| 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 |
| 双极值模糊集在半环上的应用 |
| Application of Bipolar Fuzzy Sets in Semirings |
| 投稿时间：2012-12-16 修订日期：2013-06-04 |
| DOI：10.3770/j.issn:2095-2651.2014.01.006 |
| 中文关键词: 双极模糊子半环(理想) 半环 等价关系 正规双极模糊理想. |
| 英文关键词:bipolar fuzzy subsemiring (resp., ideal) semiring equivalence relation normal bipolar fuzzy ideal. |
| 基金项目:国家自然科学基金 (Grant No.11071151). |
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| 中文摘要: |
| 基于双极值模糊集,我们建立了双极模糊子半环(理想)的一个新的框架.双极模糊子半环(或理想)是传统模糊子半环(理想)的一种推广.我们介绍了双极模糊子半环(理想)的概念,并通过正$t$-截集、负$s$-截集和等价关系研究了它们的相关性质.特别地,我们给出了正规双极模糊理想的定义,并刻画了它的基本性质. |
| 英文摘要: |
| 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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