Characterization of Fuzzy δg*-Closed Sets in Fuzzy Topological Spaces

Characterization of Fuzzy δg*-Closed Sets in Fuzzy Topological Spaces

Anahid Kamali (Khaje Nasir Toosi University of Technology, Tehran, Iran) and Hamid Reza Moradi (Young Researchers and Elite Club, Mashhad Branch, Islamic Azad University, Mashhad, Iran)
Copyright: © 2016 |Pages: 12
DOI: 10.4018/IJFSA.2016040101
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Abstract

The purpose of this research article is to explain the meaning of g-closed sets in fuzzy topological spaces, which is more understandable to the readers and we find some of its basic properties. The concept of fuzzy sets was introduced by Zadeh in his classical paper (1965). Thereafter many investigations have been carried out, in the general theoretical field and also in different applied areas, based on this concept. The idea of fuzzy topological space was introduced by Chang (1968). The idea is more or less a generalization of ordinary topological spaces. Different aspects of such spaces have been developed, by several investigators. This paper is also devoted to the development of the theory of fuzzy topological spaces.
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1. Introduction

In (1970), Levine introduced the concept of -closed sets in general topology. Many researchers like Cao and Ganster (2002, 2005), Noiri and Popa (2006) and Daraby (2007) and etc. have worked on -closed sets, their generalization in general topology. After the introduction of fuzzy sets by Zadeh in (1965) and fuzzy topology by Chang in (1968), several researchers were conducted on generalization of the notion of fuzzy sets and fuzzy topology. In Chang’s fuzzy topological spaces, each fuzzy set is either open or not. Later, the notion of an intuitionistic fuzzy sets which is a generalization of fuzzy sets were introduced by Atanassov (1986).

Coker (1997) proposed the notion of intuitionistic fuzzy topological spaces. Rajarajeswari and Krishna Moorthy (2011) extended the concepts of fuzzy weakly generalized closed set in intuitionistic fuzzy topological spaces.

Recently, many generalizations of intuitionistic fuzzy -closed sets like intuitionistic fuzzy -closed sets (Thakur and Chaturvedi, 2006), intuitionistic fuzzy -closed sets (Thakur and Jyoti, 2010a), intuitionistic fuzzy -closed sets (Thakur and Jyoti, 2010b), intuitionistic fuzzy -closed sets (Sakthivel, 2010) and intuitionistic fuzzy -closed sets (Santhi and Jayanthi, 2011) have been appeared in the literature.

Ganguly and Saha (1988) introduced the idea of the fuzzy -closure. Dontchev (1996) gave the definition of -closed sets and Kumar studied -closed sets in (2006). Hanafy (2000) and Lee (2011), have worked on -compactness and -separation in fuzzy topological spaces respectively.

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