A novel approach to neutrosophic sets in UP-algebras

Volume 21, Issue 1, pp 78--98 http://dx.doi.org/10.22436/jmcs.021.01.08

Publication Date: March 26, 2020 Submission Date: November 04, 2019 Revision Date: January 21, 2020 Accteptance Date: February 10, 2020

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Authors

Metawee Songsaeng - Department of Mathematics, School of Science, University of Phayao, Phayao 56000, Thailand. Aiyared Iampan - Department of Mathematics, School of Science, University of Phayao, Phayao 56000, Thailand.

Abstract

The notion of neutrosophic sets in UP-algebras was introduced by Songsaeng and Iampan [M. Songsaeng, A. Iampan, Eur. J. Pure Appl. Math., \(\bf12\) (2019), 1382--1409]. In this paper, the notions of special neutrosophic UP-subalgebras, special neutrosophic near UP-filters, special neutrosophic UP-filters, special neutrosophic UP-ideals, and special neutrosophic strong UP-ideals of UP-algebras are introduced, and several properties are investigated. Conditions for neutrosophic sets to be special neutrosophic UP-subalgebras, special neutrosophic near UP-filters, special neutrosophic UP-filters, special neutrosophic UP-ideals, and special neutrosophic strong UP-ideals of UP-algebras are provided. Relations between special neutrosophic UP-subalgebras (resp., special neutrosophic near UP-filters, special neutrosophic UP-filters, special neutrosophic UP-ideals, special neutrosophic strong UP-ideals) and their level subsets are considered.

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Keywords

• UP-algebra
• special neutrosophic UP-subalgebra
• special neutrosophic near UP-filter
• special neutrosophic UP-filter
• special neutrosophic UP-ideal
• special neutrosophic strong UP-ideal

MSC

•  03G25
•  03B52
•  03B60

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