Ideals Of Hemirings Research Articles

Applications of Soft Union Sets in $$h$$ h -Hemiregular and $$h$$ h - $$Intra$$ I n t r a -hemiregular Hemirings

The aim of this paper is to lay a foundation for providing a soft algebraic tool in considering many problems that contain uncertainties. In order to provide these soft algebraic structures, we introduce the concepts of soft union \(h\)-\(bi\)-ideals and soft union \(h\)-\(quasi\)-ideals of hemirings by means of soft-intersection–union sum and soft-intersection–union product. Some related properties are obtained. Finally, we investigate some characterizations of \(h\)-hemiregular and \(h\)-\(intra\)-hemiregular hemirings using some kinds of soft union \(h\)-ideals.

Interval valued (α, β)-intuitionistic fuzzy ideals in hemirings

In this paper, we introduced the concept interval valued intuitionistic fuzzy point. We combine the concept of an interval valued intutionistic fuzzy set with interval valued intuitionistic fuzzy point, to introduce the notion of an (α, β)-intuitionistic fuzzy sub-hemiring (left, right, two sided) ideal of hemirings, where α, β are any two of {∈ ,q , ∈∨ q, ∈∧ q} with α/ =∈ ∧q. Moreover, we define prime (semiprime) interval valued (α, β)-intuitionistic fuzzy ideals of hemirings and investigate some different properties of these ideals.

Note on \((\lambda, \mu)\)-fuzzy interior ideals of Hemirings.

A definition of \((\lambda ,\mu )\)-fuzzy ideals and \((\lambda ,\mu )\)-fuzzy interior ideals of hemirings are discussed. Some properties of \((\lambda ,\mu )\)-fuzzy interior ideals such that intersection of any two \((\lambda ,\mu )\)-fuzzy interior ideals and the product of two \((\lambda ,\mu )\)-fuzzy interior ideals \((\lambda ,\mu )\)-fuzzy interior ideals, have been discussed. Some other results related to \((\lambda ,\mu )\)-fuzzy interior ideals have been proved.

Falling fuzzy ideals of hemirings

Based on the theory of falling shadows and fuzzy sets, the notion of falling fuzzy ideals of a hemiring is introduced. The relations between fuzzy ideals and falling fuzzy ideals are provided. Finally, we apply the concept of falling fuzzy inference relations to hemirings and obtain an important result.

Proper Fuzzification of Prime Ideals of a Hemiring

Prime fuzzy ideals, prime fuzzyk-ideals, and prime fuzzyh-ideals are roped in one condition. It is shown that this way better fuzzification is achieved. Other major results of the paper are: every fuzzy ideal (resp.,k-ideal,h-ideal) is contained in a prime fuzzy ideal (resp.,k-ideal,h-ideal). Prime radicals and nil radicals of a fuzzy ideal are defined; their relationship is established. The nil radical of a fuzzyk-ideal (resp., anh-ideal) is proved to be a fuzzyk-ideal (resp.,h-ideal). The correspondence theorems for different types of fuzzy ideals of hemirings are established. The concept of primary fuzzy ideal is introduced. Minimum imperative for proper fuzzification is suggested and it is shown that the fuzzifications introduced in this paper are proper fuzzifications.

A new view of fuzzy k-ideals of hemirings

By means of a kind of new idea, we redefine fuzzy k-ideals and fuzzy k-interior ideals of hemirings. Some new characterization theorems of these kinds of fuzzy ideals of a hemiring are also given. In particular, we show that the semiregular hemirings and semisimple hemirings can be described by using some of their generalized fuzzy k-ideals.