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

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.