Normal Bipolar Fuzzy Ideals in Non-involutive Residuated Lattices
Received:August 20, 2019  Revised:March 19, 2020
Key Words: non-classical logic   non-involutive residuated lattice   bipolar fuzzy set   normal bipolar fuzzy ideal  
Fund Project:Supported by the Higher School Research Foundation of Inner Mongolia (Grant No.NJZY18206).
Author NameAffiliation
Chunhui LIU School of Mathematics and Computer Science, Chifeng University, Inner Mongolia 024001, P. R. China 
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      In this paper, the problem of bipolar fuzzy ideal is further studied in non-involutive residuated lattices. The notion of normal bipolar fuzzy ideal is introduced, some important properties and equivalent characterizations of normal bipolar fuzzy ideals are obtained. In addition, two special types of normal bipolar fuzzy ideals are defined, which are called maxima and completely normal bipolar fuzzy ideals, respectively, and their relationships are discussed. This work further expands the way for revealing the structural characteristics of non-involutive residuated lattices.
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