Theoretical analysis reveals structural relationships between KM-fuzzy pseudo metrics and L-fuzzifying rough sets, suggesting unified frameworks for uncertainty modeling.
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 dₐM. Besides, we investigate the relationships between the L-fuzzifying rough set induced by a famliy of crisp pseudo metrics D and the L-fuzzifying rough set induced by the corresponding KM-fuzzy pseudo metric {M}D. Finally, we get the conclusions that {R}D≤ {{R}M}D and {R̄M}D≤ R̄D.
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Zhong et al. (2026) studied this question.
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