Aggregating Fuzzy Subgroups and T-vague Groups

Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 581)

Abstract

Fuzzy subgroups and T-vague groups are interesting fuzzy algebraic structures that have been widely studied. While fuzzy subgroups fuzzify the concept of crisp subgroup, T-vague groups can be identified with quotient groups of a group by a normal fuzzy subgroup and there is a close relation between both structures and T-indistinguishability operators (fuzzy equivalence relations).

In this paper the functions that aggregate fuzzy subgroups and T-vague groups will be studied. The functions aggregating T-indistinguishability operators have been characterized [9] and the main result of this paper is that the functions aggregating T-indistinguishability operators coincide with the ones that aggregate fuzzy subgroups and T-vague groups. In particular, quasi-arithmetic means and some OWA operators aggregate them if the t-norm is continuous Archimedean.

References

1. 1.
Chon, I.: On T-fuzzy groups. Kangweon-Kyungki Math. J. 9, 149–156 (2001)Google Scholar
2. 2.
Demirci, M.: Vague groups. J. Math. Anal. Appl. 230, 142–156 (1999)
3. 3.
Demirci, M., Recasens, J.: Fuzzy groups, fuzzy functions and fuzzy equivalence relations. Fuzzy Sets and Syst. 144, 441–458 (2004)
4. 4.
Gottwald, S.: Fuzzy Sets, Fuzzy Logic: The Foundations of Application from a Mathematical Point of View. Springer, Heidelberg (1993). Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Wiesbaden
5. 5.
Hájek, P.: Metamathematics of Fuzzy Logic. Kluwer Academic Publishers, New York (1998)
6. 6.
Jacas, J., Recasens, J.: Aggregation of T-transitive relations. Int. J. Intell. Syst. 18, 1193–1214 (2003)
7. 7.
Klement, E.P., Mesiar, R., Pap, E.: Triangular Norms. Kluwer, Dordrecht (2000)
8. 8.
Mashour, A.S., Ghanim, M.H., Sidky, F.I.: Normal fuzzy subgroups. Univ. u Novom Sadu Zb. Rad. Prirod.-Mat. Fak. Ser. Mat 20(2), 53–59 (1990)Google Scholar
9. 9.
Mayor, G., Recasens, J.: Preserving T-transitivity. In: CCIA 2016, Barcelona, pp. 79–87 (2016)Google Scholar
10. 10.
Mesiar, R., Novak, V.: Operations fitting triangular-norm-based biresiduation. Fuzzy Sets Syst. 104, 77–84 (1999)
11. 11.
Mordeson, J., Bhutani, K., Rosenfeld, A.: Fuzzy Group Theory. Studies in Fuzziness and Soft Computing, vol. 182. Springer, Heidelberg (2005)
12. 12.
Pradera, A., Trillas, E., Castiñeira, E.: On the aggregation of some classes of fuzzy relations. In: Bouchon-Meunier, B., Gutiérrez, J., Magdalena, L., Yager, R. (eds.) Technologies for Constructing Intelligent Systems, pp. 125–147. Springer, Heidelberg (2002)
13. 13.
Pradera, A., Trillas, E.: A note on pseudometrics aggregation. Int. J. Gen. Syst. 41–51 (2002)Google Scholar
14. 14.
Recasens, J.: Indistinguishability Operators. Modelling Fuzzy Equalities and Fuzzy Equivalence Relations. Studies in Fuzziness and Soft Computing, vol. 260. Springer, Heidelberg (2010)
15. 15.
Recasens, J.: Permutable indistinguishability operators, perfect vague groups and fuzzy subgroups. Inf. Sci. 196, 129–142 (2012)
16. 16.
Rosenfeld, A.: Fuzzy groups. J. Math. Anal. Appl. 35, 512–517 (1971)
17. 17.
Schweizer, B., Sklar, A.: Probabilistic Metric Spaces. North-Holland, Amsterdam (1983)
18. 18.
Zadeh, L.A.: Similarity relations and fuzzy orderings Information. Science 3, 177–200 (1971)