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In this study, under the condition that L is a completely distributive lattice, a generalized definition of fuzzy subrings is introduced. By means of four kinds of cut sets of fuzzy subset, the equivalent characterization of L ‐fuzzy subring measures are presented. The properties of L ‐fuzzy subring measures under these two kinds of product operations are further studied. In addition, an L ‐fuzzy convexity is directly induced by L ‐fuzzy subring measure, and it is pointed out that ring homomorphism can be regarded as L ‐fuzzy convex preserving mapping and L ‐fuzzy convex‐to‐convex mapping. Next, we give the definition and related properties of the measure of L ‐fuzzy quotient ring and give a new characterization of L ‐fuzzy quotient ring when the measure of L ‐fuzzy quotient ring is 1.
An et al. (Sat,) studied this question.
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