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

Kim, Dojin; Kim, Hyeonseo; Jang, Lee-Chae

doi:10.22111/ijfs.2024.48347.8504

Document Type : Research Paper

Authors

¹ Department of Mathematics, 308-114, Science Building, Donguk University,

² Department of Mathematics, 308-114, Science Building, Dongguk University

³ Graduate School of Education, Konkuk University,

https://doi.org/10.22111/ijfs.2024.48347.8504

Abstract

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.

Keywords

Main Subjects

Fuzzy Math

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

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Volume 21, Issue 6November and December 2024Pages 83-99

Volume 21, Issue 6
November and December 2024
Pages 83-99