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Generalized Fuzzy Closed Sets in Smooth Bitopological Spaces
Abstract
This chapter is devoted to the study of r-generalized fuzzy closed sets (briefly, gfc sets) in smooth bitopological spaces (briefly, smooth bts) in view definition of Šostak (1985). The chapter is divided into seven sections. The aim of Sections 1-2 is to introduce the fundamental concepts related to the work. In Section 3, the concept of r-(ti,tj)-gfc sets in the smooth bts's is introduce and investigate some notions of these sets, generalized fuzzy closure operator induced from these sets. In Section 4, (i,j)-GF-continuous (respectively, irresolute) mappings are introduced. In Section 5, the supra smooth topology which generated from a smooth bts is used to introduce and study the notion of r-t12-gfc sets for smooth bts's and supra generalized fuzzy closure operator . The present notion of gfc sets and the notion which introduced in section 3, are independent. In Section 6, two types of generalized supra fuzzy closure operators introduced by using two different approaches. Finally, Section 7 introduces and studies different types of fuzzy continuity which are related to closure.
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