Hello!INTRODUCTION TO FUZZY LOGIC AND FUZZY

DECISION MAKING SYSTEM USING SCILAB

U11CO015

What is Fuzzy Logic ?

Fuzzy logic is an approach to computing based on "degrees of truth" rather than the usual "true or false" boolean logic

It was first advanced by Dr. Lotfi Zadeh of the University of California

He said any logical system could be fuzzified.

LET’S REVIEW SOME CONCEPTS

Fuzzy Sets

Let X be a non empty set, A fuzzy set A in X is characterized by its membership function µA: X -> [0,1], where µA(x) is

the degree of membership of element x in fuzzy set A for each x ∈ X .

Operations

UnionIntersectionComplementComtainment

Membership Function

They map elements of a fuzzy set to real numbered values in the interval 0

to 1. Example:- Triangular, Trapezoidal, S-

shaped, Sigmoid, Pi-function

Fuzzification

The process of transforming crisp

(bivalued) input values into linguistic values is called

fuzzification

Defuzzification

Defuzzification converts the fuzzy values into crisp (bivalued) value.

Types :- Max-membership method Centroid method Weighted average method

➜ sciFLT is a Fuzzy Logic Toolbox for scilab. The toolbox was written in a mix of C, Fortran, TK/TCL and scilab Code.

➜ sciFLT was fully tested under Windows and Linux, both using Scilab 3.0

➜ sciFLT works with Mamdani and Sugeno fuzzy logic systems (FLS).

sciFLT Tool of Scilab

➜ atomsInstall('sciFLT')

➜ ATOMS Module manager –> Modeling and Control Tools –> Fuzzy Logic Toolbox or use Start the sciFLT graphical user interface with the command “editfls”

➜ GUI editor: Built in editor to change properties, inputs/outputs variables, member functions, rules.

sciFLT Tool of Scilab

STEPS

Mamdani or Sugeno

1.CHOOSE TYPE OF

FLS

Method used to defuzzify, complement, union and

intersection

2.FILL OUT

DESCRIPTION LINK

3.DEFINE INPUTS

4.DEFINE OUTPUTS

5.DEFINE RULES

➜ We can plot it using plotsurf( filename )

➜ We can evaluate it using evalfls([points], filename)

eg y = evalfls([5,5],tipfls)

Important commands

For commandline

people

Seeing input variables

Seeing output variables

Seeing the surface formed

Thanks!Any questions?

Types of Fuzzy Logic systems: At this stage, sciFLT can deal with Takagi-Sugeno Fuzzy and Mamdani fuzzy systems usage.

XCOS support: Member functions, S-Norm, T-Norm, Complement and Fuzzy Logic System (fls) are supported. Also include a palette.

S-Norm Class supported: Dubois-Prade, Yager, Drastic sum, Einstein, sum, Algebraic sum, Maximum.

T-Norm Class supported: Dubois-Prade, Yager, Drastic product, Einstein product, Algebraic product, Minimum

Complement Class supported: One (classic), Yager, Dubois.

Implication method supported: Product, Minimum

Aggregation method supported: Algebraic Sum, Maximum

Defuzzification method supported: Centroide, Bisector, Mean of Maximum, Largest of Maximum, Smallest of Maximu, Weighted Average, Center Average.

Member functions supported: Triangular, Trapezoidal, Gaussian, ExtendedGaussian, Sigmoidal, Product of two Sigmoidal, Difference of two sigmoidal,S-Shaped, Z-Shaped, Pi-Shaped. Linear and Const as output for Takagi-Sugenotype.

Properties ?

The main difference between Mamdani and Sugeno is that the Sugeno output membership functions are either linear or constant.

Advantages of the Sugeno MethodIt is computationally efficient.It works well with linear techniques (e.g., PID control).It works well with optimization and adaptive techniques.It has guaranteed continuity of the output surface.It is well suited to mathematical analysis.

Advantages of the Mamdani MethodIt is intuitive.It has widespread acceptance.It is well suited to human input.

This minimum operator is one of the "triangular norms".With the T-norms there are the T-conorms, also called the S-norms.

They model union. The maximum operator is an S-norm. It is the blue line in the picture above.