Abstract: Incline algebra plays an important role in the field of automaton theory, logic of binary relations, medical diagnosis and Markov chains, etc.. In this paper, we firstly introduce the concept of $(\overline\in,\overline\in\vee{\overline q _{(\lambda,\mu)}})$-fuzzy subinclines and discuss its equivalent characterizations. Then we prove an important property that the union of $(\overline\in,\overline\in\vee{\overline q _{(\lambda,\mu)}})$-fuzzy subinclines is also an $(\overline\in,\overline\in\vee{\overline q _{(\lambda,\mu)}})$-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 $(\overline\in,\overline\in\vee{\overline q _{(\lambda,\mu)}})$-fuzzy subinclines is still an $(\overline\in,\overline\in\vee{\overline q _{(\lambda,\mu)}})$-fuzzy subincline. Finally, we introduce the new concepts of Noetherian subinclines and Artinian subinclines and discuss the relationships between Noetherian subinclines, Artinian subinclines and $(\overline\in,\overline\in\vee{\overline q _{(\lambda,\mu)}})$-fuzzy subinclines.

Key words: $(\overline\in,\overline\in\vee{\overline q _{(\lambda,\mu)}})$-fuzzy subinclines, generalized anti-fuzzy subinclines, chain condition, anti-direct product, isomorphic image, homomorphic preimage