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\(L\)-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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