FUZZY MODELS

Takagi-Sugeno and Tsukamoto

UNIVERSITATEA „POLITEHNICA” TIMIŞOARA

FACULTATEA DE AUTOMATICĂ ŞI CALCULATOARE

Index1. Tsukamoto fuzzy models 2. A Rule in a TSK fuzzy models3. Particular cases of TSK fuzzy model4. Inference mechanisms involved in

TSK fuzzy models5. Operation mode of two input-single

output first-order Sugeno fuzzy model6. Tsukamoto fuzzy models7. Operation mode of a Tsukamoto fuzzy

model

Takagi-Sugeno fuzzy modelsIntroductionKnown as

◦Takagi-Sugeno-Kang (TSK)◦Sugeno

◦Suggested as an alternative to the development of systematic approaches capable of generating fuzzy rules from a given input-output data set

A Rule in a TSK fuzzy modelsIF (x = A AND y = B) THEN (z = f

(x, y))◦A and B are FSs in the premise

(antecedent)◦f (x, y) is a crisp function in the

conclusion(consequent)

◦f (x, y) must describe the output of model z in the fuzzy region specified by the rule antecedent

◦f (x, y) is a polynomial with input x and y

◦f (x, y) can be any linear or nonlinear function

Particular cases of TSK fuzzy modelFirst-order Sugeno fuzzy

model◦f (x, y) is a first-order polynomial

Zero-order Sugeno fuzzy model◦f (x, y) is a constant◦consequent is specified by a

singleton or a predefuzzified consequent

Inference mechanisms involved in TSK fuzzy modelsSimilar to inference mechanisms

in Mamdani fuzzy models (fuzzy inference systems)

Defuzzification method◦the weighted area method◦the calculation of the crisp control

signal is of type

Operation mode of two input-single output first-order Sugeno fuzzy model

Operation mode

◦w and 2 w stand for the firing strengths of the two rules, and the rule consequents in the two rules, 1

z and 2 z , that represent the fuzzy consequent

Operation mode◦w1,w2

the firing strengths of the two rules

◦z1,z2 the fuzzy consequent expressed as

weighted area method of defuzzification:

Tsukamoto fuzzy models◦Consequents

represented using fuzzy sets with monotonically membership functions

◦Inferred output/rule defined as a crisp value induced by the rule’s

firing strength

◦z - the crisp output of the fuzzy model, is obtained with weighted area method of

defuzzification taking the weighted average of each rule’s

output

Operation mode of a Tsukamoto fuzzy model

Operation mode of a Tsukamoto fuzzy model (continue)

◦Similar to the case of Takagi-Sugeno fuzzy models

◦Defuzzification method application of the weighted average

method avoids time-consuming defuzzification

methods

◦Tsukamoto models are not often used not as transparent as Takagi-Sugeno or

Mamdani models