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Green’s relations in L-E-fuzzy skew lattices

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Abstract

In this paper, we introduce a concept of L-E-fuzzy skew lattices as a particular fuzzified version of skew lattices relative to lattice-valued algebraic structures, with fuzzy equality and fuzzy identities. In particular, L-E-fuzzy version of Green’s relations are also introduced as fuzzified forms of their classical ones in semigroup theory, and several equivalent forms of the fuzzy relations are obtained. Finally, we mainly prove that: (1) The L-E-fuzzy Green’s relations of L-E-fuzzy skew lattices are fuzzy compatible equalities on them; (2) The cut sets of L-E-fuzzy skew lattices are classical subalgebras in underlying algebras and, finally, we prove two important decomposition theorems concerning quotient algebras of cut sets over the fuzzy Green’s relations.

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All data, models, and code generated or used during the study appear in the submitted article titled “Green’s relations in L-E-fuzyy skew lattices”. (DOI:https://doi.org/10.1007/s00500-022-07119-3).

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Acknowledgements

We are extremely grateful to the editors and reviewers for their valuable comments and helpful suggestions which helped to improve the presentation of this paper.

Funding

This work is supported by the Foundation of Educational Commission of Hubei Province, China (Nos. B2020140) and Project of Hubei University of Arts and Science, China (Nos. XK2020039).

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Authors and Affiliations

  1. College of Mathematics and Statistics, HuBei University of Arts and Sciences, Xiangyang, 410053, People’s Republic of China

    Yuan Zhi

  2. College of Mathematics, Hunan University, Changsha, 410082, People’s Republic of China

    Yuan Zhi, Xiangnan Zhou & Qingguo Li

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  1. Yuan Zhi
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  2. Xiangnan Zhou
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  3. Qingguo Li
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All the authors contributed equally to this research paper.

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Correspondence to Yuan Zhi.

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Zhi, Y., Zhou, X. & Li, Q. Green’s relations in L-E-fuzzy skew lattices. Soft Comput 26, 6481–6494 (2022). https://doi.org/10.1007/s00500-022-07119-3

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