Pythagorean fuzzy multigroups

Meryem Fakhraoui; Idris Bakhadach; M'hamed Elomari; Said Melliani

doi:10.5269/bspm.77219

Meryem Fakhraoui Sultan Moulay Slimane University https://orcid.org/0009-0003-0677-9780
Idris Bakhadach National School of Applied Sciences, Sultan Moulay Slimane University https://orcid.org/0000-0003-2328-6147
M'hamed Elomari Sultan Moulay Slimane University https://orcid.org/0000-0002-4256-1434
Said Melliani Faculty of Sciences and Technologies, Sultan Moulay Slimane University https://orcid.org/0000-0002-5150-1185

Abstract

This paper introduces Pythagorean fuzzy multigroups as an extension of intuitionistic fuzzy multigroups, addressing limitations in uncertainty representation. We establish the theoretical framework for these algebraic structures, deriving fundamental properties including closure under group operations and characterizing intersection and union behaviors. Key results include necessary and sufficient conditions for Pythagorean fuzzy multigroup properties and comprehensive analysis of their algebraic structure. The developed theory provides enhanced tools for decision-making under uncertainty with multiple membership degrees

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References

Atanassov, K. T., Intuitionistic fuzzy sets, VII ITKR’s Session, Sofia, (1983).

Atanassov, K. T., Intuitionistic fuzzy sets, Fuzzy Sets Syst. 20(1), 87–96, (1986).

Bakhadach, I., Fakhraoui, M., Achik, S., Melliani, S., Pythagorean fuzzy sublattices and ideals, J. Fuzzy Extens. Appl. 5(3), 365–373, (2024).

Ejegwa, P. A., Pythagorean fuzzy multiset and its application to course placements, Open J. Discrete Appl. Math. 3(1), 55–74, (2020).

Ejegwa, P. A., Mathematical techniques to transform intuitionistic fuzzy multisets to fuzzy sets, J. Inform. Comput. Sci. 10(2), 169–172, (2015).

Ejegwa, P. A., Some operations on intuitionistic fuzzy multisets, J. Fuzzy Math. 24(4), 761–768, (2016).

Miyamoto, S., Basic operations of fuzzy multisets, J. Japan Soc. Fuzzy Theory Syst. 8(4), 639–645, (1996).

Nazmul, S., Majumdar, P., Samanta, S. K., On multisets and multigroups, Ann. Fuzzy Math. Inform. 6(3), 643–656, (2013).

Rosenfeld, A., Fuzzy groups, J. Math. Anal. Appl. 35, 512–517, (1971).

Shinoj, T. K., John, S. J., Intuitionistic fuzzy multigroups, Ann. Pure Appl. Math. 9(1), 133–143, (2015).

Shinoj, T. K., John, S. J., Intuitionistic fuzzy multisets and its application in medical diagnosis, World Acad. Sci. Eng. Technol. 6(1), 1418–1421, (2012).

Shinoj, T. K., Baby, A., Sunil, J. J., On some algebraic structures of fuzzy multisets, Ann. Fuzzy Math. Inform. 9(1), 77–90, (2015).

Syropoulos, A., Mathematics of multisets, Springer-Verlag, Berlin Heidelberg, 347–358, (2001).

Talhaoui, A., Melliani, S., Bakhadach, I., Achik, S., Pythagorean fuzzy nil radical of Pythagorean fuzzy ideal, Bol. Soc. Paran. Mat. 42, (2024).

Yager, R. R., Pythagorean fuzzy subsets, in Proc. 2013 Joint IFSA World Congr. NAFIPS Annu. Meet., 57–61, (2013).

Yager, R. R., On the theory of bags, Int. J. Gen. Syst. 13, 23–37, (1986).

Yager, R. R., Pythagorean membership grades in multicriteria decision making, Tech. Rep. MII 3301, Mach. Intell. Inst., Iona Coll., New Rochelle, NY, (2013).

Zadeh, L. A., Fuzzy sets, Inform. Control 8, 338–353, (1965)