On Aggregations of Algebraic Objects in Data Modeling

Abstract

Aggregation operators are mathematical tools that, under certain constraints in the form of properties imposed on those mathematical functions, provide a representative value for the whole set of input values or structures. The question of when and what properties of input structures, with particular emphasis on fuzzy groups, and in particular (Formula presented.) -groups, are preserved during the aggregation process is the main focus of this paper. This paper proposes a new technique for the aggregation of special fuzzy groups in a lattice-valued framework based on the aggregation of lattice-valued weak equivalence relations. Necessary and sufficient conditions for aggregation operators on complete lattices to aggregate (Formula presented.) -groups is the main result.