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On t-reverse of t-norms. (English) Zbl 0954.03060
Summary: A commutative, associative, non-decreasing function $$T: [0,1]^2 \to[0,1]$$ satisfying the boundary condition $$T(x,1)=x$$ is called a t-norm. A t-reverse of t-norm is a function $$T^*$$ defined by $$T^*(x,y)= \max \{0,x+y-1 +T(1-x, 1-y)\}$$. If $$T^*$$ is t-norm then $$T$$ is t-reversible. The main results characterise t-reversibility of t-norms and their ordinal sums.

##### MSC:
 03E72 Theory of fuzzy sets, etc. 26B35 Special properties of functions of several variables, Hölder conditions, etc.