BE-代数的一类新的广义模糊理想

Generalized fuzzy ideals of BE-algebras

目的在BE-代数中引入(∈,∈∨q)-模糊理想的概念,研究这类模糊理想的重要性质。方法利用模糊拓扑中模糊点重于和属于模糊集概念研究模糊代数结构。结果得到了BE-代数中(∈,∈∨q)-模糊理想的若干等价条件,研究了BE-代数的模糊理想和(∈,∈∨q)-模糊理想的关系,特别是利用水平集刻划了(∈,∈∨q)-模糊理想。结论拓展了模糊代数结构的研究和方法。其结果和方法稍作修改可用于工程、计算机科学、人工智能和其他模糊代数结构等的研究。

Aim To introduce the concept of(∈,∈∨q)-fuzzy ideals in BE-algebras.Its important properties are established.Methods The concept of fuzzy points quasicoinciding with and belonging to fuzzy sets in fuzzy topology is applied to study fuzzy algebraic structures.Results Some equivalent conditions of(∈,∈∨q)-fuzzy ideals in BE-algebras are obtained.The relationship between fuzzy ideals and(∈,∈∨q)-fuzzy ideals is discussed.In particular,some characterizations of(∈,∈∨q)-fuzzy ideals in BE-algebras are established by using level sets.Conclusion The results are useful for the development of fuzzy algebras,which can be applied in engineering;computer science;artificial integence;other fuzzy algebraic structures with appropriate adjustments.