3_membership functions.pdf - Fuzzy set definition Specification of membership functions and Multi-dimensional fuzzy sets Typical membership functions

# 3_membership functions.pdf - Fuzzy set definition...

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Unformatted text preview: Fuzzy set definition Specification of membership functions and Multi-dimensional fuzzy sets Typical membership functions ! "# Typical membership functions "# gaussmf x, c, s = e µ A : X → [0,1] µ Typical membership functions ! triangularmf x, c, h = max min h − c + x , c + h − x , 0 h h \$ ⊂ − 2 x−c 2 2⋅s "# trapmf x, a, b, c, d = max min x − a , 1, d − x , 0 b−a d −c Typical membership functions \$ "# gbellmf x, a, b, c = x a 1 − c 2⋅b a +1 1 Typical membership functions \$ "# gbellmf x, a, b, c = x a % 1 − c 2⋅b a Typical membership functions sigmf x, a, c = +1 Typical membership functions ! "# "# 1 e −a x−c +1 Multi-dimensional fuzzy sets ' () & "# µ * ∈ =µ * ∈ "# Multi-dimensional fuzzy sets Base set A Multi-dimensional fuzzy sets Cylindrical Ext. of A +, ) µR X i 1× X i 2 × × X ik ( xi1 , xi 2 , , xik ) = max X j 1 , X j 2 , , X jn µ R (x1 , x2 , , xn ) 2 Multi-dimensional fuzzy sets . 0 1 / Multi-dimensional fuzzy sets Two-dimensional Projection Projection MF onto X onto Y ) 23 ! - 1 3 RX = max µ R ( x, y) | x y X RY = max µ R ( x, y) | y Y 4 / x Multi-dimensional fuzzy sets 6 7 ) 5 Multi-dimensional fuzzy sets ,8 * "# % - 9* :; f x, y = e − y−4 2 ⋅e 2 − x−3 2 2 ,8 * 9* :; f x, y = e f x, y = e − y−4 2− x − 3 2 2 2 − y−4 2 2 fx x, y = e 2 2 − x−3 2 2 2 8 ⋅e 9; fy x, y = e 2 − x−3 2 2 2 − y−4 8 Multi-dimensional fuzzy sets fx x, y = e − x−3 2 2 2 2 2 fy x, y = e 2 − y−4 f x, y = e "# − y−4 2 ⋅e 2 :; Multi-dimensional fuzzy sets − x−3 2 2 2 2 2 fx x, y = e − x−3 2 2 2 2 2 fy x, y = e 2 − y−4 f ( x, y ) = fx ( x, y ) ∪ fy ( x, y ) ! - - 3 Multi-dimensional fuzzy sets ! * f x, y = x−3 ⋅ y−4 +1 − 2.5 4 ...
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• Winter '16
• ganeshan
• Membership functions, Fuzzy set, Multi-dimensional fuzzy sets, Typical membership functions

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