Re: Separation Axioms In Fuzzy Topological Spaces Pdf Download
Marq Pargman
Abstract:In this study, we present the concept of the interval-valued fuzzy soft point and then introduce the notions of its neighborhood and quasi-neighborhood in interval-valued fuzzy soft topological spaces. Separation axioms in an interval-valued fuzzy soft topology, so-called q-Ti for i=0,1,2,3,4, are introduced, and some of their basic properties are also studied.Keywords: interval-valued fuzzy soft set; interval-valued fuzzy soft topology; interval-valued fuzzy soft point; interval-valued fuzzy soft neighborhood; interval-valued fuzzy soft quasi-neighborhood; interval-valued fuzzy soft separation axioms
In this paper, the definition of the bipolar fuzzy (bf) point has been generalized, and using this, the concept of separation axioms has been introduced in bipolar fuzzy settings. Moreover, the relation between these separation axioms has been established.
The fuzzy topological space was introduced by Dip in 1999 depending on the notion of fuzzy spaces. Dip's approach helps to rectify the deviation in some definitions of fuzzy subsets in fuzzy topological spaces. In this paper, further definitions, and theorems on fuzzy topological space fill the lack in Dip's article. Different types of fuzzy topological space on fuzzy space are presented such as co-finite, co-countable, right and left ray, and usual fuzzy topology. Furthermore, boundary, exterior, and isolated points of fuzzy sets are investigated and illustrated based on fuzzy spaces. Finally, separation axioms are studied on fuzzy spaces.
The aim of this article is to introduce and characterize almost-s-Menger and almost-co-s-Menger selection properties in ditopological texture spaces. We prove that every s-Menger ditopological texture space is almost-s-Menger and every s-compact ditopological texture space is almost-s-Menger, and give an example which shows that the converse is not true in general.
The aim of this paper is to investigate the structure of fuzzes, introduced by Hutton. We shall not be concerned here with fuzzy topology, but we think that a deeper knowledge of the properties of fuzzes may be helpful in several fields of fuzzy set theory, and in the study of fuzzy topological spaces in particular.