Abstract
In this article, we deal with partial orders induced by the smallest and greatest nullnorms on bounded lattices, respectively. We first obtain the conditions for the partial orders induced by the smallest and greatest nullnorms to be a lattice, respectively. Then, we completely characterize the distributivity of the partial orders induced by the smallest and greatest nullnorms, respectively.
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Acknowledgements
The authors are grateful to the anonymous referees for their valuable comments and suggestions, which helps the authors to improve the earlier version of this paper.
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This paper is supported by the National Natural Science Foundation of China (No.12071325).
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Dr. Zhi-qiang Liu supplied the main results. Dr. Xue-ping Wang wrote the main manuscript text.
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Liu, Zq., Wang, Xp. Partial orders induced by the smallest and greatest nullnorms on bounded lattices. Soft Comput 26, 8245–8252 (2022). https://doi.org/10.1007/s00500-022-07256-9
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DOI: https://doi.org/10.1007/s00500-022-07256-9