in this paper, new definitions of $l$-fuzzy closure operator, $l$-fuzzy interior operator, $l$-fuzzy remote neighborhood system, $l$-fuzzy neighborhood system and $l$-fuzzy quasi-coincident neighborhood system are proposed. it is proved that the category of $l$-fuzzy closure spaces, the category of $l$-fuzzy interior spaces, the category of $l$-fuzzy remote neighborhood spaces, the category of ...

In this paper, the concept of (∈,∈ ∨ qk)-fuzzy quasi-ideals of an ordered semigroup S is introduced by the ordered fuzzy points of S, which is a generalization of fuzzy quasi-ideal of S, and related properties are investigated. Furthermore, we introduce the concepts of prime and completely semiprime (∈,∈ ∨ qk)-fuzzy quasi-ideals of ordered semigroups, and characterize bi-regular ordered semigro...

Two generalized uniform structures namely fuzzy quasi-uniformity and fuzzy local quasi-uniformity are introduced. Conditions of fuzzy quasi-uniformizability and quasi-metrizability are examined. Mathematics Subject Classification: 54E15, 54A20

It is well-known that on quasi-pseudometric space $(X,q)$, every $q^s$-Cauchy sequence left (or right) $K$-Cauchy but the converse does not hold in general. In this article, we study a class of maps preserve (right) sequences call sequentially-regular maps. Moreover, characterize totally bounded sets terms and right uniformly locally semi-Lipschitz

we consider the concept of fuzzy quasi-contractions initiated by '{c}iri'{c} in the setting of fuzzy metric spaces and establish fixed point theorems for quasi-contractive mappings and for fuzzy $mathcal{h}$-contractive mappings on m-complete fuzzy metric spaces in the sense of george and veeramani.the results are illustrated by a representative example.

Given any preorder on a finite set X, we present an algorithm to construct a partial pseudometric p on X which generates in the sense that a b if and only if p(a, b) ≤ p(a, a). The specialization topology generated by agrees with the topology generated by the partial pseudometric p-balls, and consequently any topology on X is generated by a partial pseudometric. AMS Subject classification: 54A0...

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...

Removing the condition of symmetry in the notion of a fuzzy (pseudo)metric, in Kramosil and Michalek’s sense, one has the notion of a fuzzy quasi-(pseudo-)metric. Then for each fuzzy quasi-pseudo-metric on a set X we construct a fuzzy quasipseudo-metric on the collection of all nonempty subsets of X, called the Hausdorff fuzzy quasi-pseudo-metric. We investigate several properties of this struc...

In this paper we define intuitionistic fuzzy quasi-ideals of ordered semigroups. The main result of the paper is a characterization of quasi-ideals in terms of intuitionistic fuzzy quasi-ideals. We also characterize left simple, right simple, and completely regular ordered semigroups in terms of intuitionistic fuzzy quasi-ideals. We study the decomposition of left and right simple ordered semig...

The focus of this paper is the pseudometric used as a key concept in our previous work on optimal supervisory control of probabilistic discrete event systems. The pseudometric is employed to measure the behavioural similarity between probabilistic systems, and initially was defined as a greatest fixed point of a monotone function. This paper further characterizes the pseudometric. First, it giv...