A New Approach to the Fuzzification of Convex Structures

A New Approach to the Fuzzification of Convex Structures

A new approach to the fuzzification of convex structures is introduced. It is also called an M-fuzzifying convex structure. In the definition of M-fuzzifying convex structure, each subset can be regarded as a convex set to some degree. An M-fuzzifying convex structure can be characterized by means o...

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Main Authors: Fu-Gui Shi, Zhen-Yu Xiu
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2014/249183
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spelling doaj-94e1a067dbb14122a10f68f54316cb112020-11-24T23:23:54ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/249183249183A New Approach to the Fuzzification of Convex StructuresFu-Gui Shi0Zhen-Yu Xiu1School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, ChinaSchool of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, ChinaA new approach to the fuzzification of convex structures is introduced. It is also called an M-fuzzifying convex structure. In the definition of M-fuzzifying convex structure, each subset can be regarded as a convex set to some degree. An M-fuzzifying convex structure can be characterized by means of its M-fuzzifying closure operator. An M-fuzzifying convex structure and its M-fuzzifying closure operator are one-to-one corresponding. The concepts of M-fuzzifying convexity preserving functions, substructures, disjoint sums, bases, subbases, joins, product, and quotient structures are presented and their fundamental properties are obtained in M-fuzzifying convex structure.http://dx.doi.org/10.1155/2014/249183
collection DOAJ
language English
format Article
sources DOAJ
author Fu-Gui Shi
Zhen-Yu Xiu
spellingShingle Fu-Gui Shi
Zhen-Yu Xiu
A New Approach to the Fuzzification of Convex Structures
Journal of Applied Mathematics
author_facet Fu-Gui Shi
Zhen-Yu Xiu
author_sort Fu-Gui Shi
title A New Approach to the Fuzzification of Convex Structures
title_short A New Approach to the Fuzzification of Convex Structures
title_full A New Approach to the Fuzzification of Convex Structures
title_fullStr A New Approach to the Fuzzification of Convex Structures
title_full_unstemmed A New Approach to the Fuzzification of Convex Structures
title_sort new approach to the fuzzification of convex structures
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2014-01-01
description A new approach to the fuzzification of convex structures is introduced. It is also called an M-fuzzifying convex structure. In the definition of M-fuzzifying convex structure, each subset can be regarded as a convex set to some degree. An M-fuzzifying convex structure can be characterized by means of its M-fuzzifying closure operator. An M-fuzzifying convex structure and its M-fuzzifying closure operator are one-to-one corresponding. The concepts of M-fuzzifying convexity preserving functions, substructures, disjoint sums, bases, subbases, joins, product, and quotient structures are presented and their fundamental properties are obtained in M-fuzzifying convex structure.
url http://dx.doi.org/10.1155/2014/249183
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AT zhenyuxiu anewapproachtothefuzzificationofconvexstructures
AT fuguishi newapproachtothefuzzificationofconvexstructures
AT zhenyuxiu newapproachtothefuzzificationofconvexstructures
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