Polynomial verification for safe codiagnosability of decentralized fuzzy discrete-event systems

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

Fuzzy Sets and Systems Pub Date : 2024-06-11 DOI:10.1016/j.fss.2024.109041

Fuchun Liu , Weihua Cao , Zbigniew Dziong

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引用次数: 0

Abstract

Since fuzzy discrete-event systems (FDESs) modeled by fuzzy automata were put forward, extensive research on FDESs has been successfully conducted from different perspectives. Recently, the safe codiagnosability of decentralized FDESs was introduced and an approach of constructing the safe codiagnoser to verify the safe codiagnosability was proposed. However, the complexity of constructing the safe codiagnoser of decentralized FDESs is exponential. In this paper, we present a polynomial verification. Firstly, the recognizer and the safe coverifier are constructed to recognize the prohibited strings in the illegal language and carry out safe diagnosis of decentralized FDESs, respectively. Then the necessary and sufficient condition for safe codiagnosability of decentralized FDESs is presented. In particular, an algorithm for verifying the safe codiagnosability of decentralized FDESs is proposed based on the safe coverifier. Notably, both complexities of constructing the safe coverifier and verifying the safe codiagnosability are polynomial in the numbers of fuzzy events and fuzzy states of FDESs. Finally, two examples are provided to illustrate the proposed algorithm and the derived results.

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分散模糊离散事件系统安全可诊断性的多项式验证

自从以模糊自动机为模型的模糊离散事件系统（FDES）被提出以来，人们已经从不同的角度成功地对 FDES 进行了广泛的研究。最近，有人提出了分散 FDES 的安全可编译性，并提出了一种构建安全编译器来验证安全可编译性的方法。然而，构建分散式 FDES 的安全编码诊断器的复杂度是指数级的。本文提出了一种多项式验证方法。首先，构建了识别器和安全覆盖器，分别用于识别非法语言中的禁止字符串和对分散式 FDES 进行安全诊断。然后，提出了分散式 FDES 安全可编码性的必要条件和充分条件。特别是，基于安全覆盖器，提出了验证分散式 FDES 安全可编译性的算法。值得注意的是，构建安全覆盖器和验证安全可编译性的复杂度都是 FDES 的模糊事件数和模糊状态数的多项式。最后，我们提供了两个例子来说明所提出的算法和推导结果。

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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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.