广义hukuhara次可微预逆区间值向量优化问题的最优性条件和对偶性结果

IF 3.2 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems Pub Date : 2025-04-15 DOI:10.1016/j.fss.2025.109416

Zai-Yun Peng , Jian-Yi Peng , Debdas Ghosh , Yong Zhao , Dan Li

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引用次数: 0

摘要

研究了一类涉及h -次可微函数的预倒向量区间优化问题，并导出了最优性条件和对偶性结果。首先给出了h -差分下预逆区间值函数的次梯度的定义；通过算例验证了本文所提出的亚梯度与已有的亚梯度的区别。其次，利用h-次微分，研究了预渐近VIOP的Karush-Kuhn-Tucker充要条件。然后，建立了具有预逆函数的VIOP的Mond-Weir和Wolfe对偶性结果。利用所提出的h -子微分，给出了弱对偶、强对偶和逆对偶定理。给出了一些例子来说明主要结果。主要结果在一定程度上概括了已有的相关结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Optimality conditions and duality results for generalized-Hukuhara subdifferentiable preinvex interval-valued vector optimization problems

This study investigates a class of preinvex vector interval optimization problems (VIOP) involving gH-subdifferentiable functions and derives both optimality conditions and duality results. At first, a definition of subgradient for preinvex interval-valued function under gH-difference is given; examples are provided to verify the difference between the subgradient in this paper and the existing ones. Next, by means of gH-subdifferential, the Karush-Kuhn-Tucker sufficient and necessary optimality conditions for preinvex VIOP are studied. Then, the Mond-Weir and Wolfe duality results for VIOP with preinvex functions are established. Weak duality, strong duality, and converse duality theorems are reported by using the proposed gH-subdifferential. Some examples are given to illustrate the main results. To some extent, the main results generalize the existing relevant results.

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来源期刊

Fuzzy Sets and Systems 数学-计算机：理论方法

CiteScore

6.50

自引率

17.90%

发文量

321

审稿时长

6.1 months

期刊介绍： Since its launching in 1978, the journal Fuzzy Sets and Systems has been devoted to the international advancement of the theory and application of fuzzy sets and systems. The theory of fuzzy sets now encompasses a well organized corpus of basic notions including (and not restricted to) aggregation operations, a generalized theory of relations, specific measures of information content, a calculus of fuzzy numbers. Fuzzy sets are also the cornerstone of a non-additive uncertainty theory, namely possibility theory, and of a versatile tool for both linguistic and numerical modeling: fuzzy rule-based systems. Numerous works now combine fuzzy concepts with other scientific disciplines as well as modern technologies. In mathematics fuzzy sets have triggered new research topics in connection with category theory, topology, algebra, analysis. Fuzzy sets are also part of a recent trend in the study of generalized measures and integrals, and are combined with statistical methods. Furthermore, fuzzy sets have strong logical underpinnings in the tradition of many-valued logics.