关键词: (ˉ∈,ˉ&isin, ∨ˉq_(λ,μ))-模糊理想；滤子；链式条件；同态原像；同构像

Abstract: Firstly, this paper introduces the concept of (ˉ∈,ˉ∈ ∨ˉq_(λ,μ))-fuzzy ideal of incline algebra and discusses some equivalent characterizations. Then this paper proves that the union and the anti-direct product of (ˉ∈,ˉ∈ ∨ˉq_(λ,μ))- fuzzy ideals of incline algebras are still (ˉ∈,ˉ∈ ∨ˉq_(λ,μ))-fuzzy ideals of incline algebras, and obtains some relative properties of its isomorphic image and homomorphic preimage based on the anti-extension principle. Finally, this paper discusses some basic properties of (ˉ∈,ˉ∈ ∨ˉq_(λ,μ))-fuzzy ideals of incline algebras through the chain condition of filters of incline algebras. The new concept of (ˉ∈,ˉ∈ ∨ˉq_(λ,μ))-fuzzy ideal of incline algebras expands the study of incline algebraic theory.The properties of chain condition of filters of incline algebras can also be applied to other algebraic structures, these new results enrich the soft algebra theory.

Key words: (ˉ∈,ˉ&isin, ∨ˉq_(λ,μ))-fuzzy ideals, filters, chain condition, homomorphic preimage, isomorphic image