On Aggregations of Algebraic Objects in Data Modeling

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 Ω-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 Ω-groups is the main result.