Fuzzy Λ gX r -sets and generalization of closed sets in generalized fuzzy topological spaces

• Main Authors: Jayasree Chakraborty, Baby Bhattacharya, Arnab Paul
• Format: Article
• Language: English
• Published: Prince of Songkla University 2017-06-01
• Series: Songklanakarin Journal of Science and Technology (SJST)
• Subjects: fuzzy Λ g X r -set; fuzzy Λ X g -closed set; fuzzy Λ g X r -closed set; Λ g X r gf-gX - closed set; fuzzy (Λ; ) g X r Y g -continuity
• Online Access: http://rdo.psu.ac.th/sjstweb/journal/39-3/39-3-2.pdf

The aim of this paper is to introduce fuzzy ΛgXr-set and to study some of its generalized forms. The structure constituted by fuzzy Λ g X r -set is also included in the treatise. Moreover we define generalized fuzzy gX -closed set and fuzzy Λ g X r -closed set, which are the weaker forms of fuzzy gX -closed set. The above two weaker forms are independent to each other but jointly they imply fuzzy gX -closed set. Finally, in addition, as the application of fuzzy Λ g X r -closed set, we study fuzzy (Λ , ) g X r Y g - continuity and fuzzy (Λ , ) gf g X r X Y  g g -continuity and a few of their properties. In general, fuzzy contra ( , ) X Y g g -continuity does not imply fuzzy ( , ) X Y g g -continuity, but this paper provides one condition under which the fact is true.