Fuzzy interval numbers (FINs, for short) is a unifying data representation analyzable in the context of lattice theory. This work shows how FINs improve the design of popular neural/fuzzy paradigms.

in this paper we continue development of formal theory of a special class offuzzy logics, called eq-logics. unlike fuzzy logics being extensions of themtl-logic in which the basic connective is implication, the basic connective ineq-logics is equivalence. therefore, a new algebra of truth values calledeq-algebra was developed. this is a lower semilattice with top element endowed with two binary...

We introduce the concept of a ⊗-closed set and a ⊗-homomorphism in lattice implication algebras, and we discuss some of their properties. Next, we introduce the fuzzy implicative filter and obtain equivalent conditions. Finally, we discuss the operation ⊗, fuzzy filters, and fuzzy implicative filters. 2000 Mathematics Subject Classification. 03G10, 06B10, 94D05.

In this paper, we investigate the properties of fuzzy Galois (dual Galois, residuated, and dual residuated) connections in a complete residuated lattice L. We give their examples. In particular, we study fuzzy Galois (dual Galois, residuated, dual residuated) connections induced by L-fuzzy relations.

In this paper, we introduce a good definition of semiprecompactness in L-fuzzy topological spaces in Šostak’s sense, where L is a fuzzy lattice. We define this concept on arbitrary L-fuzzy sets, obtain a different characterization and study some of its properties. 2010 AMS Classification: 54A40, 54D30, 53A05

The aim of this paper is to show several iso morphic structures between fuzzy relations and operators from the family of fuzzy sets into itself In particular we prove that the preorders family is able to embed itself in the class of fuzzy consequence operators by way of a lattice monomorphism

In this paper, we apply the concept of fuzzy soft sets to ordered semigroup theory. The concepts of (∈γ ,∈γ ∨qδ)-fuzzy left (right) ideals, (∈γ ,∈γ ∨qδ)-fuzzy biideals and (∈γ ,∈γ ∨qδ)-fuzzy quasi-ideals are introduced and some related properties are obtained. Three kinds of lattice structures of the set of all (∈γ ,∈γ ∨qδ)-fuzzy soft left (right) ideals of an ordered semigroup are derived. The...

In this work we prove that the set of congruences on an nd-groupoid under suitable conditions is a complete lattice which is a sublattice of the lattice of equivalence relations on the nd-groupoid. The study of these conditions allowed to construct a counterexample to the statement that the set of (fuzzy) congruences on a hypergroupoid is a complete lattice.

The Mamdani model [1] of Fuzzy Systems is the earliest and the most widely studied type of Fuzzy Systems. In this work, Residuated Implication (R-implication) operators have been explored for rule reduction in Mamdani-Type Fuzzy Systems with lossless inferencing.

In this article, we propose an axiomatic system for fuzzy “cardinality” measures (referred to as fuzzy c-measures for short) assigning to each finite fuzzy set a generalized cardinal that expresses the number of elements that the fuzzy set contains. The system generalizes an axiomatic system introduced by J. Casasnovas and J. Torrens (2003). We show that each fuzzy c-measure is determined by tw...