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Chapter 6 FUZZY FUNCTION Chi-Yuan Yeh

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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

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Function with fuzzy constraint 3

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Fuzzy extension function 4 tes

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Fuzzy extension function 5

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Single fuzzifying function 6

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Fuzzy bunch of functions 9

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Fuzzy bunch of functions 11

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Fuzzy bunch of functions 12

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Fuzzy bunch of functions 13

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Maximizing set 14

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

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Maximizing set 16

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Maximizing set 17

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Maximizing set 18

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Maximum value in crisp domain 19

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Maximum value in crisp domain 20

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Maximum value in crisp domain 21

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Maximum value in fuzzy domain 22

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Maximum value in fuzzy domain 23

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Maximum value in fuzzy domain 24

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Maximum value in fuzzy domain 25

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Maximum value in fuzzy domain 26

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Integration of fuzzying function 27

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Integration of fuzzying function 28

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Integration of fuzzying function 29

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Integration of fuzzying function 30

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Integration in fuzzy interval 31

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Integration in fuzzy interval 32

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Differentiation of crisp function in fuzzy interval 34

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Differentiation of crisp function in fuzzy interval 35

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36 Differentiation of fuzzifying function function

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37 Thanks for your attention!

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Extension Principle Adriano Cruz ©2002 NCE e IM/UFRJ

Extension Principle Adriano Cruz ©2002 NCE e IM/UFRJ

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