正则剩余格的fuzzy⊙理想

Fuzzy⊙-ideals in regular residuated lattices

剩余格在模糊逻辑的研究中扮演着一个重要的角色。首先在剩余格中引入fuzzy⊙理想的概念,讨论了(正则)剩余格中fuzzy⊙理想性质,给出了正则剩余格中fuzzy⊙理想的若干等价刻画。其次,利用fuzzy⊙理想概念构造了一个同余关系,证明一个正则剩余格在该同余关系下的商代数还是正则剩余格。

Residuated lattices play an important role in studies of fuzzy logic. First, the notions of fuzzy ⊙ -ideals in residuated lattices are introduced. Some properties of fuzzy ⊙-ideals in （regular） residuated lattices are discussed and some equivalent characterizations are given. Second, a congruence relation is structured in terms of the notion of fuzzy ⊙-ideal in regular residuated lattices. It is proved that the quotient algebra of a regular residuated lattice under a congruence relation is also a regular residuated lattice.