シナジーのメタファー１

The gamma operator is more important, because it mirrors the human feeling for compensatory AND appropriately.

(27) μAλB(x) = [μA(x)・μB(x)]1-Y. [1 - (1- μA (x))・(1 - μB (X))]Γ mitγ∈[0;1]

Similar to λ, it is determined by parameter Gamma, where the operator is located between pure AND, and pure OR.

(28) Gamma = Zero
μAλB(x) |γ=0 =μA(x)・μB(x)=μA and B

(29) Gamma = One
μAλB(x) γ=1 = 1 - (1 -μA(x)・(1 - μB(x))= 1 – [1 - μA(x) + μB(x) +μA(x)・μB(x)]
=μA(x) + μB(x) -μA(x)・μB(x)=μA OR B

(30) Graphically

AND OR
-----------------------------------------------------------------------------
Lambda =1 Lambda = 0
Gamma = 0 Gamma = 1
zero < ----------------------------------------------- > full
Compensation

The negation happens very simply. The assumption is certainly the normalized Description.

(31) Negation
μA/(x) = 1 -μA(x)

The modifiers (e.g. very, more or less) are seen as operators that influence a truth value but basically don’t change. They strengthen the features of the considered element or weakens them. The linguistic “very” can be mathematically obtained (as very much) by squaring the membership function. “More or less” can be mathematically described by the square root of the membership function.

(34) Modification
heated
not heated = 1 – heated patient
more or less patient= √patient
very patient = patient2
not very patient = 1 – very patient= 1 - patient2

Instead of the combination of a fuzzy set with a modifier, independent fuzzy sets can be also defined. Moreover, it has the advantage that the border of the separate sets can be individually determined.

花村嘉英（2005）「計算文学入門−Thomas Mannのイロニーはファジィ推論といえるのか？」より英訳 translated by Yoshihisa Hanamura