On Single-Valued Neutrosophic Ideals in Šostak Sense

Yaser Saber,Fahad Alsharari,Florentin Smarandache

doi:10.3390/sym12020193

Yaser Saber, Fahad Alsharari + Show 1 more

Open Access

https://doi.org/10.3390/sym12020193

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Abstract

Neutrosophy is a recent section of philosophy. It was initiated in 1980 by Smarandache. It was presented as the study of origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. In this paper, we introduce the notion of single-valued neutrosophic ideals sets in Šostak’s sense, which is considered as a generalization of fuzzy ideals in Šostak’s sense and intuitionistic fuzzy ideals. The concept of single-valued neutrosophic ideal open local function is also introduced for a single-valued neutrosophic topological space. The basic structure, especially a basis for such generated single-valued neutrosophic topologies and several relations between different single-valued neutrosophic ideals and single-valued neutrosophic topologies, are also studied here. Finally, for the purpose of symmetry, we also define the so-called single-valued neutrosophic relations.

Highlights

The notion of fuzzy sets, employed as an ordinary set generalization, was introduced in 1965 byZadeh [1]
Afterwards, many properties in fuzzy topological spaces have been explored by various researchers [3,4,5,6,7,8,9,10,11,12,13]
It is to be emphasized that being fuzzy or what is termed as fuzzy topology in fuzzy openness concept is not highlighted and well-studied

Summary

Introduction

The notion of fuzzy sets, employed as an ordinary set generalization, was introduced in 1965 by. More specialists in the field like Çoker and Demirci [22], in addition to Samanta and Mondal [23,24], have provided definitions to the concept of graduation intuitionistic openness of fuzzy sets based on Šostak’s sense [25] according to Atanassov’s [26] intuitionistic fuzzy sets. They focused on intuitionistic gradation of openness in light of Chang. Some of their characteristic properties are considered. Several preservation properties and some characterizations concerning single-valued neutrosophic ideal open compatible have been obtained

Preliminaries

Single-Valued Neutrosophic Ideal Open Local Function in Šostak Sense

Conclusions