Optimization Techniques in Engineering

16Slightly and Almost Neutrosophic gsα*—Continuous Function in Neutrosophic Topological Spaces

P. Anbarasi Rodrigo and S. Maheswari^*

Department of Mathematics, St. Mary’s College (Autonomous), Thoothukudi. Registration number: 20212212092003 Affiliated by Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli, India

Abstract

This study introduces the new concept on N_eu – closed set namely N_eugsα* – closed set and study about the new concept of N_eu – continuous functions, namely Slightly N_eugsα* – continuous function and Almost N_eugsα* – continuous function. Additionally, we compare the properties and characterizations of these functions with already existing N_eu – functions. We also discussed about the separation axioms for N_eugsα* – closed set and it is also used in theorems.

Keywords: N_eugsα* – closed set, N_eugsα* – open set, slightly N_eugsα* – continuous function, almost N_eugsα* – continuous function

16.1 Introduction

The intuitionistic fuzzy sets was first suggested by Atanassov [1]. Then, the concept of fuzzy sets was introduced by Zadeh [2]. In the continuation of fuzzy sets, Smarandache [3] has introduced the new concept called N_eu – set theory. It includes three components, truth, indeterminancy and false membership function. Dhavaseelan and Page [4] have discussed about the concept of almost N_eu – continuous function. The real-life application of N_eugsα* – topology is applied in Information Systems, Applied Mathematics, etc. Here, we suggested some new ideas ...