What is it about?
In this paper, the notion of M-fuzzifying restricted hull operators is introduced and several equivalent characterizations are given. It is shown that there is a one-to-one correspondence between M-fuzzifying restricted hull operators and M-fuzzifying convex structures. As applications, some properties of the cut convex structures of an M-fuzzifying convex structure and of M-fuzzifying convexity preserving functions and of M-fuzzifying convex-to-convex functions are derived. In addition, using M-fuzzifying restricted hull operators, some M-fuzzifying convexities are naturally constructed from M-fuzzy quasi-orders.
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Why is it important?
And as expected, M-fuzzifying convex structure can be characterized by its M-fuzzifying hull operator (called closure operator in ), or even by its effect on finite sets.
Read the Original
This page is a summary of: The restricted hull operator of M-fuzzifying convex structures1, Journal of Intelligent & Fuzzy Systems, October 2015, IOS Press, DOI: 10.3233/ifs-151765.
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