Choquet Integrals of fuzzifying measurable functions and their applications

This study introduces the Choquet integral of fuzzifying functions with respect to a fuzzymeasure. To express various phenomena or ambiguous values in many applications may notbe enough to show them as a function, in which case a fuzzifying function can be applied toachieve better expressions or flexibility for given function values. To apply Choquet integralsof fuzzifying functions, we consider Choquet integrals of interval-valued functions as anoperator which are α-level functions of fuzzifying functions. In this study, we investigatesome 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 autility function.