In this work, we introduce an intuitionistic fuzzy ideal on a KU-semigroup as a generalization of the fuzzy ideal of a KU-semigroup. An intuitionistic fuzzy k-ideal and some related properties are studied. Also, a number of characteristics of the intuitionistic fuzzy k-ideals are discussed. Next, we introduce the concept of intuitionistic fuzzy k-ideals under homomorphism along with the Cartesian products.

We have studied some types of ideals in a KU-semigroup by using the concept of a bipolar fuzzy set. Bipolar fuzzy S-ideals and bipolar fuzzy k-ideals are introduced, and some properties are investigated. Also, some relations between a bipolar fuzzy k-ideal and k-ideal are discussed. Moreover, a bipolar fuzzy k-ideal under homomorphism and the product of two bipolar fuzzy k-ideals are studied.

In this paper, the definition of fuzzy anti-inner product in a linear space is introduced. Some results of fuzzy anti-inner product spaces are given, such as the relation between fuzzy inner product space and fuzzy anti-inner product. The notion of minimizing vector is introduced in fuzzy anti-inner product settings.

We introduce the notion of interval value fuzzy ideal of TM-algebra as a generalization of a fuzzy ideal of TM-algebra and investigate some basic properties. Interval value fuzzy ideals and T-ideals are defined and several examples are presented. The relation between interval value fuzzy ideal and fuzzy T-ideal is studied. Abstract We introduce the notion of interval value fuzzy ideal of TM-algebra as a generalization of a fuzzy ideal of TM-algebra and investigate some basic properties. Interval value fuzzy ideals and T- ideals are defined and several examples are presented. The relation between interval value fuzzy ideal and fuzzy T-ideal is studied.

           This paper introduce two types of edge degrees (line degree and near line degree) and total edge degrees (total line degree and total near line degree) of an edge in a fuzzy semigraph, where a fuzzy semigraph is defined as (V, σ, μ, η) defined on a semigraph G^* in which σ : V → [0, 1], μ : VxV → [0, 1] and η : X → [0, 1] satisfy the conditions that for all the vertices u, v in the vertex set,  μ(u, v) ≤ σ(u) ᴧ σ(v) and  η(e) = μ(u₁, u₂) ᴧ μ(u₂, u₃) ᴧ … ᴧ μ(u_n-1, u_n) ≤ σ(u₁) ᴧ σ(u_n), if e = (u₁, u₂, …, u_n), n ≥ 2 is an edge in the semigraph G

The notion of interval value fuzzy k-ideal of KU-semigroup was studied as a generalization of afuzzy k-ideal of KU-semigroup. Some results of this idea under homomorphism are discussed. Also, we presented some properties about the image (pre-image) for interval~ valued fuzzy~k-ideals of a KU-semigroup. Finally, the~ product of~ interval valued fuzzyk-ideals is established.

     Let R1be a commutative2ring with identity and M be a unitary R-module. In this6work we7present almost pure8ideal (submodule) concept as a9generalization of pure10ideal (submodule).  lso, we1generalize some9properties of8almost pure ideal (submodule). The 7study is almost regular6ring (R-module).

     In this paper, we shall investigate and study some kinds of ideals in an intuitionistic fuzzy setting, they are called complete intuitionistic fuzzy subalgebra, complete intuitionistic fuzzy ideal, and complete intuitionistic fuzzy ideal. In this study, we have also proposed some hypotheses to explain some of the relationships between these kinds of intuitionistic fuzzy ideals.

    Let R be a commutative ring with identity. A proper ideal I of R is called semimaximal if I is a finite intersection of maximal ideals of R. In this paper we fuzzify this concept to fuzzy ideals of R, where a fuzzy ideal A of R is called semimaximal if A is a finite intersection of fuzzy maximal ideals. Various basic properties are given. Moreover some examples are given to illustrate this concept.

        Zadah in [1] introduced the notion of a fuzzy subset A of a nonempty set S as a mapping from S into [0,1], Liu in [2] introduced the concept of a fuzzy ring, Martines [3] introduced the notion of a fuzzy ideal of a fuzzy ring.         A non zero proper ideal I of a ring R is called an essential ideal if I  J  (0), for any non zero ideal J of R, [4].         Inaam in [5] fuzzified this concept to essential fuzzy ideal of fuzzy ring and gave its basic properties.         Nada in [6] introduced and studied notion of semiessential ideal in a ring R, where a non zero i