Application of Bipolar Fuzzy Sets in Semirings  

作　　者：Min ZHOU Shenggang LI 

机构地区：[1]College of Mathematics and Information Science, Shaanxi Normal University

出　　处：《Journal of Mathematical Research with Applications》2014年第1期61-72,共12页数学研究及应用（英文版）

基　　金：Supported by the National Natural Science Foundation of China (Grant No.11071151)

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.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.

关 键 词：bipolar fuzzy subsemiring （resp.  ideal） SEMIRING equivalence relation normalbipolar fuzzy ideal. 

分 类 号：O153.3[理学—数学]