首页|PYTHAGOREAN FUZZY SETS: A NEW PERSPECTIVE ON IUP-ALGEBRAS

PYTHAGOREAN FUZZY SETS: A NEW PERSPECTIVE ON IUP-ALGEBRAS

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Zadeh introduced the concept of fuzzy sets in 1965. In 1986, Atanassov introduced intuitionistic fuzzy sets, a generalization of fuzzy sets. Pythagorean fuzzy sets are a recent extension of intuitionistic fuzzy sets introduced by Yager. The aim of this study is to apply the concept of Pythagorean fuzzy sets to IUP-algebras and introduce the notions of Pythagorean fuzzy IUP-subalgebras, Pythagorean fuzzy IUP-ideals, Pythagorean fuzzy IUP-filters, and Pythagorean fuzzy strong IUP-ideals. The study identified a relationship between four concepts, showing that Pythagorean fuzzy IUP-ideals and Pythagorean fuzzy IUP-subalgebras are generalizations of Pythagorean fuzzy strong IUP-ideals in IUP-algebras, where the latter can only be a constant Pythagorean fuzzy set. Additionally, Pythagorean fuzzy IUP-filters were found to be a further generalization of Pythagorean fuzzy IUP-ideals and IUP-subalgebras. Their properties are investigated, and the characteristic Pythagorean fuzzy sets, the upper t- (strong) level subsets, and the lower t-(strong) level subsets of the Pythagorean fuzzy set are studied.

IUP-algebraPythagorean fuzzy setPythagorean fuzzy IUP-subalgebraPythagorean fuzzy IUP-idealPythagorean fuzzy IUP-filterPythagorean fuzzy strong IUP-idealUpper t-(strong) level subsetLower t-(strong) level subset

KANNIRUN SUAYNGAM、RUKCHART PRASERTPONG、WARUD NAKKHASEN、PONGPUN JULATHA、ALYARED IAMPAN

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Department of Mathematics School of Science University of Phayao 19 Moo 2, Tambon Mae Ka, Amphur Mueang, Phayao 56000, Thailand

Division of Mathematics and Statistics Faculty of Science and Technology Nakhon Sawan Rajabhat University 398 Moo 9, Tambon Nakhon Sawan Tok, Amphur Mueang, Nakhon Sawan 60000, Thailand

Department of Mathematics Faculty of Science Mahasarakham University 41/20 Tambon Khamriang, Amphur Kantarawichai, Maha Sarakham 44150, Thailand

Department of Mathematics Faculty of Science and Technology Pibulsongkram Rajabhat University 156 Moo 5, Tambon Phlai Chumphon, Amphur Mueang, Phitsanulok 65000, Thailand

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2025

10.24507/ijicic.21.02.339

International journal of innovative computing, information and control

International journal of innovative computing, information and control

ISSN：1349-4198
年,卷(期)：2025.21(2)
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