{"title":"分散模糊离散事件系统安全可诊断性的多项式验证","authors":"Fuchun Liu , Weihua Cao , Zbigniew Dziong","doi":"10.1016/j.fss.2024.109041","DOIUrl":null,"url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"490 ","pages":"Article 109041"},"PeriodicalIF":3.2000,"publicationDate":"2024-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Polynomial verification for safe codiagnosability of decentralized fuzzy discrete-event systems\",\"authors\":\"Fuchun Liu , Weihua Cao , Zbigniew Dziong\",\"doi\":\"10.1016/j.fss.2024.109041\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>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.</p></div>\",\"PeriodicalId\":55130,\"journal\":{\"name\":\"Fuzzy Sets and Systems\",\"volume\":\"490 \",\"pages\":\"Article 109041\"},\"PeriodicalIF\":3.2000,\"publicationDate\":\"2024-06-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Fuzzy Sets and Systems\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0165011424001878\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"COMPUTER SCIENCE, THEORY & METHODS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fuzzy Sets and Systems","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0165011424001878","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
Polynomial verification for safe codiagnosability of decentralized fuzzy discrete-event systems
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.
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.
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