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Characterizations for the migrativity of uninorms over N-ordinal sum implications

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Abstract

The migrative equations offer an important tool to characterize new fuzzy logic connectives, and play a significant role in image processing. The migrative equations of disjunctive aggregation functions over fuzzy implications, together with their dualities, provide a unified framework for the study of migrativity between fuzzy logic connectives which will include, as special cases, the migrative equations studied in the literature. In this paper, we focus on the migrativity of uninorms over N-ordinal sum implications due to the respective fundamental roles of them in aggregation functions and fuzzy implications. We characterize the \(\alpha \)-migrativity of uninorms over N-ordinal sum implications depending on the position where \(\alpha \) lies in the range of N. The necessary and sufficient conditions under which a uninorm is \(\alpha \)-migrative over an N-ordinal sum implication are obtained by giving ordinal sum representations of the underlying t-norms or t-conorms of the uninorm and the representations of the \(\alpha \)-vertical section of the implication function.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 12171292) and the Fundamental Research Funds For the Central Universities (Grant No. GK202101009).

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Authors and Affiliations

  1. Institute of Mathematics, Shaanxi Normal University, Xi’an, 710119, China

    Qing Chang & Hongjun Zhou

  2. Faculty of Science and Technology, University of Silesia in Katowice, Bankowa 14, 40-007, Katowice, Poland

    Michał Baczyński

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  1. Qing Chang
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  2. Hongjun Zhou
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  3. Michał Baczyński
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Correspondence to Hongjun Zhou.

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Chang, Q., Zhou, H. & Baczyński, M. Characterizations for the migrativity of uninorms over N-ordinal sum implications. Comp. Appl. Math. 42, 172 (2023). https://doi.org/10.1007/s40314-023-02319-5

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