## $$L$$-valued convex non-correlation structures.(English)Zbl 1465.52007

Summary: In this paper, we propose a concept of $$L$$-valued weakly independent system for characterizing $$L$$-fuzzifying convexity and show that there exists a one-to-one correspondence between them. By convex ideals, $$L$$-valued convex non-correlation structure is given for studying $$L$$-fuzzifying convexity. It follows from relationship between $$L$$-valued weakly independent systems and $$L$$-fuzzifying convexities that the category of $$L$$-valued convex non-correlation structures is isomorphic to the category of $$L$$-fuzzifying convex spaces.

### MSC:

 52A01 Axiomatic and generalized convexity 03E72 Theory of fuzzy sets, etc. 06A15 Galois correspondences, closure operators (in relation to ordered sets)
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