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

Wang, Kai

J. Nonlinear Convex Anal. 21, No. 12, 2647-2658 (2020).

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)

Keywords:

\(L\)-fuzzifying convexity; \(L\)-valued convex non-correlation structure; \(L\)-valued weakly independent system