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Open AccessArticle

On Single-Valued Neutrosophic Ideals in Šostak Sense

1
Department of Mathematics, College of Science and Human Studies, Hotat Sudair, Majmaah University, Majmaah 11952, Saudi Arabia
2
Department of Mathematics, Faculty of Science Al-Azhar University, Assiut 71524, Egypt
3
Department of Mathematics, University of New Mexico, Gallup, NM 87301, USA
*
Author to whom correspondence should be addressed.
Symmetry 2020, 12(2), 193; https://doi.org/10.3390/sym12020193
Received: 15 December 2019 / Revised: 6 January 2020 / Accepted: 6 January 2020 / Published: 25 January 2020
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. View Full-Text
Keywords: single-valued neutrosophic closure; single-valued neutrosophic ideal; single-valued neutrosophic ideal open local function; single-valued neutrosophic ideal closure; single-valued neutrosophic ideal interior; single-valued neutrosophic ideal open compatible single-valued neutrosophic closure; single-valued neutrosophic ideal; single-valued neutrosophic ideal open local function; single-valued neutrosophic ideal closure; single-valued neutrosophic ideal interior; single-valued neutrosophic ideal open compatible
MDPI and ACS Style

Saber, Y.; Alsharari, F.; Smarandache, F. On Single-Valued Neutrosophic Ideals in Šostak Sense. Symmetry 2020, 12, 193.

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