L-fuzzifying rough sets based on KM-fuzzy pseudo metrics

Abstract

In this paper, we construct an L-fuzzifying lower and an L-fuzzifying upper approximation operator (L denotes a completely distributive De Morgan algebra) based on a KM-fuzzy pseudo metric and study their properties. Then we discuss some equivalent characterizations of the corresponding axiom of $KM$-fuzzy pseudo metrics via its induced L-fuzzifying rough set, respectively. Moreover, we explore the relationships between the crisp rough set induced by a KM-fuzzy pseudo metric M and the crisp rough set induced by the corresponding crisp pseudo metrics d_{a}^{M}. Besides, we investigate the relationships between the L-fuzzifying rough set induced by a famliy of crisp pseudo metrics \mathcal{D} and the L-fuzzifying rough set induced by the corresponding KM-fuzzy pseudo metric {M}^{\mathcal{D}}. Finally, we get the conclusions that \underline{R}^{\mathcal{D}}\leq {\underline{R}^{M}}^{\mathcal{D}} and {\overline{R}^{M}}^{\mathcal{D}}\leq \overline{R}^{\mathcal{D}}.

Keywords

• L-fuzzifying lower approximation operator
• L-fuzzifying upper approximation operator
• L-fuzzifying rough set
• KM-fuzzy pseudo metric

Supporting Institution

North China University of Technology; Jinyinhu high school; Nanjing Institute of Technology

Project Number

National Natural Science Foundation of China (No.11901007), North China University of Technology organized scientific research project (No. 2023YZZKY19,~No.2024NCUTYXCX104), Natural Science Foundation of Jiangsu Province (BK20230411)

Ethical Statement

The authors declare that there are no Ethical Data in our paper.

Thanks

The authors would like to express their sincere thanks to the anonymous reviewers for their careful reading and constructive comments.

References

1. [1] Y.L. Bao, H.L. Yang and Y.H. She, Using one axiom to characterize L-fuzzy rough approximation operators based on residuated lattices, Fuzzy Sets Syst. 336, 87–115, 2018