COMPACTNESS IN QUIN TERRANEAN FUZZY TOPOLOGICAL SPACES

Abstract

                     Quin-Terranean fuzzy sets are newly introduced concept of fuzzy witch is an extension of Fermatean fuzzy sets, Pythagorean fuzzy sets, Intuitionistic fuzzy sets and fuzzy sets. Quin-Terranean fuzzy sets are most effective tool to deal the uncertainty. By using the concept of Quin-Terranean fuzzy sets, Quin-Terranean fuzzy topological spaces are defined by us. In this paper we introduce the concept of Quin-Terranean fuzzy  compactness. Also we have defined various types of Quin-Terranean fuzzy compactness namely Quin-Terranean fuzzy almost compactness and Quin-Terranean fuzzy near compactness. Quin-Terranean fuzzy almost compactness is described in terms of Quin-Terranean fuzzy regular closed or Quin-Terranean fuzzy regular open.Moreover, we analyze how Quin-Terranean fuzzy compactness interacts with various forms of Quin-Terranean fuzzy continuity. Also we have studied various properties of Quin-Terranean fuzzy compactness. We prove that the image of a Quin Terranean fuzzy compact space under a fuzzy continuous mapping which is also surjective remains Quin Terranean fuzzy compact.