2( 1113857 L2 L4 L7 L81113864 1113865

F P3( 1113857 L1 L5 L6 L81113864 1113865

F P4( 1113857 L4 L71113864 1113865

(1)

Note that each approximation has two parts predicate p

and approximate value set For example the predicate isPM10 density and the approximate value set is L1 L2 L31113864 1113865

for F(P1) Additionally the summary information of thissoft set is represented in Table 1

Definition 2 (see [25]) Let Ψ(U) denote the set of all fuzzysets of U and let Ai sub E A pair (Fi Ai) is called a fuzzy softset over U where Fi is a mapping given byFi Ai ⟶Ψ(U)

Example 2 We consider the same setup as in Example 1 Anexample of a fuzzy soft set is

F P1( 1113857 L1

071113874 1113875

L2

091113874 1113875

L3

11113874 1113875

L4

041113874 1113875

L5

021113874 1113875

L6

031113874 1113875

L7

041113874 1113875

L8

051113874 11138751113882 1113883

F P2( 1113857 L1

051113874 1113875

L2

081113874 1113875

L3

011113874 1113875

L4

11113874 1113875

L5

021113874 1113875L50

L6

031113874 1113875

L7

061113874 1113875

L8

11113874 11138751113882 1113883

F P3( 1113857 L1

081113874 1113875

L2

021113874 1113875

L3

011113874 1113875

L4

01113874 1113875

L5

091113874 1113875

L6

071113874 1113875

L7

021113874 1113875

L8

081113874 11138751113882 1113883

F P4( 1113857 L1

021113874 1113875

L2

041113874 1113875

L3

041113874 1113875

L4

071113874 1113875

L5

11113874 1113875

L6

051113874 1113875

L7

061113874 1113875

L8

041113874 11138751113882 1113883

(2)

Table 2 provides the summary information of this fuzzysoft set

Definition 3 For a given fuzzy soft set with a universal set U

and parameter set P we denote lij as the membership valueof Li in F(Pj)



ci 1113944

n

j1lij (3)


Remark 1






Ii 1113944n

j1eij (4)


Di 1113944n

i1eij (5)


ci Ii minus Di (6)






ciprime

ci minus mini

ci1113864 1113865

maxi

ci1113864 1113865 minus mini

ci1113864 1113865

siprime

si minus mini

si1113864 1113865

maxi

si1113864 1113865 minus mini

s

(7)


cmaxprime maxi

ciprime1113864 1113865


prime1113868111386811138681113868

1113868111386811138681113868

smaxprime maxi

siprime1113864 1113865


prime1113868111386811138681113868

1113868111386811138681113868



(8)



Δciprime + 05Δmax


Δsiprime + 05Δmax

(9)







c Li( 1113857 05cc ci( 1113857 + 05cs si( 1113857 (10)





cwi 1113944n

j1wjlij (11)


eij 1113944n

i1wj1 lik ge ljk1113872 1113873 (12)



0 otherwise1113896 (13)


Remark 2



Definition 9







F P1( 1113857 L1

071113874 1113875

L2

091113874 1113875

L3

11113874 1113875

L4

041113874 1113875

L5

021113874 1113875

L6

031113874 1113875

L7

041113874 1113875

L8

051113874 11138751113882 1113883

F P2( 1113857 L1

051113874 1113875

L2

081113874 1113875

L3

011113874 1113875

L4

11113874 1113875

L5

01113874 1113875

L6

031113874 1113875

L7

061113874 1113875

L8

11113874 11138751113882 1113883

F P3( 1113857 L1

081113874 1113875

L2

021113874 1113875

L3

011113874 1113875

L4

01113874 1113875

L5

091113874 1113875

L6

071113874 1113875

L7

021113874 1113875

L8

081113874 11138751113882 1113883

F P4( 1113857 L1

021113874 1113875

L2

041113874 1113875

L3

041113874 1113875

L4

071113874 1113875

L5

11113874 1113875

L6

051113874 1113875

L7

061113874 1113875

L8

041113874 11138751113882 1113883

F P5( 1113857 L1

041113874 1113875

L2

021113874 1113875

L3

081113874 1113875

L4

091113874 1113875

L5

021113874 1113875

L6

041113874 1113875

L7

071113874 1113875

L8

071113874 11138751113882 1113883

F P6( 1113857 L1

051113874 1113875

L2

011113874 1113875

L3

011113874 1113875

L4

031113874 1113875

L5

051113874 1113875

L6

071113874 1113875

L7

11113874 1113875

L8

051113874 11138751113882 1113883

F P7( 1113857 L1

051113874 1113875

L2

051113874 1113875

L3

041113874 1113875

L4

081113874 1113875

L5

021113874 1113875

L6

041113874 1113875

L7

021113874 1113875

L8

071113874 11138751113882 1113883

F P8( 1113857 L1

0751113874 1113875

L2

11113874 1113875

L3

11113874 1113875

L4

0751113874 1113875

L5

0751113874 1113875

L6

051113874 1113875

L7

0751113874 1113875

L8

0751113874 11138751113882 1113883

(14)













cwiprime swi


(s) cw(Li)

L1 0702 0648 0298 0352 0627 0587 0607L2 0851 0802 0149 0198 0770 0717 0744L3 0830 0857 0170 0143 0746 0778 0762L4 1 1 0 0 1 1 1L5 0 0 1 1 0333 0333 0333L6 0383 0341 0617 0659 0448 0431 0439L7 0766 0758 0234 0242 0681 0674 0678L8 0936 0868 0064 0132 0887 0791 0839


L1 L2 L3 L4 L5 L6 L7 L8

L1 14 5 5 7 13 11 7 6L2 10 14 9 6 12 8 9 7L3 9 10 14 6 12 8 8 9L4 9 8 8 14 12 12 12 9L5 4 4 2 4 14 3 4 3L6 5 6 7 2 11 14 2 4L7 9 6 6 7 13 12 14 7L8 9 9 7 7 11 12 9 14


Iwi Dwi swi






000

5000

10000

15000

20000

25000

30000






PM10

den

sity

(μg

m3 )

























μF(x)

x

120 xlt 120

1 xge 120

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(15)



μF(x) x minus m

M minus m (16)



μF(x) M minus x

M minus m (17)







1 1 1)w2 (5 2 1 2 2 1 2)w3 (10 2 1 2 2 1 2)w4




subject to


0lew1 le 30

0lew2 w3 w7 le 10

α 0 001 002 099 1

(18)




8700875088008850890089509000905091009150

108 110 112 114 116 118 120 122

Aver

age a

ccur

acy

ratio

()

reshold values
















No warning signal

No




threshold

Yes Warning signal




w1 () w2 () w3 () w4 () w5 ()









μF(x) x minus m

M minus m (19)



μF(x) M minus x

M minus m (20)








(1 1 1 1 1 1 1) w2 (5 2 1 2 2 1 2) w3 (10 2 1

2 2 1 2) w4 (15 2 1 2 2 1 2) and w5 (20 2




subject to


0lew1 le 30

0lew2 w3 w7 le 10

(21)



43 Discussion


















5 Conclusions




w1 () w2 () w3 () w4 () w5 ()





Score values 5713 (18 1 0 2 2 3 3)









Data Availability




Acknowledgments


References







































ci 1113944

n

j1lij (3)


Remark 1






Ii 1113944n

j1eij (4)


Di 1113944n

i1eij (5)


ci Ii minus Di (6)






ciprime

ci minus mini

ci1113864 1113865

maxi

ci1113864 1113865 minus mini

ci1113864 1113865

siprime

si minus mini

si1113864 1113865

maxi

si1113864 1113865 minus mini

s

(7)


cmaxprime maxi

ciprime1113864 1113865


prime1113868111386811138681113868

1113868111386811138681113868

smaxprime maxi

siprime1113864 1113865


prime1113868111386811138681113868

1113868111386811138681113868



(8)



Δciprime + 05Δmax


Δsiprime + 05Δmax

(9)







c Li( 1113857 05cc ci( 1113857 + 05cs si( 1113857 (10)





cwi 1113944n

j1wjlij (11)


eij 1113944n

i1wj1 lik ge ljk1113872 1113873 (12)



0 otherwise1113896 (13)


Remark 2



Definition 9







F P1( 1113857 L1

071113874 1113875

L2

091113874 1113875

L3

11113874 1113875

L4

041113874 1113875

L5

021113874 1113875

L6

031113874 1113875

L7

041113874 1113875

L8

051113874 11138751113882 1113883

F P2( 1113857 L1

051113874 1113875

L2

081113874 1113875

L3

011113874 1113875

L4

11113874 1113875

L5

01113874 1113875

L6

031113874 1113875

L7

061113874 1113875

L8

11113874 11138751113882 1113883

F P3( 1113857 L1

081113874 1113875

L2

021113874 1113875

L3

011113874 1113875

L4

01113874 1113875

L5

091113874 1113875

L6

071113874 1113875

L7

021113874 1113875

L8

081113874 11138751113882 1113883

F P4( 1113857 L1

021113874 1113875

L2

041113874 1113875

L3

041113874 1113875

L4

071113874 1113875

L5

11113874 1113875

L6

051113874 1113875

L7

061113874 1113875

L8

041113874 11138751113882 1113883

F P5( 1113857 L1

041113874 1113875

L2

021113874 1113875

L3

081113874 1113875

L4

091113874 1113875

L5

021113874 1113875

L6

041113874 1113875

L7

071113874 1113875

L8

071113874 11138751113882 1113883

F P6( 1113857 L1

051113874 1113875

L2

011113874 1113875

L3

011113874 1113875

L4

031113874 1113875

L5

051113874 1113875

L6

071113874 1113875

L7

11113874 1113875

L8

051113874 11138751113882 1113883

F P7( 1113857 L1

051113874 1113875

L2

051113874 1113875

L3

041113874 1113875

L4

081113874 1113875

L5

021113874 1113875

L6

041113874 1113875

L7

021113874 1113875

L8

071113874 11138751113882 1113883

F P8( 1113857 L1

0751113874 1113875

L2

11113874 1113875

L3

11113874 1113875

L4

0751113874 1113875

L5

0751113874 1113875

L6

051113874 1113875

L7

0751113874 1113875

L8

0751113874 11138751113882 1113883

(14)













cwiprime swi


(s) cw(Li)

L1 0702 0648 0298 0352 0627 0587 0607L2 0851 0802 0149 0198 0770 0717 0744L3 0830 0857 0170 0143 0746 0778 0762L4 1 1 0 0 1 1 1L5 0 0 1 1 0333 0333 0333L6 0383 0341 0617 0659 0448 0431 0439L7 0766 0758 0234 0242 0681 0674 0678L8 0936 0868 0064 0132 0887 0791 0839


L1 L2 L3 L4 L5 L6 L7 L8

L1 14 5 5 7 13 11 7 6L2 10 14 9 6 12 8 9 7L3 9 10 14 6 12 8 8 9L4 9 8 8 14 12 12 12 9L5 4 4 2 4 14 3 4 3L6 5 6 7 2 11 14 2 4L7 9 6 6 7 13 12 14 7L8 9 9 7 7 11 12 9 14


Iwi Dwi swi






000

5000

10000

15000

20000

25000

30000






PM10

den

sity

(μg

m3 )

























μF(x)

x

120 xlt 120

1 xge 120

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(15)



μF(x) x minus m

M minus m (16)



μF(x) M minus x

M minus m (17)







1 1 1)w2 (5 2 1 2 2 1 2)w3 (10 2 1 2 2 1 2)w4




subject to


0lew1 le 30

0lew2 w3 w7 le 10

α 0 001 002 099 1

(18)




8700875088008850890089509000905091009150

108 110 112 114 116 118 120 122

Aver

age a

ccur

acy

ratio

()

reshold values
















No warning signal

No




threshold

Yes Warning signal




w1 () w2 () w3 () w4 () w5 ()









μF(x) x minus m

M minus m (19)



μF(x) M minus x

M minus m (20)








(1 1 1 1 1 1 1) w2 (5 2 1 2 2 1 2) w3 (10 2 1

2 2 1 2) w4 (15 2 1 2 2 1 2) and w5 (20 2




subject to


0lew1 le 30

0lew2 w3 w7 le 10

(21)



43 Discussion


















5 Conclusions




w1 () w2 () w3 () w4 () w5 ()





Score values 5713 (18 1 0 2 2 3 3)









Data Availability




Acknowledgments


References







































c Li( 1113857 05cc ci( 1113857 + 05cs si( 1113857 (10)





cwi 1113944n

j1wjlij (11)


eij 1113944n

i1wj1 lik ge ljk1113872 1113873 (12)



0 otherwise1113896 (13)


Remark 2



Definition 9







F P1( 1113857 L1

071113874 1113875

L2

091113874 1113875

L3

11113874 1113875

L4

041113874 1113875

L5

021113874 1113875

L6

031113874 1113875

L7

041113874 1113875

L8

051113874 11138751113882 1113883

F P2( 1113857 L1

051113874 1113875

L2

081113874 1113875

L3

011113874 1113875

L4

11113874 1113875

L5

01113874 1113875

L6

031113874 1113875

L7

061113874 1113875

L8

11113874 11138751113882 1113883

F P3( 1113857 L1

081113874 1113875

L2

021113874 1113875

L3

011113874 1113875

L4

01113874 1113875

L5

091113874 1113875

L6

071113874 1113875

L7

021113874 1113875

L8

081113874 11138751113882 1113883

F P4( 1113857 L1

021113874 1113875

L2

041113874 1113875

L3

041113874 1113875

L4

071113874 1113875

L5

11113874 1113875

L6

051113874 1113875

L7

061113874 1113875

L8

041113874 11138751113882 1113883

F P5( 1113857 L1

041113874 1113875

L2

021113874 1113875

L3

081113874 1113875

L4

091113874 1113875

L5

021113874 1113875

L6

041113874 1113875

L7

071113874 1113875

L8

071113874 11138751113882 1113883

F P6( 1113857 L1

051113874 1113875

L2

011113874 1113875

L3

011113874 1113875

L4

031113874 1113875

L5

051113874 1113875

L6

071113874 1113875

L7

11113874 1113875

L8

051113874 11138751113882 1113883

F P7( 1113857 L1

051113874 1113875

L2

051113874 1113875

L3

041113874 1113875

L4

081113874 1113875

L5

021113874 1113875

L6

041113874 1113875

L7

021113874 1113875

L8

071113874 11138751113882 1113883

F P8( 1113857 L1

0751113874 1113875

L2

11113874 1113875

L3

11113874 1113875

L4

0751113874 1113875

L5

0751113874 1113875

L6

051113874 1113875

L7

0751113874 1113875

L8

0751113874 11138751113882 1113883

(14)













cwiprime swi


(s) cw(Li)

L1 0702 0648 0298 0352 0627 0587 0607L2 0851 0802 0149 0198 0770 0717 0744L3 0830 0857 0170 0143 0746 0778 0762L4 1 1 0 0 1 1 1L5 0 0 1 1 0333 0333 0333L6 0383 0341 0617 0659 0448 0431 0439L7 0766 0758 0234 0242 0681 0674 0678L8 0936 0868 0064 0132 0887 0791 0839


L1 L2 L3 L4 L5 L6 L7 L8

L1 14 5 5 7 13 11 7 6L2 10 14 9 6 12 8 9 7L3 9 10 14 6 12 8 8 9L4 9 8 8 14 12 12 12 9L5 4 4 2 4 14 3 4 3L6 5 6 7 2 11 14 2 4L7 9 6 6 7 13 12 14 7L8 9 9 7 7 11 12 9 14


Iwi Dwi swi






000

5000

10000

15000

20000

25000

30000






PM10

den

sity

(μg

m3 )

























μF(x)

x

120 xlt 120

1 xge 120

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(15)



μF(x) x minus m

M minus m (16)



μF(x) M minus x

M minus m (17)







1 1 1)w2 (5 2 1 2 2 1 2)w3 (10 2 1 2 2 1 2)w4




subject to


0lew1 le 30

0lew2 w3 w7 le 10

α 0 001 002 099 1

(18)




8700875088008850890089509000905091009150

108 110 112 114 116 118 120 122

Aver

age a

ccur

acy

ratio

()

reshold values
















No warning signal

No




threshold

Yes Warning signal




w1 () w2 () w3 () w4 () w5 ()









μF(x) x minus m

M minus m (19)



μF(x) M minus x

M minus m (20)








(1 1 1 1 1 1 1) w2 (5 2 1 2 2 1 2) w3 (10 2 1

2 2 1 2) w4 (15 2 1 2 2 1 2) and w5 (20 2




subject to


0lew1 le 30

0lew2 w3 w7 le 10

(21)



43 Discussion


















5 Conclusions




w1 () w2 () w3 () w4 () w5 ()





Score values 5713 (18 1 0 2 2 3 3)









Data Availability




Acknowledgments


References















































cwiprime swi


(s) cw(Li)

L1 0702 0648 0298 0352 0627 0587 0607L2 0851 0802 0149 0198 0770 0717 0744L3 0830 0857 0170 0143 0746 0778 0762L4 1 1 0 0 1 1 1L5 0 0 1 1 0333 0333 0333L6 0383 0341 0617 0659 0448 0431 0439L7 0766 0758 0234 0242 0681 0674 0678L8 0936 0868 0064 0132 0887 0791 0839


L1 L2 L3 L4 L5 L6 L7 L8

L1 14 5 5 7 13 11 7 6L2 10 14 9 6 12 8 9 7L3 9 10 14 6 12 8 8 9L4 9 8 8 14 12 12 12 9L5 4 4 2 4 14 3 4 3L6 5 6 7 2 11 14 2 4L7 9 6 6 7 13 12 14 7L8 9 9 7 7 11 12 9 14


Iwi Dwi swi






000

5000

10000

15000

20000

25000

30000






PM10

den

sity

(μg

m3 )

























μF(x)

x

120 xlt 120

1 xge 120

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(15)



μF(x) x minus m

M minus m (16)



μF(x) M minus x

M minus m (17)







1 1 1)w2 (5 2 1 2 2 1 2)w3 (10 2 1 2 2 1 2)w4




subject to


0lew1 le 30

0lew2 w3 w7 le 10

α 0 001 002 099 1

(18)




8700875088008850890089509000905091009150

108 110 112 114 116 118 120 122

Aver

age a

ccur

acy

ratio

()

reshold values
















No warning signal

No




threshold

Yes Warning signal




w1 () w2 () w3 () w4 () w5 ()









μF(x) x minus m

M minus m (19)



μF(x) M minus x

M minus m (20)








(1 1 1 1 1 1 1) w2 (5 2 1 2 2 1 2) w3 (10 2 1

2 2 1 2) w4 (15 2 1 2 2 1 2) and w5 (20 2




subject to


0lew1 le 30

0lew2 w3 w7 le 10

(21)



43 Discussion


















5 Conclusions




w1 () w2 () w3 () w4 () w5 ()





Score values 5713 (18 1 0 2 2 3 3)









Data Availability




Acknowledgments


References









































000

5000

10000

15000

20000

25000

30000






PM10

den

sity

(μg

m3 )

























μF(x)

x

120 xlt 120

1 xge 120

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(15)



μF(x) x minus m

M minus m (16)



μF(x) M minus x

M minus m (17)







1 1 1)w2 (5 2 1 2 2 1 2)w3 (10 2 1 2 2 1 2)w4




subject to


0lew1 le 30

0lew2 w3 w7 le 10

α 0 001 002 099 1

(18)




8700875088008850890089509000905091009150

108 110 112 114 116 118 120 122

Aver

age a

ccur

acy

ratio

()

reshold values
















No warning signal

No




threshold

Yes Warning signal




w1 () w2 () w3 () w4 () w5 ()









μF(x) x minus m

M minus m (19)



μF(x) M minus x

M minus m (20)








(1 1 1 1 1 1 1) w2 (5 2 1 2 2 1 2) w3 (10 2 1

2 2 1 2) w4 (15 2 1 2 2 1 2) and w5 (20 2




subject to


0lew1 le 30

0lew2 w3 w7 le 10

(21)



43 Discussion


















5 Conclusions




w1 () w2 () w3 () w4 () w5 ()





Score values 5713 (18 1 0 2 2 3 3)









Data Availability




Acknowledgments


References




























































μF(x)

x

120 xlt 120

1 xge 120

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(15)



μF(x) x minus m

M minus m (16)



μF(x) M minus x

M minus m (17)







1 1 1)w2 (5 2 1 2 2 1 2)w3 (10 2 1 2 2 1 2)w4




subject to


0lew1 le 30

0lew2 w3 w7 le 10

α 0 001 002 099 1

(18)




8700875088008850890089509000905091009150

108 110 112 114 116 118 120 122

Aver

age a

ccur

acy

ratio

()

reshold values
















No warning signal

No




threshold

Yes Warning signal




w1 () w2 () w3 () w4 () w5 ()









μF(x) x minus m

M minus m (19)



μF(x) M minus x

M minus m (20)








(1 1 1 1 1 1 1) w2 (5 2 1 2 2 1 2) w3 (10 2 1

2 2 1 2) w4 (15 2 1 2 2 1 2) and w5 (20 2




subject to


0lew1 le 30

0lew2 w3 w7 le 10

(21)



43 Discussion


















5 Conclusions




w1 () w2 () w3 () w4 () w5 ()





Score values 5713 (18 1 0 2 2 3 3)









Data Availability




Acknowledgments


References










































μF(x)

x

120 xlt 120

1 xge 120

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(15)



μF(x) x minus m

M minus m (16)



μF(x) M minus x

M minus m (17)







1 1 1)w2 (5 2 1 2 2 1 2)w3 (10 2 1 2 2 1 2)w4




subject to


0lew1 le 30

0lew2 w3 w7 le 10

α 0 001 002 099 1

(18)




8700875088008850890089509000905091009150

108 110 112 114 116 118 120 122

Aver

age a

ccur

acy

ratio

()

reshold values
















No warning signal

No




threshold

Yes Warning signal




w1 () w2 () w3 () w4 () w5 ()









μF(x) x minus m

M minus m (19)



μF(x) M minus x

M minus m (20)








(1 1 1 1 1 1 1) w2 (5 2 1 2 2 1 2) w3 (10 2 1

2 2 1 2) w4 (15 2 1 2 2 1 2) and w5 (20 2




subject to


0lew1 le 30

0lew2 w3 w7 le 10

(21)



43 Discussion


















5 Conclusions




w1 () w2 () w3 () w4 () w5 ()





Score values 5713 (18 1 0 2 2 3 3)









Data Availability




Acknowledgments


References


















































No warning signal

No




threshold

Yes Warning signal




w1 () w2 () w3 () w4 () w5 ()









μF(x) x minus m

M minus m (19)



μF(x) M minus x

M minus m (20)








(1 1 1 1 1 1 1) w2 (5 2 1 2 2 1 2) w3 (10 2 1

2 2 1 2) w4 (15 2 1 2 2 1 2) and w5 (20 2




subject to


0lew1 le 30

0lew2 w3 w7 le 10

(21)



43 Discussion


















5 Conclusions




w1 () w2 () w3 () w4 () w5 ()





Score values 5713 (18 1 0 2 2 3 3)









Data Availability




Acknowledgments


References









































μF(x) x minus m

M minus m (19)



μF(x) M minus x

M minus m (20)








(1 1 1 1 1 1 1) w2 (5 2 1 2 2 1 2) w3 (10 2 1

2 2 1 2) w4 (15 2 1 2 2 1 2) and w5 (20 2




subject to


0lew1 le 30

0lew2 w3 w7 le 10

(21)



43 Discussion


















5 Conclusions




w1 () w2 () w3 () w4 () w5 ()





Score values 5713 (18 1 0 2 2 3 3)









Data Availability




Acknowledgments


References












































5 Conclusions




w1 () w2 () w3 () w4 () w5 ()





Score values 5713 (18 1 0 2 2 3 3)









Data Availability




Acknowledgments


References








































Data Availability




Acknowledgments


References


















































Date post:	24-Jan-2021
Category:	Documents
Upload:	others
View:	3 times
Download:	0 times

AFuzzySoftModelforHazePollutionManagementin NorthernThailand · occurred: Mae Hong Son, Chiang Mai,...

Documents