On generating sets of the clone of aggregation functions on finite lattices. (English) Zbl 1446.06010

Summary: In a recent paper [the first and the third author, Inf. Sci. 329, 381–389 (2016; Zbl 1390.06006)] we have shown that aggregation functions on a bounded lattice \(L\) form a clone, i.e., the set of functions closed under projections and composition of functions. Moreover, for any finite lattice \(L\) we gave a finite set of unary and binary aggregation functions on \(L\) from which the aggregation clone is generated. In this paper, a general method for constructing generating sets of the aggregation clone on \(L\) is presented. Our approach is based on extending of \(L\)-valued capacities leading to so-called full systems of aggregation functions. Several full systems on \(L\) are presented (including singleton ones) and their arities are discussed.


06B05 Structure theory of lattices
06A15 Galois correspondences, closure operators (in relation to ordered sets)
08A40 Operations and polynomials in algebraic structures, primal algebras


Zbl 1390.06006
Full Text: DOI


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