{"title":"Construction of interpretable hierarchical fuzzy systems subject to incomplete data","authors":"Changle Sun , Haitao Li , Jun-e Feng","doi":"10.1016/j.fss.2025.109273","DOIUrl":null,"url":null,"abstract":"<div><div>Hierarchical fuzzy systems (HFSs) are a significant branch of fuzzy systems. In this paper, the algebraic formulation of interpretable HFSs is investigated, and two algorithms are developed for the construction of interpretable HFSs subject to incomplete data. Firstly, the interpretable fuzzy logic unit (FLU) is presented and its algebraic formulation is developed by using the semi-tensor product of matrices. Secondly, by substituting the interpretable FLUs into the hierarchical structure, the interpretable HFSs are obtained. Thirdly, based on the proximal policy optimization, both direct and indirect algorithms are established to construct the interpretable HFSs subject to incomplete input-output data. Finally, the effectiveness of obtained results is verified by the on-ramp metering of freeway.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"505 ","pages":"Article 109273"},"PeriodicalIF":3.2000,"publicationDate":"2025-01-09","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/S0165011425000120","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}
引用次数: 0
Abstract
Hierarchical fuzzy systems (HFSs) are a significant branch of fuzzy systems. In this paper, the algebraic formulation of interpretable HFSs is investigated, and two algorithms are developed for the construction of interpretable HFSs subject to incomplete data. Firstly, the interpretable fuzzy logic unit (FLU) is presented and its algebraic formulation is developed by using the semi-tensor product of matrices. Secondly, by substituting the interpretable FLUs into the hierarchical structure, the interpretable HFSs are obtained. Thirdly, based on the proximal policy optimization, both direct and indirect algorithms are established to construct the interpretable HFSs subject to incomplete input-output data. Finally, the effectiveness of obtained results is verified by the on-ramp metering of freeway.
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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