否定非对合剩余格的双极值模糊素理想

Bipolar fuzzy prime 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作进一步深入研究。引入双极值模糊素理想(简称BF-素理想)概念并考察其性质特征。获得了BF-素理想的一些等价刻画,建立了预线性否定非对合剩余格中的BF-素理想定理,证明了BF-素理想的NRL-同态像与原像仍为BF-素理想。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。

The problem of bipolar fuzzy ideals is further studied in negative non-involutive residuated lattices. The concept of bipolar fuzzy prime ideal(BF-prime ideal for short) is introduced and its properties are investigated. Some equivalent characterizations of BF-prime ideal are obtained. The BF-prime ideal theorem in a prelinearity negative non-involutive residuated lattice is established. It is proved that the NRL-homomorphism image and the inverse image of a BF-prime ideal are also BF-prime ideals. This work further expands the way for revealing the structural characteristics of negative non-involutive residuated lattices.