Bart Van Gasse

ON THE PROPERTIES OF A GENERALIZED CLASS OF T-NORMS IN INTERVAL-VALUED FUZZY LOGICS

Since it does not generate any MTL-algebra (prelinear residuated lattice), the lattice

Fuzzy implications: classification and a new class

\mathcal{L}^I

On a New Class of Implications in Fuzzy Logic

of closed subintervals of [0, 1] falls outside the mainstream of research on formal fuzzy logics. However, due to the intimate connection between logical connectives on

Triangle algebras: towards an axiomatization of interval-valued residuated lattices

\mathcal{L}^I

The role a fuzzy implication plays in a multi-criteria decision algorithm

and those on [0, 1], many relevant logical properties can still be maintained, sometimes in a slightly weaker form. In this paper, we focus on a broad class of parametrized t-norms on

Interval-Valued Algebras and Fuzzy Logics

\mathcal{L}^I

Implications in Fuzzy Logic: Properties and a New Class

. We derive their corresponding residual implicators, and examine commonly imposed logical properties. Importantly, we formally establish one-to-one correspondences between ∨-definability (respectively, weak divisibility) for t-norms of this class and strong ∨-definability (resp., divisibility) for their counterparts on [0, 1].

An Overview of the Fuzzy Axiomatic Systems and Characterizations Proposed at Ghent University

One of the most important and interesting topics in fuzzy mathematics is the study of fuzzy connectives and in particular fuzzy implications. Fuzzy implications are supposed to have at least some fundamental properties in common with the classical binary implication. Besides these fundamental properties there are many additional potential properties for fuzzy implications, among which eight are widely used in the literature. Fuzzy implications satisfying different subsets of these eight properties have been constructed and some interrelationships between these eight properties have been established. This paper aims to lay bare all the interrelationships between the eight additional properties. Where needed suitable counterexamples are provided. In our search for these counterexamples we discovered a new class of fuzzy implications that is completely determined by a fuzzy negation. For this new class we examine the conditions under which the eight properties are satisfied and we obtain the intersection with the class of strong and residual fuzzy implications.

A multi-criteria group decision algorithm for policy analysis

We define and study a new class of implications determined only by a negation. We examine under which conditions the most popular eight axioms for implications are satisfied. We obtain the intersection of the new class of implications with the S- and R- implications.

A thorough study of interrelationship in fuzzy implication axioms

In this paper, we present triangle algebras: residuated lattices equipped with two modal, or approximation, operators and with a third angular point u, different from 0 (false) and 1 (true), intuitively denoting ignorance about a formula’s truth value. We prove that these constructs, which bear a close relationship to several other algebraic structures including rough approximation spaces, provide an equational representation of interval-valued residuated lattices; as an important case in point, we consider