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...

Recently, Phiangsungnoen et al. [J. Inequal. Appl. 2014:201 (2014)] studied fuzzy mappings in the framework of Hausdorff fuzzy metric spaces. Following this direction of research, we establish the existence of fixed fuzzy points of fuzzy mappings. An example is given to support the result proved herein; we also present a coincidence and common fuzzy point result. Finally, as an application of o...

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 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...

In this paper, we introduce and study a class of generalized nonlinear vector quasi-variationallike inequalities with set-valued mappings in Hausdorff topological vector spaces which includes generalized nonlinear mixed variational-like inequalities, generalized vector quasi-variational-like inequalities, generalizedmixed quasi-variational-like inequalities and so on. Bymeans of fixed point the...

This paper examines type-2 fuzzy arithmetic using interval analysis. It relies heavily on alpha-cuts and alpha-planes. Furthermore, we discuss the use of quasi type-2 fuzzy sets proposed by Mendel and Liu and define quasi type-2 fuzzy numbers. Arithmetic operations of such numbers are defined and a worked example is presented. Keywords— Fuzzy Arithmetic, Type-2 Fuzzy Arithmetic, Type-2 Fuzzy Nu...

The classical theorems of Riesz [l] on compact operators have been extended by Leray [2] and Williamson [3] to the context of topological linear spaces. Ringrose [4] has shown that if an operator on such a space is compact, the square of its adjoint is also compact, where the topology on the dual space is that of uniform convergence on bounded sets. Thus if an operator is continuous and some po...

In this paper, a new definition of locally convex L-topological vector spaces is given. The relationship between this new definition and the previous definition of locally convex L-topological vector spaces given by Yan and Fang in 1999 is investigated. Moreover, the concept of generalized L-fuzzy semi-norm is introduced. By using a family of generalized L-fuzzy semi-norms, a characterization o...