A protolocalisation of a regular category is a full reflective regular subcategory, whose reflection preserves pullbacks of regular epimorphisms along arbitrary morphisms. We devote special attention to the epireflective protolocalisations of an exact Mal’cev category; we characterise them in terms of a corresponding closure operator on equivalence relations. We give some examples in algebra an...

In this paper, we study the concept of an interval valued fuzzy bi-interior ideal. We investigate properties ideal in semigroups. characterize a regular semigroup terms

In this paper we present completeness results of several fuzzy logics trying to capture different notions of necessity (in the sense of Possibility theory) for Gödel logic formulas. In a first attempt, based on different characterizations of necessity measures on fuzzy sets, a group of logics, with Kripke style semantics, are built over a restricted language, indeed a two level language compose...

A special algebra called EQ-algebra has been recently introduced by Vilém Novák. Its original motivation comes from fuzzy type theory, in which the main connective is fuzzy equality. EQ-algebras have three binary operations meet, multiplication, fuzzy equality and a unit element. They open the door to an alternative development of fuzzy (manyvalued) logic with the basic connective being fuzzy e...

We define the notion of weak relative pseudo-complement on meet semi-lattices, and we show that it is strictly weaker than relative pseudo-complementation, but stronger than pseudo-complementation. Our main result is that if a complete lattice L is meet-continuous, then every closure operator on L admits weak relative pseudo-complements with respect to continuous closure operators on L.

Due to importance of the concepts of θ-closure and δ-closure, it is natural to try for their extensions to fuzzy topological spaces. So, Ganguly and Saha introduced and investigated the concept of fuzzy δ-closure by using the concept of quasicoincidence in fuzzy topological spaces. In this paper, we will introduce the concept of δ-closure in intuitionistic fuzzy topological spaces, which is a g...

We introduce the notions of anti fuzzy right ideal, anti fuzzy right k-ideal and intuitionistic fuzzy right k-ideal of semirings. We investigate the their properties and connections with right k-ideal, fuzzy right k-ideal, anti fuzzy right k-ideal. We characterize regular semiring through intuitionistic fuzzy right ideal. The semi regularity of semirings is characterized by intuitionistic fuzzy...

The notions of pure ideals and pure submodules play an important role in the study of rings and their module categories. In this paper, we introduce right t-pure fuzzy ideals and pure fuzzy submodules of an R-module. We establish their basic properties, and use them to obtain fuzzy theoretic characterizations of right weakly regular rings. Among other results, we prove that a ring R is right we...