| Application of Bipolar Fuzzy Sets in Semirings |
| Received:December 16, 2012 Revised:June 04, 2013 |
| Key Words:
bipolar fuzzy subsemiring (resp., ideal) semiring equivalence relation normal bipolar fuzzy ideal.
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11071151). |
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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. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2014.01.006 |
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