Some Group Theoretic Aspects of t-Norms

Continuous archimedean t-norms are generated by automorphisms f of ([0; 1]; ), the unit interval with its usual order structure. Such strict t-norms 4 are given by x 4 y = f 1 (f(x)f(y)) and nilpotent ones by x4y = f 1 ((f(x)+f(y) 1)_0). Let A be the group of automorphisms of ([0; 1]; ), the group operation being composition of functions. Certain subgroups of A play an important role in the theory, for example the multiplicative group R+ of positive real numbers, which is embedded in A by r(x) = xr : Some standard families of t-norms are in natural one-to-one correspondence with subgroups of A. We examine this phenomenon, and various other group theoretic aspects of t-norm theory.

• Type: Journal
• Year: 2000
• Where: IJUFKS
• Authors: Fred Richman, Elbert A. Walker
• Keywords: Continuous Archimedean T-norms, IJUFKS 2000, Such Strict T-norms, Usual Order Structure