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M-fuzzifying k-pseudo metric space and its induced M-fuzzifying structures

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Abstract

In this paper, the definition of an M-fuzzifying k-pseudo metric and its examples are introduced. Additionally, some M-fuzzifying structures induced by an M-fuzzifying k-pseudo metric are given, such as an M-fuzzifying neighborhood system, an M-fuzzifying topology, an M-fuzzifying closure operator and an M-fuzzifying convex structure. Besides, it is shown that there is a one-to-one correspondence between M-fuzzifying k-pseudo metrics and nests of crisp k-pseudo metrics. Finally, we prove that the M-fuzzifying structures induced by an M-fuzzifying k-pseudo metric coincide with those induced by nests of k-pseudo metrics.

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Acknowledgements

The authors are thankful to the anonymous reviewers and the editors.

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Authors and Affiliations

  1. College of Science, North China University of Technology, Beijing, 100144, People’s Republic of China

    Yu Zhong & Shuang Lin

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  1. Yu Zhong
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  2. Shuang Lin
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Correspondence to Yu Zhong.

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Communicated by Regivan Hugo Nunes Santiago.

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This work is supported by the National Natural Science Foundation of China (No. 11901007), Beijing Natural Science Foundation (No. 1204029), Fundamental Research Funds of Beijing Municipal Education Commission (No. 110052972027/143), North China University of Technology Research Fund Program for Young Scholars (No. 110051360002), Undergraduate Innovation and Entrepreneurship Training Program of North China University of Technology (No. 108051360021XN216/005) North China University of Technology Research Fund Program for Key Discipline (No. 110052972027/014).

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Zhong, Y., Lin, S. M-fuzzifying k-pseudo metric space and its induced M-fuzzifying structures. Comp. Appl. Math. 41, 70 (2022). https://doi.org/10.1007/s40314-021-01720-2

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  • DOI: https://doi.org/10.1007/s40314-021-01720-2

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