Some Inequalities for Generalized Choquet Integrals of Triangular Fuzzy Number-Valued Functions and Its Application

Recently, D. Zhang et al. introduced the generalized Choquet integral, extending pseudo-integrals and Choquet-like integrals while exploring their foundational properties. Building on this framework, we introduce the concept of generalized Choquet integrals for triangular fuzzy number (TFN)-valued functions, referred to as TGC-integrals. This work investigates the key properties of TGC-integrals, including monotone non-decreasing convergence theorems and inequalities such as the Fatou type, Jensen type, Minkowski type, and H\"older type inequalities, specifically tailored for TFN-valued functions. Furthermore, we provide illustrative examples that demonstrate practical applications of TGC-integrals, such as TFN-valued Choquet expected utility and pseudo-functional analysis. These results establish a robust theoretical foundation for analyzing TFN-valued functions and highlight their potential for addressing uncertainty and ambiguity in real-world problems.

Some Inequalities for Generalized Choquet Integrals of Triangular Fuzzy Number-Valued Functions and Its Application Keywords:

Generalized Choquet integral , Jensen type inequality , Triangular fuzzy number , Minkowski type inequality , Holder type inequality