Choquet integrals of fuzzifying measurable functions and their applications

Abstract

This study introduces the Choquet integral of fuzzifying functions with respect to a fuzzy measure. To express various phenomena or ambiguous values in many applications may not be enough to show them as a function, in which case a fuzzifying function can be applied to achieve better expressions or flexibility for given function values. To apply Choquet integrals of fuzzifying functions, we consider Choquet integrals of interval-valued functions as an operator which are alpha-level functions of fuzzifying functions. In this study, we investigate some properties of Choquet integral of fuzzifying functions and present their applications. As part of this, a series of relevant examples and their subsequent applications are provided, along with the fuzzification of two integrands: A probability density function (PDF) and a utility function.