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Invariant characterizations of fuzzy relation information systems under homomorphisms

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Abstract

A homomorphism is an important mathematical tool to study relationships between fuzzy relation information systems. This paper is devoted to investigating reduction in a fuzzy relation information system and its invariant characterizations under homomorphisms. Intersection-reduction, union-reduction, and reduction in a fuzzy relation information system are first proposed. Then, properties of intersection-reduction, union-reduction, and reduction are given. Next, fuzzy relations in a fuzzy relation information system are divided into necessary, relatively necessary, and unnecessary fuzzy relations according to the importance. Finally, some invariant and inverse invariant characterizations of fuzzy relation information systems under consistency and compatible homomorphisms are obtained, respectively. It is worth mentioning that by means of homomorphism, we can get the relatively smaller image system that has the same data structures (i.e., invariant characterizations) as a given original system.

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Acknowledgements

The authors would like to thank the editors and the anonymous reviewers for their valuable suggestions which have helped immensely in improving the quality of this paper. This work is supported by National Natural Science Foundation of China (11461005, 11261005, 11161029, 11461002), , Natural Science Foundation of Guangxi (2016GXNSFAA380045, 2016GXNSFAA380282, 2016GXNSFAA380286), Natural Science Foundation for Young Scholar of Guangxi (2013GXNSFBA019020), Guangxi Province Universities and Colleges Excellence Scholar and Innovation Team Funded Scheme, Key Discipline of Quantitative Economics in Guangxi University of Finance and Economics (2014YBKT07), Key Laboratory of Quantitative Economics in Department of Guangxi Education (2014SYS01) and Guangxi Key Laboratory Cultivation Base of Cross-border E-commerce Intelligent Information Processing.

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Authors and Affiliations

  1. School of Information and Statistics, Guangxi University of Finance and Economics, Nanning, 530003, Guangxi, People’s Republic of China

    Bin Qin, Fanping Zeng & Kesong Yan

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  1. Bin Qin
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  2. Fanping Zeng
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  3. Kesong Yan
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Correspondence to Bin Qin.

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Communicated by A. Di Nola.

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Qin, B., Zeng, F. & Yan, K. Invariant characterizations of fuzzy relation information systems under homomorphisms. Soft Comput 23, 5273–5288 (2019). https://doi.org/10.1007/s00500-018-3451-z

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