| A New View on Fuzzy Hypermodules |
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| 作者姓名： | Jian Ming ZHAN Bijan DAVVAZ K. P. SHUM |
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| 作者单位： | [1]Department of Mathematics, Hubei Institute for Nationalities, Enshi 445000, P. R. China [2]Department of Mathematics, Yazd University, Yazd, Iran [3]Faculty of Science, The Chinese University of Hong Kong, Shatin, Hong Kong （SAR）, P. R. China |
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| 基金项目： | The research of the first author is partially supported by the National Natural Science Foundation of China （60474022） and the Key Science Foundation of Education Commission of Hubei Province, China （D200729003; D200529001） and the research of the third author is partially supported by an RGC grant （CUHK） #2060297 （05/07） The authors are highly grateful to the referees for their valuable comments and suggestions for improving the paper. |
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| 摘 要： | We describe the relationship between the fuzzy sets and the algebraic hyperstructures. In fact, this paper is a continuation of the ideas presented by Davvaz in （Fuzzy Sets Syst., 117： 477- 484, 2001） and Bhakat and Das in （Fuzzy Sets Syst., 80： 359-368, 1996）. The concept of the quasicoincidence of a fuzzy interval value with an interval-valued fuzzy set is introduced and this is a natural generalization of the quasi-coincidence of a fuzzy point in fuzzy sets. By using this new idea, the concept of interval-valued （α,β）-fuzzy sub-hypermodules of a hypermodule is defined. This newly defined interval-valued （α,β）-fuzzy sub-hypermodule is a We shall study such fuzzy sub-hypermodules and sub-hypermodules of a hypermodule. generalization of the usual fuzzy sub-hypermodule. consider the implication-based interval-valued fuzzy
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| 关 键 词： | 超级模数 区间值 模糊集 代数超级结构 |
| 收稿时间： | 25 May 2006 |
| 修稿时间： | 2006-05-25 |
A New View on Fuzzy Hypermodules |
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| Jian Ming ZHAN Bijan DAVVAZ K. P. SHUM.A New View on Fuzzy Hypermodules[J].Acta Mathematica Sinica,2007,23(8):1345-1356. |
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| Authors: | Jian Ming Zhan Bijan Davvaz K P Shum |
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| Institution: | (1) Department of Mathematics, Hubei Institute for Nationalities, Enshi, 445000, P. R. China;(2) Department of Mathematics, Yazd University, Yazd, Iran;(3) Faculty of Science, The Chinese University of Hong Kong, Shatin, Hong Kong (SAR), P. R. China |
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| Abstract: | We describe the relationship between the fuzzy sets and the algebraic hyperstructures. In fact, this paper is a continuation
of the ideas presented by Davvaz in (Fuzzy Sets Syst., 117: 477– 484, 2001) and Bhakat and Das in (Fuzzy Sets Syst., 80: 359–368, 1996). The concept of the quasicoincidence of a fuzzy interval value with an interval-valued fuzzy set is introduced
and this is a natural generalization of the quasi-coincidence of a fuzzy point in fuzzy sets. By using this new idea, the
concept of interval-valued (α, β)-fuzzy sub-hypermodules of a hypermodule is defined. This newly defined interval-valued (α, β)-fuzzy sub-hypermodule is a generalization of the usual fuzzy sub-hypermodule. We shall study such fuzzy sub-hypermodules
and consider the implication-based interval-valued fuzzy sub-hypermodules of a hypermodule.
The research of the first author is partially supported by the National Natural Science Foundation of China (60474022) and
the Key Science Foundation of Education Commission of Hubei Province, China (D200729003; D200529001) and the research of the
third author is partially supported by an RGC grant (CUHK) #2060297 (05/07) |
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| Keywords: | hypermodule interval-valued (α β )-fuzzy sub-hypermodule interval-valued (∈ ∈ ∨ q)- fuzzy sub-hypermodule fuzzy logic implication operator |
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