Aggregating Fuzzy Subgroups and T-vague Groups
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  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.
- 1.Chon, I.: On T-fuzzy groups. Kangweon-Kyungki Math. J. 9, 149–156 (2001)Google Scholar
- 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.Mayor, G., Recasens, J.: Preserving T-transitivity. In: CCIA 2016, Barcelona, pp. 79–87 (2016)Google Scholar
- 13.Pradera, A., Trillas, E.: A note on pseudometrics aggregation. Int. J. Gen. Syst. 41–51 (2002)Google Scholar