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Journal of Applied Mathematics
Volume 2014, Article ID 249183, 12 pages
Research Article

A New Approach to the Fuzzification of Convex Structures

School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China

Received 26 April 2014; Revised 19 June 2014; Accepted 27 June 2014; Published 31 August 2014

Academic Editor: Jin Liang

Copyright © 2014 Fu-Gui Shi and Zhen-Yu Xiu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A new approach to the fuzzification of convex structures is introduced. It is also called an -fuzzifying convex structure. In the definition of -fuzzifying convex structure, each subset can be regarded as a convex set to some degree. An -fuzzifying convex structure can be characterized by means of its -fuzzifying closure operator. An -fuzzifying convex structure and its -fuzzifying closure operator are one-to-one corresponding. The concepts of -fuzzifying convexity preserving functions, substructures, disjoint sums, bases, subbases, joins, product, and quotient structures are presented and their fundamental properties are obtained in -fuzzifying convex structure.