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.


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