Homomorphisms between fuzzy information systems revisited
Ping Zhu, Qiaoyan Wen
TL;DR
This paper revisits the concept of homomorphisms in fuzzy information systems, classifying consistent functions and enhancing the understanding of fuzzy relation mappings to improve theoretical foundations.
Contribution
It introduces a classification of consistent functions into predecessor- and successor-consistent types and refines existing characterizations of fuzzy relation mappings.
Findings
Classified consistent functions into two new categories.
Provided improved properties of fuzzy relation mappings.
Enhanced theoretical understanding of homomorphisms in fuzzy systems.
Abstract
Recently, Wang et al. discussed the properties of fuzzy information systems under homomorphisms in the paper [C. Wang, D. Chen, L. Zhu, Homomorphisms between fuzzy information systems, Applied Mathematics Letters 22 (2009) 1045-1050], where homomorphisms are based upon the concepts of consistent functions and fuzzy relation mappings. In this paper, we classify consistent functions as predecessor-consistent and successor-consistent, and then proceed to present more properties of consistent functions. In addition, we improve some characterizations of fuzzy relation mappings provided by Wang et al.
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Taxonomy
TopicsRough Sets and Fuzzy Logic · Advanced Algebra and Logic · Data Management and Algorithms