\((L,M)\)-fuzzy convex structures

Volume 10, Issue 7, pp 3655--3669 http://dx.doi.org/10.22436/jnsa.010.07.25

Publication Date: July 25, 2017 Submission Date: April 07, 2016

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Authors

Fu-Gui Shi - School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China. Zhen-Yu Xiu - College of Applied Mathematics, Chengdu University of Information Technology, Chengdu 610000, China.

Abstract

In this paper, the notion of \((L,M)\)-fuzzy convex structures is introduced. It is a generalization of L-convex structures and \(M\)-fuzzifying convex structures. In our definition of \((L,M)\)-fuzzy convex structures, each \(L\)-fuzzy subset can be regarded as an \(L\)-convex set to some degree. The notion of convexity preserving functions is also generalized to lattice-valued case. Moreover, under the framework of \((L,M)\)-fuzzy convex structures, the concepts of quotient structures, substructures and products are presented and their fundamental properties are discussed. Finally, we create a functor \(\omega\) from MYCS to LMCS and show that MYCS can be embedded in LMCS as a coreflective subcategory, where MYCS and LMCS denote the category of \(M\)-fuzzifying convex structures and the category of \((L,M)\)-fuzzy convex structures, respectively.

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Keywords

• quotient structures
• substructures
• \((L،M)\)-fuzzy convex structure
• \((L،M)\)-fuzzy convexity preserving function
• products.

MSC

•  03E72
•  52A01

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