Calculus and study of fuzzy dynamic equations for fuzzy vector functions on time scales

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

Fuzzy Sets and Systems Pub Date : 2025-02-12 DOI:10.1016/j.fss.2025.109307

M. Shahidi , T. Allahviranloo , M. Arana-Jiménez

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引用次数: 0

Abstract

In this paper, we introduce the

Δ_{g H}

-derivative as a novel concept for characterizing the differentiability of fuzzy vector functions on time scales. Building on this, we define two distinct types of

Δ_{g H}

-differentiability: (i)-

Δ_{g H}

-differentiability and

(i i)

Δ_{g H}

-differentiability, and study some of their properties. Within this framework, we investigate fuzzy dynamic equations for fuzzy vector functions on time scales and establish an existence theorem for these equations. Moreover, we examine first-order linear fuzzy dynamic equations and provide general expressions for their solutions. In the end, we present several examples to demonstrate our 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.