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arXiv · 1812.09529

On generating of idempotent aggregation functions on finite lattices

Michal Botur·Radomír Halaš·Radko Mesiar·Jozef Pócs
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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.

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Michal Botur, Radomír Halaš, Radko Mesiar, Jozef Pócs. 2018-12-22. On generating of idempotent aggregation functions on finite lattices. https://doi.org/10.1016/j.ins.2017.11.031

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