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Migrativity of extended binary operations on fuzzy truth values

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Abstract

Migrativity is a recently studied property of binary operations defined on the unit interval, introduced by Durante and Sarkoci for studying convex combinations of a continuous t-norm and a drastic product t-norm \(T_D\). Inspired by the thought of it, in this paper, we introduce migrativity of extended general binary operations on fuzzy truth values by Zadeh extension principle, where a slight modification is considered. Based on the migrativity equation for fuzzy truth values, we discuss and present some of its characterizations specific to the binary operation that is migrative over a class of particular fuzzy truth values related to characteristic functions of elements in [0, 1] and then extend it to the rather general cases, which leads to the connections and equivalence between two concepts of migrativity under specific conditions. The results of this paper can be applied immediately to the extensions of some familiar aggregation functions like t-norms and overlap functions, revealing the preliminary traits of migrativity on type-2 set.

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Acknowledgements

The authors are extremely grateful to the editor and anonymous referees for their valuable comments and helpful suggestions which helped to improve the presentation of this paper. This research was supported by the National Natural Science Foundation of China (Grant No. 12101500) and the Chinese Universities Scientific Fund (Grant Nos. 2452018054 and 2452022370).

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Authors and Affiliations

  1. College of Science, Northwest A &F University, YangLing, 712100, People’s Republic of China

    Minghui Xu, Chenhui Zhu, Wei Li & Bin Yang

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  1. Minghui Xu
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  2. Chenhui Zhu
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  3. Wei Li
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  4. Bin Yang
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Correspondence to Bin Yang.

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Communicated by Graçaliz Pereira Dimuro.

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Xu, M., Zhu, C., Li, W. et al. Migrativity of extended binary operations on fuzzy truth values. Comp. Appl. Math. 43, 330 (2024). https://doi.org/10.1007/s40314-024-02638-1

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