# Chapter 6 FUZZY FUNCTION Chi-Yuan Yeh. Kinds of fuzzy function Crisp function with fuzzy constraint Fuzzy extension function which propagates the fuzziness.

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Chapter 6 FUZZY FUNCTION Chi-Yuan Yeh

Kinds of fuzzy function Crisp function with fuzzy constraint Fuzzy extension function which propagates the fuzziness of independent variable to dependent variable Fuzzifying function which blurs the image of a crisp independent variable 2

Function with fuzzy constraint 3

Fuzzy extension function 4 tes

Fuzzy extension function 5

Single fuzzifying function 6

7

8

Fuzzy bunch of functions 9

10

Fuzzy bunch of functions 11

Fuzzy bunch of functions 12

Fuzzy bunch of functions 13

Maximizing set 14

Minimizing set Minimizing set of f is defined as the maximizing set of -f 15

Maximizing set 16

Maximizing set 17

Maximizing set 18

Maximum value in crisp domain 19

Maximum value in crisp domain 20

Maximum value in crisp domain 21

Maximum value in fuzzy domain 22

Maximum value in fuzzy domain 23

Maximum value in fuzzy domain 24

Maximum value in fuzzy domain 25

Maximum value in fuzzy domain 26

Integration of fuzzying function 27

Integration of fuzzying function 28

Integration of fuzzying function 29

Integration of fuzzying function 30

Integration in fuzzy interval 31

Integration in fuzzy interval 32

33

Differentiation of crisp function in fuzzy interval 34

Differentiation of crisp function in fuzzy interval 35

36 Differentiation of fuzzifying function function

37 Thanks for your attention!

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