(■,■∨■_((λ,μ)))-模糊子坡

(■,■∨■_((λ,μ)))-Fuzzy Subinclines

坡代数在自动机理论、逻辑二元关系、疾病诊断、马可尔夫链等领域有重要作用.本文首先给出了(■,■∨■_((λ,μ)))-模糊子坡的概念,并研究了它的等价刻画,得到了(■,■∨■_((λ,μ)))-模糊子坡的并仍是(■,■∨■_((λ,μ)))-模糊子坡.其次,利用反扩张原理获得了(■,■∨■_((λ,μ)))-模糊子坡同态像与原像的性质.再次,通过引入模糊集的反直积的概念,给出了(■,■∨■_((λ,μ)))-模糊子坡在反直积运算下封闭的结论.最后,引入诺特子坡、阿丁子坡的新概念,并讨论了诺特子坡及阿丁子坡与(■,■∨■_((λ,μ)))-模糊子坡的关系.

Incline algebra plays an important role in the eld of automaton theory, logic of binary relations, medical diagnosis and Markov chains, etc.. In this paper, we rstly introduce the concept of (∈; ∈ ∨ q(;))-fuzzy subinclines and discuss its equivalent characterizations.Then we prove an important property that the union of (∈;∈ ∨ q(;))-fuzzy subinclines is also an (∈; ∈ ∨ q(;))-fuzzy subincline. We also obtain the properties of homomorphic image and homomorphic preimage based on the anti-extension principle. Besides, after introducing the concept of anti-direct product of fuzzy sets, we prove the anti-direct product of (∈; ∈ ∨q(;))-fuzzy subinclines is still an (∈; ∈ ∨ q(;))-fuzzy subincline. Finally, we introduce the new concepts of Noetherian subinclines and Artinian subinclines and discuss the relationships between Noetherian subinclines, Artinian subinclines and (∈; ∈ ∨ q(;))-fuzzy subinclines.