Fuzzy set theory applied to IUP-algebras

Volume 34, Issue 2, pp 128--143 https://dx.doi.org/10.22436/jmcs.034.02.03

Publication Date: March 01, 2024 Submission Date: November 23, 2023 Revision Date: January 15, 2024 Accteptance Date: January 23, 2024

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Authors

K. Kuntama - Department of Mathematics, School of Science, University of Phayao, Mae Ka, Mueang, Phayao 56000, Thailand. P. Krongchai - Department of Mathematics, School of Science, University of Phayao, Mae Ka, Mueang, Phayao 56000, Thailand. P. Prasertpong - Division of Mathematics and Statistics, Faculty of Science and Technology, Nakhon Sawan Rajabhat University, Nakhon Sawan 60000, Thailand. P. Julatha - Department of Mathematics, Faculty of Science and Technology, Pibulsongkram Rajabhat University, Phitsanulok 65000, Thailand. A. Iampan - Department of Mathematics, School of Science, University of Phayao, Mae Ka, Mueang, Phayao 56000, Thailand.

Abstract

In this article, we apply fuzzy set theory to IUP-algebras, introducing four new concepts: fuzzy IUP-subalgebras, fuzzy IUP-filters, fuzzy IUP-ideals, and fuzzy strong IUP-ideals, and examining their properties and relationships. We also found a relationship between characteristic functions and the four concepts of fuzzy sets. In addition, the concepts of prime subsets and prime fuzzy sets were also applied. The notions of upper \(t\)-(strong) level subsets and lower \(t\)-(strong) level subsets of a fuzzy set are introduced in IUP-algebras.

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Keywords

• IUP-algebra
• fuzzy IUP-subalgebra
• fuzzy IUP-filter
• fuzzy IUP-ideal
• fuzzy strong IUP-ideal
• upper \(t\)-(strong) level subsets
• lower \(t\)-(strong) level subsets

MSC

•  03G25
•  03E72

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