Bipolar Fuzzy Sets in IUP-Algebras: Concepts and Analysis
Chalothon Inthachot
1
(
Department of Mathematics, School of Science, University of Phayao, 19 Moo 2, Tambon Mae Ka, Amphur Mueang, Phayao 56000, Thailand.
)
Kodchawan Moonnon
2
(
Department of Mathematics, School of Science, University of Phayao, 19 Moo 2, Tambon Mae Ka, Amphur Mueang, Phayao 56000, Thailand.
)
Mongkon Visutho
3
(
Department of Mathematics, School of Science, University of Phayao, 19 Moo 2, Tambon Mae Ka, Amphur Mueang, Phayao 56000, Thailand.
)
Pongpun Julatha
4
(
Department of Mathematics, Faculty of Science and Technology, Pibulsongkram Rajabhat University, 156 Moo 5, Tambon Phlai Chumphon, Amphur Mueang, Phitsanulok 65000, Thailand.
)
Aiyared Iampan
5
(
Department of Mathematics, School of Science, University of Phayao, 19 Moo 2, Tambon Mae Ka, Amphur Mueang, Phayao 56000, Thailand.
)
کلید واژه: IUP-algebra, Bipolar fuzzy set, Bipolar fuzzy IUP-subalgebra, Bipolar fuzzy IUP-ideal, Bipolar fuzzy IUP-filter, Bipolar fuzzy strong IUP-ideal, Negative lower ⊔ −-cut, Positive upper ⊔ +-cut, (⊔ −, ⊔ +)- cut.,
چکیده مقاله :
This paper advances the theory of bipolar fuzzy sets by integrating them into the structure of IUPalgebras. It introduces and formalizes the concepts of bipolar fuzzy IUP-subalgebras, filters, ideals, and strong ideals, establishing their foundational properties through rigorous theorems and counterexamples. The interplay between these algebraic structures and their level cuts is examined to provide a nuanced understanding of dual-valued uncertainty in abstract logic. In addition to its theoretical contributions, this research holds significant educational value, particularly for science-oriented learning environments where mathematical abstraction and logical reasoning are cultivated. By translating complex fuzzy-algebraic concepts into structured and illustrative forms, the study offers a meaningful framework that can inspire student-led investigations and enrich curricula in research-focused schools. Furthermore, it encourages collaboration between educators and researchers in developing accessible tools and learning modules that bridge advanced mathematical logic with real-world inquiry, promoting a more inclusive and research-driven academic atmosphere.
چکیده انگلیسی :
This paper advances the theory of bipolar fuzzy sets by integrating them into the structure of IUPalgebras. It introduces and formalizes the concepts of bipolar fuzzy IUP-subalgebras, filters, ideals, and strong ideals, establishing their foundational properties through rigorous theorems and counterexamples. The interplay between these algebraic structures and their level cuts is examined to provide a nuanced understanding of dual-valued uncertainty in abstract logic. In addition to its theoretical contributions, this research holds significant educational value, particularly for science-oriented learning environments where mathematical abstraction and logical reasoning are cultivated. By translating complex fuzzy-algebraic concepts into structured and illustrative forms, the study offers a meaningful framework that can inspire student-led investigations and enrich curricula in research-focused schools. Furthermore, it encourages collaboration between educators and researchers in developing accessible tools and learning modules that bridge advanced mathematical logic with real-world inquiry, promoting a more inclusive and research-driven academic atmosphere.
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