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\(\alpha \)-cross-migrativity between fuzzy implications and grouping functions

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Abstract

Grouping functions, are extensively utilized in decision-making, classification, image processing and other related domains as forms of aggregation functions. Meanwhile, the migrativity of bivariate aggregation functions, extensively explored in numerous scholarly works, emerges as a pivotal and particularly intriguing characteristic. In the present paper, we give the concept of \(\alpha \)-cross migrativity between fuzzy implications and grouping functions. And then, we discuss certain additional properties pertaining to mutual exchangeable and law of importation. Afterwards, we show these properties in a simple and clear way with examples. Ultimately, the \(\alpha \)-cross migrativity of certain specific classes of fuzzy implications over grouping functions is thoroughly characterized.

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Acknowledgements

The authors would like to express their sincerely thanks to the Editors and anonymous reviewers for their most valuable comments and suggestions in improving this paper greatly.

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Authors and Affiliations

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou, 730070, People’s Republic of China

    Yun Song & Junsheng Qiao

  2. Gansu Provincial Research Center for Basic Disciplines of Mathematics and Statistics, Lanzhou, People’s Republic of China

    Junsheng Qiao

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  1. Yun Song
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  2. Junsheng Qiao
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Correspondence to Junsheng Qiao.

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Authors Yun Song and Junsheng Qiao declare that they have no Conflict of interest.

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This work was supported by the National Natural Science Foundation of China (62166037), Science and Technology Program of Gansu Province (20JR10RA101) and Funds for Innovative Fundamental Research Group Project of Gansu Province (23JRRA684).

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Song, Y., Qiao, J. \(\alpha \)-cross-migrativity between fuzzy implications and grouping functions. Comp. Appl. Math. 44, 104 (2025). https://doi.org/10.1007/s40314-024-03028-3

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