H. Hamacher. Uber logische Aggregationen nichtbinar explizierter Entscheidungskriterien; Ein axiomatischer Beitrag zur normativen Entscheidungstheorie. R.G. Fischer Verlag, 1978.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....log x. The corresponding diagonal is ffi T P (x) x 2 and it is evident that Gamma log x 2 = 2 ( Gamma log x) 2. Let f(x) 1 x Gamma 1. Then f is an additive generator of so called Hamacher product , TH , where TH (x; y) xy x y Gammaxy for (x; y) 6= 0; 0) 0 otherwise: see [2]) The corresponding diagonal is ffi T H (x) x 2 Gammax . Example 1.7 : 1. The Lukasiewicz t norm TL is nilpotent. Its normed additive generator is f(x) 1 Gamma x and the diagonal is ffi T L (x) max(0; 2x Gamma 1) 2. Let f(x) 1 Gamma x) 2 . Then the corresponding t norm, T ....

Hamacher, H.: Uber logische Aggregationen nicht-binar explizierter Entscheidungskriterien. Rita G. Fischer Verlag, Frankfurt, 1978.

.... [0, 1] 0, 1] # [0, 1] such that T is symmetric, associative, non decreasing and T (x, 1) x, x # [0, 1] The function H # : 0, 1] 0, 1] # [0, 1] where # 0, defined by H # (u, v) uv # (1 #) u v uv) is called Hamacher norm with parameter # (H # norm for short) [6]. A symmetric triangular fuzzy number # denoted by (a, #) is defined as #(t) 8 : 1 a t # if a t # #, 0 otherwise, where a # IR is the modal value and 2# 0 is the spread of #. Let T 1 , T 2 be t norms. We say that T 1 is weaker than T 2 (and write T 1 # T 2 ) if T 1 ....

H. Hamacher, Uber logische Aggregationen nicht binar explizierter Entscheidung-kriterien, Rita G.Fischer Verlag, Frankfurt, 1978.

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H. Hamacher. Uber logische Aggregationen nichtbinar explizierter Entscheidungskriterien; Ein axiomatischer Beitrag zur normativen Entscheidungstheorie. R.G. Fischer Verlag, 1978.

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