A family of strict and discontinuous triangular norms

Abstract

Answers to some questions about triangular norms are given. Precisely, a procedure of construction of infinitely many triangular norms is obtained (one for each operation *: N2 → N such that 〈N, <,*〉 is a strictly ordered commutative semigroup). Each of them is discontinuous at each point of a dense subset of [0,1]2 and it satisfies the condition T(kx, y) = T(x, ky) for infinitely many k ∈ [0,1]. © 1998 Elsevier Science B.V. All rights reserved.