On generating of idempotent aggregation functions on finite lattices

Abstract

In a recent paper we proposed the study of aggregation functions on lattices via clone theory approach. Observing that aggregation functions on lattices just correspond to $0,1$-monotone clones, we have shown that all aggregation functions on a finite lattice $L$ can be obtained as usual composition of lattice operations $\wedge ,\vee$, and certain unary and binary aggregation functions. The aim of this paper is to present a generating set for the class of intermediate (or, equivalently, idempotent) aggregation functions. This set consists of lattice operations and certain ternary idempotent aggregation functions.

arXiv comment18 pages

References in corpus (5)

• A new characterization of the discrete Sugeno integral
• On the clone of aggregation functions on bounded lattices
• Congruences and the discrete Sugeno integrals on bounded distributive lattices
• On lattices with a smallest set of aggregation functions
• Generators of aggregation functions and fuzzy connectives