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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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/249183 |
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| _version_ | 1849404368258859008 |
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| author | Fu-Gui Shi Zhen-Yu Xiu |
| author_facet | Fu-Gui Shi Zhen-Yu Xiu |
| author_sort | Fu-Gui Shi |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-94e1a067dbb14122a10f68f54316cb11 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-94e1a067dbb14122a10f68f54316cb112025-08-20T03:37:01ZengWileyJournal 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 |
| spellingShingle | Fu-Gui Shi Zhen-Yu Xiu A New Approach to the Fuzzification of Convex Structures Journal of Applied Mathematics |
| title | 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_short | A New Approach to the Fuzzification of Convex Structures |
| title_sort | new approach to the fuzzification of convex structures |
| url | http://dx.doi.org/10.1155/2014/249183 |
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