We introduce the notion of sensible fuzzy ideals of BCK-algebras with respect to a t-conorm and investigate some of their properties. We give the conditions for a sensible fuzzy subalgebra with respect to a t-conorm to be a sensible fuzzy ideal with respect to a t-conorm. Some properties of the direct product and S-product of fuzzy ideals of BCK-algebras with respect to a t-conorm are also disc...

The Dombi operations of T-norm and T-conorm introduced by Dombi can have the advantage of good flexibility with the operational parameter. In existing studies, however, the Dombi operations have so far not yet been used for neutrosophic sets. To propose new aggregation operators for neutrosophic sets by the extension of the Dombi operations, this paper firstly presents the Dombi operations of s...

In this work we have solved an open problem related to the continuity of R-implications. We have fully characterized the class of continuous R-implications obtained from any arbitrary t-norm. Using this result, we also determine the exact intersection between the continuous subsets of R-implications and (S,N)implications. Keywords— R-implication, (S,N)-implication, Łukasiewicz implication, t-norm.

In this paper we carry out an algebraic investigation of the Weak Nilpotent Minimum logic (WNM) and its t-norm based axiomatic extensions. We consider the algebraic counterpart of this logic, the variety of WNM-algebras (WNM) and we prove that it is locally finite, so all its subvarieties are generated by finite chains. We give criteria to compare varieties generated by finite families of WNM-c...

We show that a set of three axioms, together with modus ponens, suffices to build up a formal system for the class R of all quadruples (L,6,T,J), in which (L,6) is a partially ordered set with a top element, and T is a triangular norm on (L,6) that has a residuated implication J. We show that this R is not a variety. 2004 Elsevier Inc. All rights reserved.

This paper is concerned with the problem of characterizing those functions of minimum LP-norm on their nth derivative, <=p=<, that sequentially take on the given values (ei). For p = the unique minimizing function is characterized. For p < fairly explicit necessary conditions are given.