Yan-Kuen Wu , Ching-Feng Wen , Zhaowen Li , Hsun-Chih Kuo
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引用次数: 0
Abstract
An efficient solution procedure for the preinverse (or postinverse) of a fuzzy matrix is useful for solving the well known problems of fuzzy abductive/backward reasoning. Wen, Wu and Li (2023) have presented algebraic formulas for various approximate preinverses of fuzzy matrices using the weighted norm. In this study, a novel approach is proposed to derive the best approximate preinverses of fuzzy matrices, in the sense that the weighted norm of residual error is minimized. The proposed approach requires only simple arithmetic operations, it is possible to perform real-time abductive reasoning in many reasoning systems such as intelligent diagnosis.
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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