Abstract
In this paper, we first point out that the proof of the assertions (Theorems 3.12 and 3.25) in a previous paper by Jose and Mathew [Merin Jose and Sunil C. Mathew, Generalization of LM-filters: sum, subspace, product, quotient and stratification, Soft Computing 27(2023) 809-819] is incorrect. Then, we give the new constructs of the supremum and product of a family of LM-G-filters. Moreover, we give the definition of LM-G-fuzzy congruence relations on X. And, we prove that the category of LM-G-fuzzy congruence relational spaces and the category of LM-G-filter spaces are categorically isomorphic.
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Acknowledgements
The authors would like to give heartfelt thanks to the referees for their very careful reading of the paper and for their very valuable comments and suggestions which improved the paper.
Funding
The work is supported by the National Natural Science Foundation of China (Grant No.12171386).
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Zhao, H., Zhao, YJ. Notes on “Generalization of LM-filters: sum, subspace, product, quotient and stratification” Soft Computing 27(2023) 809–819. Soft Comput 28, 1935–1942 (2024). https://doi.org/10.1007/s00500-023-09463-4
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DOI: https://doi.org/10.1007/s00500-023-09463-4