Generator Implementations of Pythagorean Power 
Uncertainty Commutative Group Structures

M. Teresa Nirmala; D. Jayalakshmi; G. Subbiah

doi:https://doi.org/10.14445/22315373/IJMTT-V71I2P104

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 71 | Issue 2 | Year 2025 | Article Id. IJMTT-V71I2P104 | DOI : https://doi.org/10.14445/22315373/IJMTT-V71I2P104

Generator Implementations of Pythagorean Power Uncertainty Commutative Group Structures

M. Teresa Nirmala, D. Jayalakshmi, G. Subbiah

Received	Revised	Accepted	Published
22 Dec 2024	27 Jan 2025	13 Feb 2025	28 Feb 2025

Abstract

In this paper, we study the concept of Pythagorean uncertainty set (PUS) to introduce the concepts of Pythagorean power uncertainty abelian subgroups (PPUAS), Pythagorean power uncertainty normal subgroups (PPUNS) and its properties. Also, we study those concepts in terms of the Cartesian product of Pythagorean power uncertainty sets. Finally, homomorphic images and pre-images of Pythagorean uncertainty sets are established.

Keywords

Uncertainty set, Pythagorean uncertainty set, Power subgroup, Pythagorean power uncertainty set, Commutative group, Homomorphism, Pre-image, Support, Normal subgroup.

References

[1] Gezahagne Mulat Addis, “Fuzzy Homomorphism Theorems on Groups,” Korean Journal of Mathematics, vol. 26, no. 3, pp. 373 385, 2018.
[CrossRef] [Google Scholar] [Publisher Link]
[2] Krassimir T. Atanassov, “Intuitionistic Fuzzy Sets,” Fuzzy Sets and Systems, vol. 20, no. 1, pp. 87-96, 1986.
[CrossRef] [Google Scholar] [Publisher Link]
[3] Muhammad Akram, and Sumera Naz, “A Novel Decision-Making Approach under Complex Pythagorean Fuzz Environment,” Mathematical and Computational Applications, vol. 24, no. 3, pp. 1-33, 2019.
[CrossRef] [Google Scholar] [Publisher Link]
[4] Ranjit Biswas, “Intuitionistic Fuzzy Subgroup,” Mathematical Forum, vol. 10, pp. 39-44, 1989.
[Google Scholar] [Publisher Link]
[5] R. Biswas, “Fuzzy Subgroups and Anti-Fuzzy Subgroups,” Fuzzy Sets and Systems, vol. 35, no. 1, pp. 121-124, 1990.
[CrossRef] [Google Scholar] [Publisher Link]
[6] Paul Augustine Ejegwa, “Pythagorean Fuzzy Set and Its Applications in Career Placements Based on Academics Performance Using Max-Min-Max Composition,” Complex & Intelligent Systems, vol. 5, pp. 165-175, 2019.
[CrossRef] [Google Scholar] [Publisher Link]
[7] Sumera Naz, Samina Ashraf, and Muhammad Akram, “A Novel Approach to Decision-Making with Pythagorean Fuzzyinformation,” Mathematics, vol. 6, no. 6, pp. 1-33, 2018.
[CrossRef] [Google Scholar] [Publisher Link]
[8] B.O. Onasanya, “Review of Some Anti-Fuzzy Properties of Some Fuzzy Subgroups,” Annals of Fuzzy Mathematics and Informatics, vol. 11, no. 6, pp. 899-904, 2016.
[Google Scholar] [Publisher Link]
[9] Xindong Peng, and Yong Yang, “Some results for Pythagorean fuzzy Sets,” International Journal of Intelligent Systems, vol. 30, pp. 1133-1160, 2015.
[CrossRef] [Google Scholar] [Publisher Link]
[10] Xindong Peng, and Yong Yang, “Fundamental Properties of Interval-Valued Pythagorean Fuzzy Aggregation Operators,” International Journal of Intelligent Systems, vol. 31, pp. 444-487, 2016.
[CrossRef] [Google Scholar] [Publisher Link]
[11] Marek Z. Reformat, and Ronald R. Yager, “Suggesting Recommendations Using Pythagorean Fuzzy Sets Illustrated Using Netflix Movie Data,” Information Processing and Management of Uncertainty in Knowledge-Based Systems, pp. 546-556, 2014.
[CrossRef] [Google Scholar] [Publisher Link]
[12] Tapan Senapati, and Ronald R. Yager, “Fermatean Fuzzy Sets,” Journal of Ambient Intelligence and Humanized Computing, vol. 11, no. 2, pp. 663-674, 2020.
[CrossRef] [Google Scholar] [Publisher Link]
[13] Tapan Senapati, and Ronald R. Yager, “Fermatean Fuzzy Weighted Averaging/Geometric Operators and Its Application in Multi Criteria Decision-Making Methods,” Engineering Applications of Artificial Intelligence, vol. 85, pp. 112-121, 2019.
[CrossRef] [Google Scholar] [Publisher Link]
[14] Umer Shuaib, Muhammad Shaheryar, and Waseem Asghar, “On Some Characterizations of O-Fuzzy Subgroups,” International Journal of Mathematics and Computer Science, vol. 13, no.2, pp. 119-131, 2018.
[Google Scholar] [Publisher Link]
[15] Umer Shuaib, and Muhammad Shaheryar, “On Some Properties of O-Anti Fuzzy Subgroups,” International Journal of Mathematics and Computer Science, vol. 14, no. 1, pp. 215-230, 2019.
[Google Scholar] [Publisher Link]
[16] Marius Tarnauceanu, “Classifying Fuzzy Normal Subgroups \ of Finite Groups,” Iranian Journal of Fuzzy Systems, vol. 12, no. 2, pp. 107-115, 2019.
[CrossRef] [Google Scholar] [Publisher Link]
[17] Ronald R. Yager, “Properties and Application of Pythagorean Fuzzy Sets,” Imprecision and Uncertainty in Information Representation and Processing, vol. 332, pp. 119-136, 2016.
[CrossRef] [Google Scholar] [Publisher Link]
[18] Ronald R. Yager, and Ali M. Abbasov, “Pythagorean Membership Grades, Complex Numbers and Decision Making,” International Journal of Intelligent System, vol. 28, pp. 436-452, 2013.
[CrossRef] [Google Scholar] [Publisher Link]
[19] Ronald R. Yager, “Pythagorean Fuzzy Subsets,” 2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS), Edmonton, AB, Canada, pp. 57-61, 2013.
[CrossRef] [Google Scholar] [Publisher Link]
[20] J. Zhan, and Z. Tan, Intuitionistic M-Fuzzy Groups, Soochow Journal of Mathematics, vol. 30, pp. 85-90, 2004.
[Google Scholar]
[21] L.A. Zadeh, “Fuzzy Sets,” Information and Control, vol. 8, no. 3, pp. 338-353, 1965.
[CrossRef] [Google Scholar] [Publisher Link]

Citation :

M. Teresa Nirmala, D. Jayalakshmi, G. Subbiah, "Generator Implementations of Pythagorean Power Uncertainty Commutative Group Structures," International Journal of Mathematics Trends and Technology (IJMTT), vol. 71, no. 2, pp. 30-36, 2025. Crossref, https://doi.org/10.14445/22315373/IJMTT-V71I2P104