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Some Inequalities for Generalized Choquet Integrals of Triangular Fuzzy Number-Valued Functions and Its Application | ||
Iranian Journal of Fuzzy Systems | ||
دوره 21، شماره 6، بهمن و اسفند 2024، صفحه 83-99 اصل مقاله (484.99 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22111/ijfs.2024.48347.8504 | ||
نویسندگان | ||
Dojin Kim* 1؛ Hyeonseo Kim2؛ Lee-Chae Jang3 | ||
1Department of Mathematics, 308-114, Science Building, Donguk University, | ||
2Department of Mathematics, 308-114, Science Building, Dongguk University | ||
3Graduate School of Education, Konkuk University, | ||
چکیده | ||
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. | ||
کلیدواژهها | ||
Generalized Choquet integral؛ Jensen type inequality؛ Triangular fuzzy number؛ Minkowski type inequality؛ Holder type inequality | ||
مراجع | ||
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