New types of domination to characterize the preservation of T-subgroups under aggregation

Abstract

This study builds upon results concerning the preservation of fuzzy structures by aggregation operators. We analyze when an aggregation operator preserves the structure of T-subgroup in the last cases remaining unresolved in the characterization of such operators. In order to characterize these operators for different groups, relaxed forms of domination are introduced and their properties and interconnections are studied. We also include a thorough review of the features that an aggregation operator must fulfill to preserve T-subgroups of an arbitrary group.