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

TL;DR

This paper introduces two new generalized notions of comonotonicity for lattice-valued vectors, leading to novel axiomatizations of Sugeno integrals that reduce computational complexity in verification.

Contribution

It proposes new generalized comonotonicity relations on bounded distributive lattices and develops simplified axiomatizations of Sugeno integrals based on these relations.

Findings

New generalized comonotonicity relations coincide on distributive lattices.

Axiomatizations of Sugeno integrals are established using these relations.

Computational complexity for verifying Sugeno integrals is significantly reduced.

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.