Miaohan Hu

(∈ , ∈ ∨ q ( λ , μ ) )-Fuzzy h -Ideals of Hemirings

The definitions of (∈ , ∈ ∨ q (λ,μ))-fuzzy left (resp. right) h-ideals of hemirings, generalized fuzzy left (resp. right) h-ideals of hemirings, prime (semiprime) (∈ , ∈ ∨ q (λ,μ))-left (resp. right) h-ideals of hemirings and prime (semiprime) generalized fuzzy left (resp. right) h-ideals of hemirings are given. Meanwhile, some fundamental properties of them are discussed. Finally, the implication-based fuzzy left (resp. right) h-ideals of hemirings are considered.

（∈，∈∨q(λ，μ)）-Fuzzy Regular Subrings

Our aim in this paper is to introduce and study the new type of fuzzy subrings of a ring called fuzzy ( resp.completely,weakly) regular subring ,generalized fuzzy (resp. completely , weakly ) regular subring , （∈，∈∨q(λ，μ)）- fuzzy( resp. completely , weakly ) regular subring and the direct products of them .Some of their algebraic properties are characterized by their level sets and extension principle. Finally,we give the properties of homomorphic image and homomorphic preimage of them.

(epsilon, epsilon Vq (lamda, mu))-Fuzzy n-Pseudo Ideals of Rings

Our aim in this paper is to introduce and study new sorts of fuzzy ideals in rings called (epsilon, epsilon Vq (lamda, mu))-fuzzy n-pseudo ideal of rings and generalized fuzzy n- pseudo ideal of rings. The equivalent connection between them are given. Besides, some of their algebraic properties are charactered.

(epsilon, epsilon Vq (lamda, mu))-Fuzzy Regular * -Semigroups

In this paper, we introduce the definitions of (epsilon, epsilon Vq (lamda, mu))-fuzzy regular * - semi groups and generalized fuzzy regular *-semi groups. Based on these, the properties of level sets and characteristic function of them are discussed. Besides, we also give their equivalent forms and properties of homomorphic image and homomorphic pre image in a homomorphim of semigroups.

Generalized fuzzy imaginary ideals of rings

Our aim in this paper is to introduce and study the new type of fuzzy ideals of a ring called generalized fuzzy imaginary right (resp. left) ideals and the direct products of them. The equivalence relation of them is given, besides, the properties of their intersection, union and level sets are discussed. Finally, we also give the properties of their homomorphic preimage.

(∈̄, ∈̄ ∨ q̄ (λ,μ) )-fuzzy weak ideals of rings

In this paper, we introduce the new type of fuzzy ideals of a ring called (∈̄, ∈̄ ∨ q̄<inf>(λ,μ)</inf>) - fuzzy weak ideals and generalized fuzzy weak ideals. The equivalence relation between them is given, besides, the properties of their intersection, union and level sets are discussed. Finally, we also give the properties of their homomorphic image and homomorphic preimage.

(epsilon, epsilon Vq (lambda, Mu)) -- Fuzzy Subrings

The definition of (epsilon, epsilon Vq (lambda, Mu))-fuzzy subring is given. Meanwhile, the equivalent forms of it and the properties of its homomorphic image, homomorphic, preimage and level sets are given based on the idea of generalized fuzzy subgrouops.

(∈,∈⋁q (λ,μ) )-fuzzy ideals

The definition of generalized fuzzy left ( right, bi-, interior) ideal, (∈,∈⋁,q<inf>(λ,μ)</inf>)- fuzzy left (right, bi-, interior) ideal are given. Meanwhile, we obtain the equivalent connection between them and discuss some algebraic properties of them. Finally, we give the properties of the homomorphic image and homomorphic preimage of (∈,∈⋁q<inf>(λ,μ)</inf>)- fuzzy ideal.

Rough Lattices

We introduced rough sets into lattices. The concepts of upper and lower approximations of a subset in a lattice are given. We discussed the properties of θ??(A)and θ_(A) when A is a sublattice, an ideal, a prime ideal and a convex sublattice of L.