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Fuzzy Granular Structures of Fuzzy Relation Vectors

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Abstract

Fuzzy granular structure is a mathematical structure to deal with fuzzy information granules. This paper studies fuzzy granular structure of a fuzzy relation vector and its uncertainty measurement. In the first place, fuzzy granular structure of a fuzzy relation vector is defined by using fuzzy set matrices. In the next place, dependence between fuzzy granular structures and some operators on the fuzzy granular structures base are investigated. After that, algebraic and lattice features of fuzzy granular structures are obtained. Lastly, as an application of fuzzy granular structures, uncertainty measurement for fuzzy relation vectors is discussed and effectiveness analysis of the proposed measures is conducted. These results will be helpful for providing the framework for granular computing of fuzzy relation vectors.

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Acknowledgements

The authors would like to thank the editors and the anonymous reviewers for their valuable comments and suggestions, which have helped immensely in improving the quality of the paper. This work is supported by National Natural Science Foundation of China (11971420), Natural Science Foundation of Guangxi (AD19245102, 2020GXNSFAA159155, 2018GXNSFDA294003), Key Laboratory of Software Engineering in Guangxi University for Nationalities (2021-18XJSY-03), Education Reform Project of Yulin Normal University (2020XJJGZD17), Special Scientific Research Project of Young Innovative Talents in Guangxi (2019AC20052), and Research projects of young and Middle-Aged Teachers in Guangxi Universities (2020KY14013, 2020KY14008).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Yulin Normal University, Yulin, 537000, People’s Republic of China

    Jiali He & Lijun Chen

  2. School of Artificial Intelligence, Guangxi University for Nationalities, Nanning, 530006, Guangxi, People’s Republic of China

    Liangdong Qu

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  1. Jiali He
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Correspondence to Liangdong Qu.

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He, J., Qu, L. & Chen, L. Fuzzy Granular Structures of Fuzzy Relation Vectors. Int. J. Fuzzy Syst. 24, 1406–1424 (2022). https://doi.org/10.1007/s40815-021-01198-4

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