否定非对合剩余格的双极值模糊理想格  

Lattice of bipolar fuzzy ideals in negative non-involutive residuated lattices

作　　者：刘春辉[1] 张海燕[1] 李玉毛[1] LIU Chun-hui;ZHANG Hai-yan;LI Yu-mao(School of Mathematics and Statistics,Chifeng University,Chifeng 024001,Inner Mongolia,China)

机构地区：[1]赤峰学院数学与统计学院

出　　处：《山东大学学报（理学版）》2019年第9期29-35,共7页Journal of Shandong University(Natural Science)

基　　金：内蒙古自治区高等学校科学研究项目(NJZY18206)

摘　　要：对否定非对合剩余格的双极值模糊理想问题做进一步深入研究,给出了由一个双极值模糊集生成的双极值模糊理想的定义并建立了其两个表示定理,证明了一个否定非对合剩余格L的全体双极值模糊理想之集BFI(L)在偏序■下构成完备Heyting代数,为进一步揭示否定非对合剩余格的结构特征拓展了研究思路。In this paper,the problem of bipolar fuzzy ideals is further studied in negative non-involutive residuated lattices.The definition of bipolar fuzzy ideal which is generated by a bipolar fuzzy set is given and its two representation theorems are established.It is proved that the set BFI(L)which containing of all bipolar fuzzy ideals in a negative non-involutive residuated lattice L,under the partial order■,forms a complete Heyting algebra.This work further expands the way for revealing the structural characteristics of negative non-involutive residuated lattices.

关 键 词：模糊逻辑 逻辑代数 否定非对合剩余格 双极值模糊理想 完备Heyting代数 

分 类 号：O141.1[理学—数学] O153.1[理学—基础数学]