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Abstract: We are interested in representations and characterizations of latticepolynomial functions f:L^n -> L, where L is a given bounded distributivelattice. In companion papers arXiv 0901.4888, arXiv 0808.2619, weinvestigated certain representations and provided various characterizations ofthese functions both as solutions of certain functional equations and in termsof necessary and sufficient conditions. In the present paper, we investigatethese representations and characterizations in the special case when L is achain, i.e., a totally ordered lattice. More precisely, we discussrepresentations of lattice polynomial functions given in terms of standardsimplices and we present new axiomatizations of these functions by relaxingsome of the conditions given in arXiv 0901.4888, arXiv 0808.2619 and byconsidering further conditions, namely comonotonic minitivity and maxitivity.



Author: Miguel Couceiro, Jean-Luc Marichal

Source: https://arxiv.org/







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