非对合剩余格的BF-弱理想和BF-强理想  

BF-weak ideals and BF-strong ideals in non-involutiveresiduated lattices

作　　者：刘春辉 LIU Chunhui(Education Science College,Chifeng University,Chifeng Inner Mongolia 024000)

机构地区：[1]赤峰学院教育科学学院,内蒙古赤峰024000

出　　处：《首都师范大学学报（自然科学版）》2023年第5期18-23,29,共7页Journal of Capital Normal University：Natural Science Edition

基　　金：内蒙古自治区高等学校科学研究项目(NJZY21138,NJZY22146);赤峰学院2022年教育教学研究项目(JYJXZ202204)。

摘　　要：对非对合剩余格的双极值模糊理想(简称BF-理想)问题进行了研究。引入了非对合剩余格的BF-弱理想和BF-强理想的概念,给出了二者的若干性质和等价刻画。讨论了BF-弱理想、BF-理想和BF-强理想的关系。利用BF-弱理想和BF-强理想的性质给出了强剩余格的特征定理。指明了在强剩余格中,BF-弱理想、BF-理想和BF-强理想三者相互等价。This paper studies the problem of bipolar fuzzy ideals(BF-ideals for short)in noninvolutive residuated lattices.The notions of BF-weak ideals and BF-strong ideals are introduced in non-involutive residuated lattices.Some their properties and characterizations are given.The relations among BF-weak ideals,BF-ideals and BF-strong ideals are discussed systematically.And the characterization theorems of strong residuated lattices are obtained by using BF-weak ideals and BFstrong ideals.It is showed that in strong residuated lattices the notions of BF-weak ideal,BF-ideal and BF-strong ideal are same.

关 键 词：模糊逻辑 非对合剩余格 BF-理想 BF-弱理想 BF-强理想 

分 类 号：O141.1[理学—数学] O153.1[理学—基础数学]