Operation Approach on 𝜶𝒈-Open Sets and Neutrosophic Soft Open Sets

Abstract

The concept of operation on topology was initially introduced by Kasahara in newlinethe year 1979. In 1991, Ogata utilized the idea of operation approach and defined newlinea new form of sets stronger than open sets called and#947;-open sets in topological spaces. newlineFollowing his work, many researchers has contributed to the theory of operation newlineapproach by studying the properties of operation on various collection of open sets newlinein topological spaces. Few researchers has introduced the concept of operation newlineapproach in different topological spaces also. newlineThe class of and#945;-generalised closed sets lies between the class of generalized newlineand#945;-closed sets and the class of generalised semi-closed sets. The study on operation newlineapproach on and#945;-generalised open sets broadens the area of research on newlineoperation approach by analysing the topological behaviours in a detailed manner. newlineThe study mainly focuses on the change in the topological properties that occurs newlinewhen the operation is defined on a non topological collection. By using the operation newlineon and#945;-generalised open sets, and#945;gand#947;-open sets are introduced. The dependency newlineand independency relation between various existing different types of open sets newlinevia and#947;-operation are determined. The topological properties of the operators such newlineas interior, closure, kernel using operation on and#945;g-open sets are examined. New newlineforms of separations axioms are constructed using operation on and#945;g-open sets and newlinesome characterization theorems for the separation axioms are derived. Analysis newlineof continuous maps using and#947;-operation on and#945;g-open sets and and#945;gand#947;-open sets are newlinecarried out. The concept of operation is extended to neutrosophic soft topological newlinespace and the properties of the operation on neutrosophic soft open sets are newlineanalysed in neutrosophic soft environment. A decision making problem is chosen newlineand priority attribute based decision making algorithm is proposed for solving the newlinechosen problem using and#947;-operation on neutrosophic soft open sets.