Congruence relation in fuzzy partial hyperalgebras

Document Type : Research Paper

Authors

1 Department of mathematics. Faculty of sciences. Golestan university. Gorgan. Iran

2 Department of Mathematics, Faculty of Sciences, Golestan University, Gorgan, Iran

3 School of Mathematics, Statistics and Computer Science, College of Sciences, University of Tehran, Tehran, Iran

Abstract

In this paper, we begin by introducing the concept of fuzzy partial hyperalgebra and exploring the relationships between congruence relations and strong congruence relations within this framework. We then construct an embedding of any fuzzy partial hyperalgebra into a fuzzy hyperalgebra, ensuring that all congruence relations on the embedded fuzzy partial
hyperalgebra can be simultaneously extended to the corresponding fuzzy hyperalgebra.

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Main Subjects

References

[1] M. Al-Tahan and B. Davvaz, N-ary hyperstructures associated to the genotypes of F2-offspring, International Journal of Biomathematics, 10 (2017), 1750118.
[2] R. Ameri and I.G. Rosenberg, Congruences of multialgebras, Journal of Multiple-Valued Logic and Soft Computing, 15 (2009), 525–536. 
[3] R. Ameri and M.M. Zahedi, Hyperalgebraic systems, Italian Journal of Pure and Applied Mathematics, 6 (1999), 21–32.
[4] R. Ameri and T. Nozari, Fuzzy hyperalgebras, Computers and Mathematics with Applications, 61 (2011), 149–154.
[5] P. Corsini and V. Leoreanu, Application of hyperstructure theory, Springer, 2003.
[6] P. Corsini and I. Tofan, On fuzzy hypergroups, PU.M.A, 8 (1997), 29–37.
[7] B. Davvaz and I. Cristea, Fuzzy Algebraic Hyperstructures, Studies in Fuzziness and Soft Computing, 321 (2015), 38–46.
[8] G. Gr¨atzer and G.H. Wenzel, On the concept of congruence relation in partial algebras, Mathematica Scandinavica, 20 (1967), 275–280.
[9] V. Leorenu-Fotea and B. Davvaz, Fuzzy hyperrings, Fuzzy Sets and Systems, 160 (2008), 2366–2378. 
[10] V. Leorenu-Fotea, Fuzzy hypermodules, Computers and Mathematics with Applications, 57 (2009), 466–475.
[11] C. G. Massouros and G. G. Massouros, An overview of the foundations of the hypergroup theory, Mathematics, 9 (2021), 1014.
[12] F. Marty, Sur une generalization de la notion de groupe, in: 8th Congress Math. Scandinaves, Stockholm (1934), 45–49.
[13] M. Nov´ak, n-ary hyperstructures constructed from binary quasi-ordered semigroups, Analele Universitatii Ovidius Constanta - Seria Matematica, 22 (2022), 147–168.
[14] D. Schweigert, Congruence relations of multialgebras, Discrete Mathematics, 53 (1985), 249–253.
[15] M.K. Sen, R. Ameri and G. Chowdhury, Fuzzy hypersemigroups, Soft Comput, 12 (2008), 891–900.
[16] A. Sonea and I. Cristea, Euler’s totient function applied to complete hypergroups, AIMS Mathematics, 8 (2023), 7731–7746.
[17] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338–353
Journal of Hyperstructures
Volume 14, Issue 1
2025
Pages 16-24

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