Generalized comonotonicity and new axiomatizations of Sugeno integrals on bounded distributive lattices

Abstract

Two new generalizations of the relation of comonotonicity of lattice-valued vectors are introduced and discussed. These new relations coincide on distributive lattices and they share several properties with the comonotonicity for the real-valued vectors (which need not hold for L-valued vectors comonotonicity, in general). Based on these newly introduced generalized types of comonotonicity of L-valued vectors, several new axiomatizations of L-valued Sugeno integrals are introduced. One of them brings a substantial decrease of computational complexity when checking an aggregation function to be a Sugeno integral.

Generalizing expected values to the case of L*-fuzzy events

“…Due to the axiomatic characterization of the Sugeno integral on bounded distributive lattices in Couceiro and Marichal (2010a), Couceiro and Marichal (2010b) and Halaš, Mesiar, and Pócs (2017), we obtain the following characterization of a class of L * -expected values on a finite universe X which are comonotone maxitive and comonotone minitive (see ( 26) and ( 27) below).…”

On $\star$-associated comonotone functions

“…Nowadays, comonotonicity is an important property in analysis, uncertainty theory, economics, financial mathematics, actuarian science, etc. There are some generalizations of comonotonicity in the available literature related to different contexts, see for instance [10] for several multivariate extensions of comonotonicity, or [5,6] for a connection with a characterization of Sugeno integral on bounded distributive lattices. Recently, in [1, Definition 2.1] the following relation between two functions, having a significant role in the theory of generalized Sugeno integrals, was introduced.…”