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.
)
الکلمات المفتاحية: 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.,
ملخص المقالة :
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.
[1] Zadeh LA. Fuzzy sets. Information and Control. 1965; 8(3): 338-353. DOI: https://doi.org/10.1016/S0019-9958(65)90241-X
[2] Zhang WR. Bipolar fuzzy sets and relations: A computational framework for cognitive modeling and multiagent decision analysis. In: NAFIPS/IFIS/NASA’94. Proceedings of the First International Joint Conference of the North American Fuzzy Information Processing Society Biannual Conference. The Industrial Fuzzy Control and Intellige. IEEE; 1994. p.305-309. DOI: https://doi.org/10.1109/IJCF.1994.375115
[3] Abughazalah N, Muhiuddin G, Elnair MEA, Mahboob A. Bipolar fuzzy set theory applied to the certain ideals in BCI-algebras. Symmetry. 2022; 14(4): 815. DOI: https://doi.org/10.3390/sym14040815
[4] Alolaiyan H, Mateen MH, Pamucar D, Mahmmod MK, Arslan F. A certain structure of bipolar fuzzy subrings. Symmetry. 2021; 13(8): 1397. DOI: https://doi.org/10.3390/sym13081397
[5] Gaketem T, Khamrot P, Julatha P, Iampan A. Bipolar fuzzy comparative UP-filters. IAENG International Journal of Applied Mathematics. 2022; 52(3): 704-709.
[6] Jun YB, Song SZ. Subalgebras and closed ideals of BCH-algebras based on bipolar-valued fuzzy sets. Scientiae Mathematicae Japonicae. 2008; 68(2): 287-297.
[7] Jun YB, Park CH. Filters of BCH-algebras based on bipolar-valued fuzzy sets. International Mathematical Forum. 2009; 4(13): 631-643.
[8] Mahmood T, Munir M. On bipolar fuzzy subgroups. World Applied Sciences Journal. 2013; 27(12): 1806-1811. DOI: https://doi.org/10.5829/idosi.wasj.2013.27.12.1686
[9] Malik N, Shabir M, Al-shami TM, Gul R, Arar M, Hosny M. Rough bipolar fuzzy ideals in semigroups. Complex & Intelligent Systems. 2023; 9: 7197-7212. DOI: https://doi.org/10.1007/s40747-023-01132-1
[10] Muhiuddin G, Al-Kadi D, Mahboob A, Shum KP. New types of bipolar fuzzy ideals of BCK-algebras. International Journal of Analysis and Applications. 2020; 18(5): 859-875. DOI: https://doi.org/10.28924/2291-8639-18-2020-859
[11] Yaqoob N, Aslam M, Rehman I, Khalaf MM. New types of bipolar fuzzy sets in Γsemihypergroups. Songklanakarin Journal of Science and Technology. 2016; 38(2): 119-127. DOI: https://doi.org/10.14456/sjst-psu.2016.16
[12] Al-Kadi D, Muhiuddin G. Bipolar fuzzy BCI-implicative ideals of BCI-algebras. Annals of Communications in Mathematics. 2020; 3(1): 88-96. DOI: https://doi.org/10.62072/acm.2020.030109
[13] Iampan A, Julatha P, Khamrot P, Romano DA. Independent UP-algebras. Journal of Mathematics and Computer Science. 2022; 27(1): 65-76. DOI: https://doi.org/10.22436/jmcs.027.01.06
[14] Chanmanee C, Prasertpong R, Julatha P, Lekkoksung N, Iampan A. On external direct products of IUP-algebras. International Journal of Innovative Computing, Information and Control. 2023; 19(3): 775-787. DOI: https://doi.org/10.24507/ijicic.19.03.775
[15] Kuntama K, Krongchai P, Prasertpong R, Julatha P, Iampan A. Fuzzy set theory applied to IUP-algebras. Journal of Mathematics and Computer Science. 2024; 34(2): 128-143. DOI: https://doi.org/10.22436/jmcs.034.02.03
[16] Suayngam K, Suwanklang T, Julatha P, Prasertpong R, Iampan A. New results on intuitionistic fuzzy sets in IUP-algebras. International Journal of Innovative Computing, Information and Control. 2024; 20(4): 1125-1141. DOI: https://doi.org/10.24507/ijicic.20.04.1125
[17] Suayngam K, Prasertpong R, Lekkoksung N, Julatha P, Iampan A. Fermatean fuzzy set theory applied to IUP-algebras. European Journal of Pure and Applied Mathematics. 2024; 17(4): 3022-3042. DOI: https://doi.org/10.29020/nybg.ejpam.v17i4.5367
[18] Suayngam K, Julatha P, Prasertpong R, Iampan A. Neutrosophic sets in IUP-algebras: A new exploration. International Journal of Neutrosophic Science. 2025; 25(3): 540-560. DOI: https://doi.org/10.54216/IJNS.250343
[19] Suayngam K, Prasertpong R, Nakkhasen W, Julatha P, Iampan A. Pythagorean fuzzy sets: A new perspective on IUP-algebras. International Journal of Innovative Computing, Information and Control. 2025; 21(2): 339-357. DOI: https://doi.org/10.24507/ijicic.21.02.339
[20] Suayngam K, Julatha P, Nakkhasen W, Iampan A. Structural insights into IUP-algebras via intuitionistic neutrosophic set theory. European Journal of Pure and Applied Mathematics. 2025; 18(2): 5857. DOI: https://doi.org/10.29020/nybg.ejpam.v18i2.5857
