Asymmetrie general choquet integrals

Abstract

A notion of a generated chain variation of a set function m with values in [- 1, 1] is proposed. The space BgV of set functions of bounded g-chain variation is introduced and properties of set functions from BgV are discussed. A general Choquet integral of bounded A-measurable function is defined with respect to a set function m ∈ BgV. A constructive method for obtaining this asymmetric integral is considered. A general fuzzy integral of bounded g-variation, comonotone ⊕-additiviteand positive ⊙-homogenous is represented by a general Choquet integral. The representation of a general Choquet integral in terms of a pseudo Lebesque-Stiltjes integral is obtained.