| 双极值模糊集在半环上的应用 |
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| 引用本文： | 周敏,李生刚.双极值模糊集在半环上的应用[J].数学研究及应用,2014,34(1):61-72. |
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| 作者姓名： | 周敏 李生刚 |
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| 作者单位： | 陕西师范大学数学与信息科学学院, 陕西 西安 710062;陕西师范大学数学与信息科学学院, 陕西 西安 710062 |
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| 基金项目： | 国家自然科学基金 (Grant No.11071151). |
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| 摘 要： | On the basis of concepts of bipolar fuzzy sets, we establish a new framework of bipolar fuzzy subsemirings（resp., ideals） which is a generalization of traditional fuzzy subsemirings（resp., ideals） in semirings. The concepts of bipolar fuzzy subsemirings（resp., ideals） are introduced and related properties are investigated by means of positive t-cut, negative s-cut and equivalence relation. Particularly, the notion of a normal bipolar fuzzy ideal is given, and some basic properties are studied in this paper.
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| 关 键 词： | 模糊集 半环 双极 模糊理想 应用 等价关系 |
| 收稿时间： | 2012/12/16 0:00:00 |
| 修稿时间： | 6/4/2013 12:00:00 AM |
Application of Bipolar Fuzzy Sets in Semirings |
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| Min ZHOU and Shenggang LI.Application of Bipolar Fuzzy Sets in Semirings[J].Journal of Mathematical Research with Applications,2014,34(1):61-72. |
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| Authors: | Min ZHOU and Shenggang LI |
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| Institution: | College of Mathematics and Information Science, Shaanxi Normal University, Shaanxi 710062, P. R. China;College of Mathematics and Information Science, Shaanxi Normal University, Shaanxi 710062, P. R. China |
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| Abstract: | On the basis of concepts of bipolar fuzzy sets, we establish a new framework of bipolar fuzzy subsemirings (resp., ideals) which is a generalization of traditional fuzzy subsemirings (resp., ideals) in semirings. The concepts of bipolar fuzzy subsemirings (resp., ideals) are introduced and related properties are investigated by means of positive $t$-cut, negative $s$-cut and equivalence relation. Particularly, the notion of a normal bipolar fuzzy ideal is given, and some basic properties are studied in this paper. |
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| Keywords: | bipolar fuzzy subsemiring (resp ideal) semiring equivalence relation normal bipolar fuzzy ideal |
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