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
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