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 ([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.