CERTIFICATE

Certified that Mr. Varun Kumar Kadian,Vaibhav Chabbra,Umesh Kumar and

Vaibhav Gaur , students of semester 4th of ICE NSIT , has undertaken the

project work on “FUZZYLOGIC” under the supervision of Ms. Deepali Sharma

as per requirement stipulated in the course curriculum. The performance of student

has been satisfactory.

Deepali Sharma

(Project Incharge)

ACKNOWLEDGEMENT

The project work on “FUZZYLOGIC” was carried out at NSIT , under guidance

of Ms. Deepali Sharma. We gratefully acknowledge the guidance of our project

incharge for the successful completion of the project. The support of Head of

Department, Director/Principal, faculty and the laboratory staff in execution of

project is gratefully acknowledged.

Varun Kumar Kadian(524/IC/09)

Vaibhav Chhabra(521/IC/09)

Umesh Kumar(520/IC/09)

Vaibhav Gaur(522/IC/09)

MODULE – 1Introduction to MATLABEtymology: MATLAB stands for Matrix Laboratory. The reason behind this is that internally, every computation done by this application is in the form of number matrices of n-dimensions. Hence, the name.

As it has already been touched in the Preface section, MATLAB is an engineering utility application which allows us to compute many kinds of problems of different fields of science and technology. This is a virtual environment which allows us to do numerical computations in a simplified manner. Developed by Mathworks, this allows matrix manipulations, function plotting, algorithm implementations and creation of Graphical User Interfaces. This designed for live interaction with other computer language programs like C++ and FORTRAN.

Many extensions are used for MATLAB files like

.fig : MATLAB Figure

.m  : MATLAB function, script, or class

.mat  : MATLAB binary file for storing variables

.mex : MATLAB executable (platform specific, e.g. ".mexmac" for the Mac.)

.jkt  : GPU Cache file generated by Jacket for MATLAB (AccelerEyes)

.mum: MATLAB CAPE-OPEN Unit Operation Model File (AmsterCHEM)

In this project we will be using .m as extension for M-file.

MATLAB can call functions and subroutines written in the C programming language or Fortran. A wrapper function is created allowing MATLAB data types to be passed and returned. The dynamically loadable object files created by compiling such functions are termed "MEX-files" (for MATLAB executable).

MATLAB has several functions:

eig(A) : to find Eigen values of matrix A

inv(A) : to find inverse of matrix A

pzmap(A) : to find pole zero mapping of transfer function A

plot(X,Y) : to plot a 2-D graph between X and Y

MATLAB is a "Matrix Laboratory", and as such it provides many convenient ways for creating vectors, matrices, and multi-dimensional arrays. In the MATLAB vernacular, a vector refers to a one dimensional (1×N or N×1) matrix, commonly referred to as an array in other programming languages. A matrix generally refers to a 2-dimensional array, i.e. an m×n array where m and n are greater than or equal to 1. Arrays with more than two dimensions are referred to as multidimensional arrays. We can define vectors and matrices using square bracket, space and semicolon in MATLAB.

UtilitiesMATAB as an application is so extremely useful, that it can be used to do almost anything. Starting from solving of nth order set of equations, it can be used in aeronautics, predicting market statistics and economic situations, in wavelet transformations, as well as genetic mapping. This application nowadays is being used in every research based industry to its benefit. In 2004, MATLAB had around one million users across industry and academia.

HistoryMATLAB was created in the late 1970s by Cleve Moler, the chairman of the computer department at the University of New Mexico. He designed it to give his students access to LINPACK and EISPACK without having to learn Fortran. It soon spread to other universities and found a strong audience within the applied mathematics community. Jack Little, an engineer, was exposed to it during a visit Moler made to Stanford University in 1983. Recognizing its commercial potential, he joined with Moler and Steve Bangert. They rewrote MATLAB in C and founded MathWorks in 1984 to continue its development. These rewritten libraries were known as JACKPAC. In 2000, MATLAB was rewritten to use a newer set of libraries for matrix manipulation, LAPACK. MATLAB was first adopted by control design engineers, Little's specialty, but quickly spread to many other domains. It is now also used in education, in

particular the teaching of linear algebra and numerical analysis, and is popular amongst scientists involved with image processing.

ToolboxesA MATLAB user is always empowered with strikingly efficient and diverse set of user-friendly toolboxes which make the job of the programmer very simple by interacting graphically and producing vivid diagrammatic results. These toolboxes may be used together to solve complex problems.

The toolboxes available in the version used through this training are:

1. Aerospace ToolboxThe Aerospace Toolbox product extends the MATLAB® technical computing environment by providing reference standards, environment models, and aerodynamic coefficient importing for performing advanced aerospace analysis to develop and evaluate your designs. The toolbox provides the following to enable you to visualize flight data in a three-dimensional environment and reconstruct behavioral anomalies in flight-test results:

Aero.Animation, Aero.Body, Aero.Camera, and Aero.Geometry objects and associated methods

An interface to the FlightGear flight simulator An interface to the Simulink® 3D Animation™ software

2. Bioinformatics ToolboxThe Bioinformatics Toolbox™ product extends the MATLAB® environment to provide an integrated software environment for genome and proteome analysis. Scientists and engineers can answer questions, solve problems, prototype new algorithms, and build applications for drug discovery and design, genetic engineering, and biological research. An introduction to these features will help you to develop a conceptual model for working with the toolbox and your biological data.Toolbox features and functions fall within these categories:

Data formats and databases — Connect to Web-accessible databases containing genomic and proteomic data. Read and convert between multiple data formats.

Sequence analysis — Determine the statistical characteristics of a sequence, align two sequences, and multiply align several

sequences. Model patterns in biological sequences using hidden Markov model (HMM) profiles.

Phylogenetic analysis — Create and manipulate phylogenetic tree data.

Microarray data analysis — Read, normalize, and visualize microarray data.

Mass spectrometry data analysis — Analyze and enhance raw mass spectrometry data.

Statistical learning — Classify and identify features in data sets with statistical learning tools.

Programming interface — Use other bioinformatic software (BioPerl and BioJava) within the MATLAB environment.

3. Communications ToolboxCommunications Toolbox software extends the MATLAB technical computing environment with functions, plots, and a graphical user interface for exploring, designing, analyzing, and simulating algorithms for the physical layer of communication systems. The toolbox helps you create algorithms for commercial and defense wireless or wireline systems.The key features of the toolbox are: Functions for designing the physical layer of communications links,

including source coding, channel coding, interleaving, modulation, channel models, and equalization

Plots such as eye diagrams and constellations for visualizing communications signals

Graphical user interface for comparing the bit error rate of your system with a wide variety of proven analytical results

Galois field data type for building communications algorithms

4. Control System ToolboxThe Control System Toolbox™ product extends the MATLAB® software to provide functions designed specifically for control engineering.This toolbox lets you construct and analyze linear models of dynamic systems. Use Control System Toolbox functions to model dynamic systems as transfer functions, in state-space form, or as arrays of frequency response data. Plot the time and frequency responses of your system to understand how your system behaves.

You can also use the toolbox to design and tune single-loop or multiple-loop control systems using various classical and state-space techniques.

5. Curve Fitting ToolboxCurve Fitting Toolbox™ software is a collection of graphical user interfaces (GUIs) and M-file functions for curve and surface fitting that operate in the MATLAB® technical computing environment. The toolbox supplements MATLAB features with:

Data preprocessing capabilities, such as sectioning, excluding data, and smoothing

Data fitting using parametric and nonparametric models:o The toolbox includes a library of parametric models, with

polynomials, exponentials, rationals, sums of Gaussians, Fourier polynomials, and many others.

o You can also define custom models to precisely reflect the goals of your data analysis.

o Nonparametric models are available through a variety of smoothers and interpolants.

Fitting methods for linear least squares, nonlinear least squares, weighted least squares, constrained least squares, and robust fitting are available

Data and fit statistics to assist you in analyzing your models Postprocessing capabilities that allow you to interpolate, extrapolate,

differentiate, and integrate the fit The ability to save your work in various formats, including workspace

variables, binary files, and automatically generated MATLAB code

6. Data Acquisition ToolboxData Acquisition Toolbox™ software is a collection of M-file functions and a MEX-file (shared library) built on the MATLAB® technical computing environment. The toolbox also includes several dynamic link libraries (DLLs) called adaptors, which enable you to interface with specific hardware. The toolbox provides you with these main features:

A framework for bringing live, measured data into the MATLAB workspace using PC-compatible, plug-in data acquisition hardware

Support for analog input (AI), analog output (AO), and digital I/O (DIO) subsystems including simultaneous analog I/O conversions

Support for these popular hardware vendors/devices:o Advantech® boards that use the Advantech Device Manager

o Measurement Computing™ Corporation (ComputerBoards) boards

o National Instruments® boards that use Traditional NI-DAQ or NI-DAQmx software

7. Database ToolboxThe Database Toolbox™ software is one of an extensive collection of toolboxes for use with the MATLAB® product. This toolbox enables you to use MATLAB functions to import and export data between the MATLAB workspace and relational databases. With the Database Toolbox software, you can bring data from a database into the MATLAB workspace, and then use MATLAB computational and analytic tools to work with the data, You can then store the results back in the database or in another database.

8. Datafeed ToolboxThis toolbox, used with the MATLAB® product, effectively turns your MATLAB workstation into a financial data acquisition terminal. The toolbox enables you to:

Retrieve and analyze a wide variety of security data from financial data servers in MATLAB.

Access market, time-series, and historical market data in MATLAB. Monitor the status and history of each connection to a supported data

service provider. Fetch data fields for multiple securities in a single call. Look up security ticker symbols from the toolbox GUI or the MATLAB

command line.

9. Econometric ToolboxThe Econometrics Toolbox™ software, combined with MATLAB®, Optimization Toolbox™, and Statistics Toolbox™ software, provides an integrated computing environment for modeling and analyzing economic and social systems. It enables economists, quantitative analysts, and social scientists to perform rigorous modeling, simulation, calibration, identification, and forecasting with a variety of standard econometrics tools.Specific functionality includes:

Univariate ARMAX/GARCH composite models with several GARCH variants (ARCH/GARCH, EGARCH, and GJR)

Dickey-Fuller and Phillips-Perron unit root tests

Multivariate VARX model estimation, simulation, and forecasting Multivariate VARMAX model simulation and forecasting Monte Carlo simulation of many common stochastic differential

equations (SDEs), including arithmetic and geometric Brownian motion, Constant Elasticity of Variance (CEV), Cox-Ingersoll-Ross (CIR), Hull-White, Vasicek, and Heston stochastic volatility

Monte Carlo simulation support for virtually any linear or nonlinear SDE Hodrick-Prescott filter Statistical tests such as likelihood ratio, Engle's ARCH, Ljung-Box Q Diagnostic tools such as Akaike information criterion (AIC), Bayesian

information criterion (BIC), and partial/auto/cross correlation functions

10. Filter Design ToolboxFilter Design Toolbox™ software is a collection of tools that provides advanced techniques for designing, simulating, and analyzing digital filters. It extends the capabilities of Signal Processing Toolbox™ software with filter architectures and design methods for complex real-time DSP applications, including adaptive filtering and multirate filtering, as well as filter transformations.

11. Financial ToolboxThe MATLAB® and Financial Toolbox™ products provide a complete integrated computing environment for financial analysis and engineering. The toolbox has everything you need to perform mathematical and statistical analysis of financial data and display the results with presentation-quality graphics. You can quickly ask, visualize, and answer complicated questions.In traditional or spreadsheet programming, you must deal with all sorts of housekeeping details: declaring, data typing, sizing, and so on. MATLAB software does all that for you. You just write expressions the way you think of problems. There is no need to switch tools, convert files, or rewrite applications.

12. Financial Derivatives ToolboxFinancial Derivatives Toolbox™ software provides components for analyzing individual derivative instruments and portfolios containing several types of interest-rate-based and equity-based financial instruments.

13. Fuzzy Logic Toolbox

Fuzzy Logic Toolbox™ software is a collection of functions built on the MATLAB® technical computing environment. It provides tools for you to create and edit fuzzy inference systems within the framework of MATLAB. You can also integrate your fuzzy systems into simulations with Simulink® software. You can even build stand-alone C programs that call on fuzzy systems you build with MATLAB. This toolbox relies heavily on graphical user interface (GUI) tools to help you accomplish your work, although you can work entirely from the command line if you prefer.

14. Genetic Algorithm and Direct Search ToolboxGenetic Algorithm and Direct Search Toolbox functions extend the capabilities of Optimization Toolbox™ software and the MATLAB®

numeric computing environment. They include routines for solving optimization problems using

Direct search Genetic algorithm Simulated annealing

These algorithms enable you to solve a variety of optimization problems that lie outside the scope of Optimization Toolbox solvers.

15. Image Acquisition ToolboxThe Image Acquisition Toolbox software is a collection of functions that extend the capability of the MATLAB® numeric computing environment. The toolbox supports a wide range of image acquisition operations, including:

Acquiring images through many types of image acquisition devices, from professional grade frame grabbers to USB-based webcams

Viewing a preview of the live video stream Triggering acquisitions (includes external hardware triggers) Configuring callback functions that execute when certain events occur Bringing the image data into the MATLAB workspace

16. Image Processing ToolboxThe Image Processing Toolbox software is a collection of functions that extend the capability of the MATLAB numeric computing environment. The toolbox supports a wide range of image processing operations, including

Spatial image transformations Morphological operations

Neighborhood and block operations Linear filtering and filter design Transforms Image analysis and enhancement Image registration Deblurring Region of interest operations

17. Instrument Control ToolboxInstrument Control Toolbox™ software is a collection of M-file functions built on the MATLAB® technical computing environment. The toolbox provides you with these features:

A framework for communicating with instruments that support the GPIB interface (IEEE®-488), the VISA standard, and the TCP/IP and UDP protocols. Note that the toolbox extends the basic serial port features included with the MATLAB software.

Support for IVI, VXI plug&play, and MATLAB instrument drivers. Functions for transferring data between the MATLAB workspace and

your instrument:o The data can be binary (numerical) or text.o The transfer can be synchronous and block access to the

MATLAB Command Window, or asynchronous and allow access to the MATLAB Command Window.

Event-based communication. Functions for recording data and event information to a text file. Tools that facilitate instrument control in an easy-to-use graphical

environment.

18. Mapping ToolboxThe Mapping Toolbox™ product comprises an extensive set of functions and graphical user interfaces (GUIs) for creating map displays and analyzing and manipulating geospatial data in the MATLAB environment. You can create maps that combine different types of data from multiple sources and display them in their correct spatial relationships. The toolbox supports spatial analysis methods such as line-of-sight calculations on terrain data and geographic computations that account for the curvature of the Earth's surface. Its library of map projections and georeferencing utilities give you precise control over projected and unprojected coordinate systems.

19. Model Predictive Control ToolboxThe Model Predictive Control Toolbox™ product is a collection of software that helps you design, analyze, and implement an advanced industrial automation algorithm. Like other MATLAB® tools, it provides a convenient graphical user interface (GUI) as well as a flexible command syntax that supports customization.

20. Neural Network ToolboxNeural networks are composed of simple elements operating in parallel. These elements are inspired by biological nervous systems. As in nature, the connections between elements largely determine the network function. You can train a neural network to perform a particular function by adjusting the values of the connections (weights) between elements.

21. OPC ToolboxOPC Toolbox™ software is a collection of functions that extend the capability of the MATLAB® environment, and blocks that extend the Simulink® simulation environment. Using OPC Toolbox functions and blocks, you can acquire live OPC data directly into MATLAB and Simulink, and write data directly to the OPC server from MATLAB and Simulink.

22. Optimization ToolboxOptimization Toolbox software extends the capability of the MATLAB®

numeric computing environment. The software includes functions for many types of optimization including

Unconstrained nonlinear minimization Constrained nonlinear minimization, including semi-infinite

minimization problems Quadratic and linear programming Nonlinear least-squares and curve fitting Constrained linear least squares Sparse and structured large-scale problems, including linear

programming and constrained nonlinear minimization Multiobjective optimization, including goal attainment problems and

minimax problemsThe toolbox also includes functions for solving nonlinear systems of equations.

23. Parallel Computing ToolboxParallel Computing Toolbox™ software allows you to offload work from one MATLAB® session (the client) to other MATLAB sessions, called workers. You can use multiple workers to take advantage of parallel processing. You can use a local worker to keep your MATLAB client session free for interactive work, or with MATLAB® Distributed Computing Server™ you can take advantage of another computer's speed.

24. Partial Differential Equation ToolboxThe objectives of Partial Differential Equation Toolbox™ software are to provide you with tools that:

Define a PDE problem, e.g., define 2-D regions, boundary conditions, and PDE coefficients.

Numerically solve the PDE problem, e.g., generate unstructured meshes, discretize the equations, and produce an approximation to the solution.

Visualize the results.

25. Robust Control ToolboxThe Robust Control Toolbox™ product is a collection of functions and tools that help you analyze and design multiinput-multioutput (MIMO) control systems with uncertain elements. You can build uncertain LTI system models containing uncertain parameters and uncertain dynamics. You get tools to analyze MIMO system stability margins and worst case performance.

26. Signal Processing ToolboxSignal Processing Toolbox™ software is a collection of tools based on the MATLAB® environment. The toolbox supports a wide range of signal processing operations, from waveform generation to filter design and implementation, parametric modeling, and spectral analysis. The toolbox provides two categories of tools, command-line functions/objects and graphical user interfaces.

27. Spline ToolboxSpline Toolbox software contains versions of the essential MATLAB®

programs of the B-spline package (extended to handle also vector-valued splines) as described in A Practical Guide to Splines, (Applied

Math. Sciences Vol. 27, Springer Verlag, New York (1978), xxiv + 392p; revised edition (2001), xviii+346p), hereafter referred to as PGS. The toolbox makes it easy to create and work with piecewise-polynomial functions.

28. Statistics ToolboxStatistics Toolbox™ software extends MATLAB® to support a wide range of common statistical tasks. The toolbox contains two categories of tools:

Building-block statistical functions for use in MATLAB programming Graphical user interfaces (GUIs) for interactive data analysis

Code for the building-block functions is open and extensible. Use the MATLAB Editor to review, copy, and edit M-file code for any function. Extend the toolbox by copying code to new M-files or by writing M-files that call toolbox functions.Toolbox GUIs allow you to perform statistical visualization and analysis without writing code. You interact with the GUIs using sliders, input fields, push buttons, etc. and the GUIs automatically call building-block functions.

29. Symbolic Math ToolboxSymbolic Math Toolbox™ software lets you to perform symbolic computations within the MATLAB® numeric environment. It provides tools for solving and manipulating symbolic math expressions and performing variable-precision arithmetic. The toolbox contains hundreds of symbolic functions that leverage the MuPAD® engine for a broad range of mathematical tasks such as:

Differentiation Integration Linear algebraic operations Simplification Transforms Variable-precision arithmetic Equation solving

30. System Identification ToolboxSystem Identification Toolbox™ software lets you estimate linear and nonlinear mathematical models of dynamic systems from measured data. Use the resulting models for analyzing system dynamics, simulating the output of a system for a given input, predicting future

outputs based on previous observations of inputs and outputs, or for control design.

31. Vehicle Network ToolboxThe Vehicle Network Toolbox™ provides the ability to communicate with in-vehicle networks using Controller Area Network (CAN) protocol. It is a comprehensive toolbox with a MATLAB® interface, Simulink® modeling support and a simple utility that allows you to monitor CAN traffic.You can learn more about the Vehicle Network Toolbox by following a simple workflow and some easy examples. This chapter introduces the toolbox and provides some guidelines and examples to use the Vehicle Network Toolbox to interface with the CAN bus.

32. Wavelet ToolboxEverywhere around us are signals that can be analyzed. For example, there are seismic tremors, human speech, engine vibrations, medical images, financial data, music, and many other types of signals. Wavelet analysis is a new and promising set of tools and techniques for analyzing these signals.Wavelet Toolbox™ software is a collection of functions built on the MATLAB® technical computing environment. It provides tools for the analysis and synthesis of signals and images, and tools for statistical applications, using wavelets and wavelet packets within the framework of MATLAB.

MODULE 1 PROGRAMS:

INPUT:-

%operations on matricesm1=[2 3 1;4 6 2;8 7 9]m2=[5 3 2;4 3 7;8 1 5]sum=m1+m2product = m1*m2inverse=m2^-1e=eig(m1)%plotting of graphstheta=linspace(0,2*pi,10)x=sin(theta)y=cos(theta)z=1:5w=3*z-2plot(x,y,z,w,'o')axis('equal')xlabel('sin(theta)')ylabel('cos(theta)')

OUTPUT:-

m1 =

2 3 14 6 28 7 9

m2 =

5 3 24 3 78 1 5

sum =

7 6 38 9 916 8 14

product =

30 16 3060 32 60140 54 110

inverse =

0.0741 -0.1204 0.13890.3333 0.0833 -0.2500-0.1852 0.1759 0.0278

e =

13.2170-0.00003.7830

theta =

Columns 1 through 5

0 0.6981 1.3963 2.0944 2.7925

Columns 6 through 10

3.4907 4.1888 4.8869 5.5851 6.2832

x =

Columns 1 through 5

0 0.6428 0.9848 0.8660 0.3420

Columns 6 through 10

-0.3420 -0.8660 -0.9848 -0.6428 -0.0000

y =

Columns 1 through 5

1.0000 0.7660 0.1736 -0.5000 -0.9397

Columns 6 through 10

-0.9397 -0.5000 0.1736 0.7660 1.0000

z =

1 2 3 4 5

w =

1 4 7 10 13

INPUT:-

%Define a transfer fn and plot its pole-zero map%file written by varun kumar kadian.load numdemo Pd Cdpzplot(Pd,'b',Cd,'r')

OUTPUT:-

MODULE 2

INTRODUCTION TO FUZZY LOGIC:

In recent years, the number and variety of applications of fuzzy logic have increased significantly. The applications range from consumer products such as cameras, camcorders, washing machines, and microwave ovens to industrial process control, medical instrumentation, decision-support systems, and portfolio selection.

Fuzzy logic has two different meanings. In a narrow sense, fuzzy logic is a logical system, which is an extension of multivalued logic. However, in a wider sense fuzzy logic (FL) is almost synonymous with the theory of fuzzy sets, a theory which relates to classes of objects with unsharp boundaries in which membership is a matter of degree. In this perspective, fuzzy logic in its narrow sense is a branch of FL. Even in its more narrow definition, fuzzy logic differs both in concept and substance from traditional multivalued logical systems.

In Fuzzy Logic Toolbox software, fuzzy logic should be interpreted as FL, that is, fuzzy logic in its wide sense. What might be added is that the basic concept underlying FL is that of a linguistic variable, that is, a variable whose values are words rather than numbers. In effect, much of FL may be viewed as a methodology for computing with words rather than numbers. Although words are inherently less precise than numbers, their use is closer to human intuition. Furthermore, computing with words exploits the tolerance for imprecision and thereby lowers the cost of solution.

A trend that is growing in visibility relates to the use of fuzzy logic in combination with neurocomputing and genetic algorithms. More generally, fuzzy logic, neurocomputing, and genetic algorithms may be viewed as the principal constituents of what might be called soft computing. Unlike the traditional, hard computing, soft computing accommodates the imprecision of the real world. The guiding principle of soft computing is: Exploit the tolerance for imprecision, uncertainty, and partial truth to achieve tractability, robustness, and low solution cost. In the future, soft computing could play an increasingly important role in the conception and design of systems whose MIQ (Machine IQ) is much higher than that of systems designed by conventional methods.

Fuzzy logic is all about the relative importance of precision: How important is it to be exactly right when a rough answer will do?

BASIC THEORY OF FUZZY LOGIC:

Fuzzy Logic Toolbox™ software is a collection of functions built on the MATLAB® technical computing environment. It provides tools to create and edit fuzzy inference systems within the framework of MATLAB. We can also integrate our fuzzy systems into simulations with Simulink® software. We can even build stand-alone C programs that call on fuzzy systems we build with MATLAB. This toolbox relies heavily on graphical user interface (GUI) tools to help us accomplish our work, although we can work entirely from the command line if we prefer.

The toolbox provides three categories of tools:

Command line functions Graphical interactive tools Simulink blocks and examples

The first category of tools is made up of functions that we can call from the command line or from our own applications. Many of these functions are MATLAB M-files, series of MATLAB statements that implement specialized fuzzy logic algorithms. We can view the MATLAB code for these functions using the statement

type function_name

We can change the way any toolbox function works by copying and renaming the M-file, then modifying our copy. We can also extend the toolbox by adding our own M-files.

Secondly, the toolbox provides a number of interactive tools that let us access many of the functions through a GUI. Together, the GUI-based tools provide an environment for fuzzy inference system design, analysis, and implementation.

The third category of tools is a set of blocks for use with Simulink. These are specifically designed for high speed fuzzy logic inference in the Simulink environment.

What makes the toolbox so powerful is the fact that most of human reasoning and concept formation is linked to the use of fuzzy rules. By providing a systematic framework for computing with fuzzy rules, the toolbox greatly amplifies the power of human reasoning. Further amplification results from the use of MATLAB and graphical user interfaces, areas in which The MathWorks™ has unparalleled expertise.

Another basic concept in FL, which plays a central role in most of its applications, is that of a fuzzy if-then rule or, simply, fuzzy rule. Although rule-based systems have a long history of use in Artificial Intelligence (AI), what is missing in such systems is a mechanism for dealing with fuzzy consequents and fuzzy antecedents. In fuzzy logic, this mechanism is provided by the calculus of fuzzy rules.

Why Use Fuzzy Logic?

Here is a list of general observations about fuzzy logic:

Fuzzy logic is conceptually easy to understand.

The mathematical concepts behind fuzzy reasoning are very simple. Fuzzy logic is a more intuitive approach without the far-reaching complexity.

Fuzzy logic is flexible.

With any given system, it is easy to layer on more functionality without starting again from scratch.

Fuzzy logic is tolerant of imprecise data.

Everything is imprecise if you look closely enough, but more than that, most things are imprecise even on careful inspection. Fuzzy reasoning builds this understanding into the process rather than tacking it onto the end.

Fuzzy logic can model nonlinear functions of arbitrary complexity.

You can create a fuzzy system to match any set of input-output data. This process is made particularly easy by adaptive techniques like Adaptive Neuro-Fuzzy Inference Systems (ANFIS), which are available in Fuzzy Logic Toolbox software.

Fuzzy logic can be built on top of the experience of experts.

In direct contrast to neural networks, which take training data and generate opaque, impenetrable models, fuzzy logic lets you rely on the experience of people who already understand your system.

Fuzzy logic can be blended with conventional control techniques.

Fuzzy systems don't necessarily replace conventional control methods. In many cases fuzzy systems augment them and simplify their implementation.

Fuzzy logic is based on natural language.

The basis for fuzzy logic is the basis for human communication. This observation underpins many of the other statements about fuzzy logic. Because fuzzy logic is built on the structures of qualitative description used in everyday language, fuzzy logic is easy to use.

The last statement is perhaps the most important one and deserves more discussion. Natural language, which is used by ordinary people on a daily basis, has been shaped by thousands of

years of human history to be convenient and efficient. Sentences written in ordinary language represent a triumph of efficient communication.

When Not to Use Fuzzy Logic

Fuzzy logic is not a cure-all. When should you not use fuzzy logic? The safest statement is the first one made in this introduction: fuzzy logic is a convenient way to map an input space to an output space. If you find it's not convenient, try something else. If a simpler solution already exists, use it. Fuzzy logic is the codification of common sense — use common sense when you implement it and you will probably make the right decision. Many controllers, for example, do a fine job without using fuzzy logic. However, if you take the time to become familiar with fuzzy logic, you'll see it can be a very powerful tool for dealing quickly and efficiently with imprecision and nonlinearity.

FUNCTIONS GENERALLY USED IN FUZZYLOGIC GUI:

GUI Tools and Plotting

anfisedit Open ANFIS Editor GUI

findcluster Interactive clustering GUI for fuzzy c-means and subclustering

fuzzy Open basic Fuzzy Inference System editor

mfedit Membership function editor

plotfis Plot Fuzzy Inference System

plotmf Plot all membership functions for given variable

ruleedit Rule editor and parser

ruleview Rule viewer and fuzzy inference diagram

surfview Open Output Surface Viewer

Membership Functions

dsigmf Built-in membership function composed of difference between two sigmoidal membership functions

gauss2mf Gaussian combination membership function

gaussmf Gaussian curve built-in membership function

gbellmf Generalized bell-shaped built-in membership function

pimf Π-shaped built-in membership function

psigmf Built-in membership function composed of product of two sigmoidally shaped membership functions

sigmf Sigmoidally shaped built-in membership function

smf S-shaped built-in membership function

trapmf Trapezoidal-shaped built-in membership function

trimf Triangular-shaped built-in membership function

zmf Z-shaped built-in membership function

FIS Data Structure

addmf Add membership function to Fuzzy Inference System

addrule Add rule to Fuzzy Inference System

addvar Add variable to Fuzzy Inference System

defuzz Defuzzify membership function

evalfis Perform fuzzy inference calculations

evalmf Generic membership function evaluation

gensurf Generate Fuzzy Inference System output surface

getfis Fuzzy system properties

mf2mf Translate parameters between membership functions

newfis Create new Fuzzy Inference System

parsrule Parse fuzzy rules

readfis Load Fuzzy Inference System from file

rmmf Remove membership function from Fuzzy Inference System

rmvar Remove variables from Fuzzy Inference System

setfis Set fuzzy system properties

showfis Display annotated Fuzzy Inference System

showrule Display Fuzzy Inference System rules

writefis Save Fuzzy Inference System to file

Advanced Fuzzy Inference Techniques

anfis Training routine for Sugeno-type Fuzzy Inference System (MEX only)

fcm Fuzzy c-means clustering

genfis1 Generate Fuzzy Inference System structure from data using grid partition

genfis2 Generate Fuzzy Inference System structure from data using subtractive clustering

genfis3 Generate Fuzzy Inference System structure from data using FCM clustering

subclust Find cluster centers with subtractive clustering

Simulink Environment

fuzblock Simulink fuzzy logic library

sffis Fuzzy inference S-function for Simulink software

MODULE 2 PROBLEM:

%Program to find the run time of washing machine when dirtness%of clothes and type of dirt are given.

INPUT:

a=newfis('washruntime');a.input(1).name='dirtnessofclothes';a.input(1).range=[0 100];a.input(1).mf(1).name='small';a.input(1).mf(1).type='trimf';a.input(1).mf(1).params=[-50 0 50];a.input(1).mf(2).name='medium';a.input(1).mf(2).type='trimf';a.input(1).mf(2).params=[0 50 100];a.input(1).mf(3).name='large';a.input(1).mf(3).type='trimf';a.input(1).mf(3).params=[50 100 150];a.input(2).name='typeofdirt';a.input(2).range=[0 100];a.input(2).mf(1).name='notgreasy';a.input(2).mf(1).type='trimf';a.input(2).mf(1).params=[-50 0 50];a.input(2).mf(2).name='medium';a.input(2).mf(2).type='trimf';a.input(2).mf(2).params=[0 50 100];a.input(2).mf(3).name='greasy';a.input(2).mf(3).type='trimf';a.input(2).mf(3).params=[50 100 150];a.output(1).name='runtime';a.output(1).range=[0 60];a.output(1).mf(1).name='veryshort';a.output(1).mf(1).type='trimf';a.output(1).mf(1).params=[0 10 15];

a.output(1).mf(2).name='short';a.output(1).mf(2).type='trimf';a.output(1).mf(2).params=[10 15 23];a.output(1).mf(3).name='medium';a.output(1).mf(3).type='trimf';a.output(1).mf(3).params=[15 23 40];a.output(1).mf(4).name='long';a.output(1).mf(4).type='trimf';a.output(1).mf(4).params=[23 40 60];a.output(1).mf(5).name='verylong';a.output(1).mf(5).type='trimf';a.output(1).mf(5).params=[40 60 75];a.rule(1).antecedent=[3 3];a.rule(1).consequent=[5];a.rule(1).weight=1;a.rule(1).connection=1;a.rule(2).antecedent=[2 3];a.rule(2).consequent=[4];a.rule(2).weight=1;a.rule(2).connection=1;a.rule(3).antecedent=[1 3];a.rule(3).consequent=[4];a.rule(3).weight=1;a.rule(3).connection=1;a.rule(4).antecedent=[3 2];a.rule(4).consequent=[4];a.rule(4).weight=1;a.rule(4).connection=1;a.rule(5).antecedent=[2 2];a.rule(5).consequent=[3];a.rule(5).weight=1;a.rule(5).connection=1;a.rule(6).antecedent=[1 2];a.rule(6).consequent=[3];a.rule(6).weight=1;a.rule(6).connection=1;a.rule(7).antecedent=[3 1];a.rule(7).consequent=[3];a.rule(7).weight=1;a.rule(7).connection=1;a.rule(8).antecedent=[2 1];a.rule(8).consequent=[2];a.rule(8).weight=1;a.rule(8).connection=1;a.rule(9).antecedent=[1 1];a.rule(9).consequent=[1];a.rule(9).weight=1;

a.rule(9).connection=1output=evalfis([20 25],a)

OUTPUT:

a =

name: 'washruntime'type: 'mamdani'andMethod: 'min'orMethod: 'max'defuzzMethod: 'centroid'impMethod: 'min'aggMethod: 'max'input: [1x2 struct]output: [1x1 struct]rule: [1x9 struct]

output =

19.3154

DETAILS OF FIS FILE:

[System]Name='washruntime'Type='mamdani'Version=2.0NumInputs=2NumOutputs=1NumRules=9AndMethod='min'OrMethod='max'ImpMethod='min'AggMethod='max'DefuzzMethod='centroid'

[Input1]Name='dirtnessofclothes'Range=[0 100]NumMFs=3MF1='small':'trimf',[-50 0 50]MF2='medium':'trimf',[0 50 100]MF3='large':'trimf',[50 100 150]

[Input2]Name='typeofdirt'Range=[0 100]NumMFs=3MF1='notgreasy':'trimf',[-50 0 50]MF2='medium':'trimf',[0 50 100]MF3='greasy':'trimf',[50 100 150]

[Output1]Name='runtime'Range=[0 60]NumMFs=5MF1='veryshort':'trimf',[0 10 15]MF2='short':'trimf',[10 15 23]MF3='medium':'trimf',[15 23 40]MF4='long':'trimf',[23 40 60]MF5='verylong':'trimf',[40 60 75]

[Rules]3 3, 5 (1) : 12 3, 4 (1) : 11 3, 4 (1) : 13 2, 4 (1) : 12 2, 3 (1) : 11 2, 3 (1) : 13 1, 3 (1) : 12 1, 2 (1) : 11 1, 1 (1) : 1

OUTPUT THROUGH GUI:

MODULE 3

PROBLEM:

%Program to control the speed of a motor by changing the input %voltage using fuzzy logic in MATLAB. When a set point is %defined, if for some reason, the motor runs faster, we need to %slow it down by reducing the input voltage. If the motor slows %below the set point, the input voltage must be increased so %that the motor speed reaches the set point.

INPUT:

a=newfis('speed_control');a.input(1).name='motorspeed';a.input(1).range=[2280 2520 ];a.input(1).mf(1).name='tooslow';a.input(1).mf(1).type='trimf';a.input(1).mf(1).params=[2280 2340 2400];a.input(1).mf(2).name='jstrght';a.input(1).mf(2).type='trimf';a.input(1).mf(2).params=[2360 2400 2440];a.input(1).mf(3).name='toofst';a.input(1).mf(3).type='trimf';a.input(1).mf(3).params=[2400 2460 2520];a.output(1).name='voltage';a.output(1).range=[2.32 2.48];a.output(1).mf(1).name='slowdown'a.output(1).mf(1).type='trimf';a.output(1).mf(1).params=[2.32 2.36 2.40];a.output(1).mf(2).name='nochange';a.output(1).mf(2).type='trimf';a.output(1).mf(2).params=[2.38 2.40 2.42];a.output(1).mf(3).name='speedup';a.output(1).mf(3).type='trimf';a.output(1).mf(3).params=[2.40 2.44 2.48];a.rule(1).antecedent=[1 ];a.rule(1).consequent=[3];a.rule(1).weight=1;a.rule(1).connection=1;a.rule(2).antecedent=[2];a.rule(2).consequent=[2];a.rule(2).weight=1;a.rule(2).connection=1;a.rule(3).antecedent=[3];a.rule(3).consequent=[1];

a.rule(3).weight=1;a.rule(3).connection=1output=evalfis([2500],a)

OUTPUT:

a =

name: 'speed_control'type: 'mamdani'andMethod: 'min'orMethod: 'max'defuzzMethod: 'centroid'impMethod: 'min'aggMethod: 'max'input: [1x1 struct]output: [1x1 struct]rule: [1x3 struct]

output =

2.3600

DETAILS OF FIS FILE:

[System]Name='speed_control'Type='mamdani'Version=2.0NumInputs=1NumOutputs=1NumRules=3AndMethod='min'OrMethod='max'ImpMethod='min'AggMethod='max'DefuzzMethod='centroid'

[Input1]Name='motorspeed'Range=[2280 2520]NumMFs=3

MF1='tooslow':'trimf',[2280 2340 2400]MF2='jstrght':'trimf',[2360 2400 2440]MF3='toofst':'trimf',[2400 2460 2520]

[Output1]Name='voltage'Range=[2.32 2.48]NumMFs=3MF1='slowdown':'trimf',[2.32 2.36 2.4]MF2='nochange':'trimf',[2.38 2.4 2.42]MF3='speedup':'trimf',[2.4 2.44 2.48]

[Rules]1, 3 (1) : 12, 2 (1) : 13, 1 (1) : 1

OUTPUT THROUGH GUI:

SUMMARY

Computation work is done effectively and accurately by implemeting fuzzlogic in no time.It is seen that working in fuzzylogy to solve day to day small problems like finding runtime of washing machine, regulating speed of motor,deciding the amount of tip and many others is easy and works effectively. We can use it almost evrywhere. It can also be combined with other toolboxes of matlab for solving complicated problems for ex. modeling inverse kinematics in robotic arm,modelingtraffic pattern using subtractive clustering,gas mileage prediction,chaotic time series prediction,temperature control in shower etc..We can also use fuzzylogic software with other technical computing software for solving problems with fuzzylogic.

REFERENCES:

1.http://www.mathworks.com/ 2.A few matlab books written by Rudra

Pratap,Otto and Denier.3.Matlab toolbox for fuzzylogic and matlab

help.4.www.google.co.in