The rotation construction for t-norms is introduced in (J. Appl. Non-Classical Logics 10 (2000) 83–92). In the present paper we characterize the widest class of operators with which the rotation construction results in left-continuous t-norms with involutive associated negations. c © 2002 Elsevier Science B.V. All rights reserved.

This paper continues and finishes other works toward proposing a method to measure the μ-T-conditionality character of any fuzzy relation for any continuous t-norm T.

We show that the sup-t-norm and inf-residuum types of fuzzy relational equations, considered in the literature as two different types, are in fact two particular instances of a single, more general type of equations. We demonstrate that several pairs of corresponding results on the sup-t-norm and inf-residuum types of equations are simple consequences of single results regarding the more genera...

We generalize min-neighborhood groups to arbitrary T -neighborhood groups, where T is a continuous triangular norm. In particular, we point out that our results accommodate the previous theory on min-neighborhood groups due to T. M. G. Ahsanullah. We show that every T -neighborhood group is T -uniformizable, therefore, T -completely regular. We also present several results of T -neighborhood gr...

We present a procedure for constructing multi-valued tnorms and t-conorms. Our construction uses a pair of single-valued t-norms and the pair of dual t-conorms to construct interval-valued t-norms u and t-conorms t. In this manner we can combine desirable characteristics of different t-norms and t-conorms; furthermore if we use the t-norm ∧ and t-conorm ∨, then (X,u,t) is a superlattice, i.e. t...

We introduce and study the noncommutative modular function spaces of measurable operators affiliated with a semifinite von Neumann algebra and show that they are complete with respect to their modular. We prove that these spaces satisfy the uniform Opial condition with respect to ρ̃-a.e.-convergence for both the Luxemburg norm and the Amemiya norm. Moreover, these spaces have the uniform Kadec–K...

In order to avoid combinatorial rule explosion in fuzzy reasoning, in this work we explore the distributive equations of implications. In details, by means of the section of I, we give out the sufficient and necessary conditions of solutions for the distributive equation of implication I(x, T1(y, z)) = T2(I(x, y), I(x, z)), when T1 is a continuous but not Archimedean triangular norm, T2 is a co...

Diagonals of continuous t-norms are studied. The characterization of all functions being diagonals of continuous t-norms is given. To a given diagonal, the class of all continuous t-norms with this diagonal is characterized.

This paper deals with Lipschitzian t-norms. A partial answer to an open problem of Alsina, Frank and Schweizer is given with regard to strict t-norms with smooth additive generators. A new notion of local Lipschitzianity for arbitrary tnorms is introduced. Some remarkable examples of non-Lipschitzian continuous triangular norms are provided.