Picture fuzzy sets in UP-algebras by means of a special type

Volume 25, Issue 1, pp 37--72 http://dx.doi.org/10.22436/jmcs.025.01.05

Publication Date: May 04, 2021 Submission Date: March 14, 2021 Revision Date: April 02, 2021 Accteptance Date: April 07, 2021

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Authors

Sunisa Yuphaphin - Department of Mathematics, School of Science, University of Phayao, Mae Ka, Phayao 56000, Thailand. Pimwaree Kankaew - Department of Mathematics, School of Science, University of Phayao, Mae Ka, Phayao 56000, Thailand. Nattacha Lapo - Department of Mathematics, School of Science, University of Phayao, Mae Ka, Phayao 56000, Thailand. Ronnason Chinram - Algebra and Applications Research Unit, Division of Computational Science, Faculty of Science, Prince of Songkla University, Hat Yai, Songkhla 90110, Thailand. Aiyared Iampan - Department of Mathematics, School of Science, University of Phayao, Mae Ka, Phayao 56000, Thailand.

Abstract

The concept of picture fuzzy sets was first introduced by Cuong and Kreinovich [B. C. Cuong, V. Kreinovich, Proceedings of the Third World Congress on Information and Communication Technologies WIICT, (2013), 1--6] in 2013, which is direct extensions of the fuzzy sets and the intuitionistic fuzzy sets. In this paper, we applied the concept of picture fuzzy sets in UP-algebras to introduce the eight new concepts of picture fuzzy sets by means of a special type: special picture fuzzy UP-subalgebras, special picture fuzzy near UP-filters, special picture fuzzy UP-filters, special picture fuzzy implicative UP-filters, special picture fuzzy comparative UP-filters, special picture fuzzy shift UP-filters, special picture fuzzy UP-ideals, and special picture fuzzy strong UP-ideals. Also, we discuss the relationship between the eight new concepts of picture fuzzy sets in UP-algebras. This idea is extended to the lower and upper level subsets of picture fuzzy sets in UP-algebras. Moreover, we define a picture fuzzy set in the same way as a characteristic function and study its characterizations from the related subset.

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Keywords

• UP-algebra
• picture fuzzy set
• special picture fuzzy UP-subalgebra
• special picture fuzzy near UP-filter
• special picture fuzzy UP-filter
• special picture fuzzy implicative UP-filter
• special picture fuzzy shift UP-filter
• special picture fuzzy UP-ideal
• special picture fuzzy strong UP-ideal

MSC

•  06F35
•  08A72
•  03E72

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