否定非对合剩余格的双极值模糊理想格

doi:10.6040/j.issn.1671-9352.0.2019.131

摘要/Abstract

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。

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

Abstract: 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.

Key words: fuzzy logic, logical algebra, negative non-involutive residuated lattice, bipolar fuzzy ideal, complete Heyting algebra

中图分类号:

O141.1

刘春辉,张海燕,李玉毛. 否定非对合剩余格的双极值模糊理想格[J]. 《山东大学学报(理学版)》, 2019, 54(9): 29-35.

LIU Chun-hui, ZHANG Hai-yan, LI Yu-mao. Lattice of bipolar fuzzy ideals in negative non-involutive residuated lattices[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(9): 29-35.

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