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 ideal I of R is called semiessential if I  P  (0) for all non zero prime ideals of R, [4]. A ring R is called uniform if every ideal of R is essential. Nada in [6] introduced and studied the notion semiuniform ring where a ring R is called semiuniform ring if every ideal of R is semiessential ideal. In this paper we fuzzify the concepts semiessential ideal of a ring, uniform ring and semiuniform ring into semiessential fuzzy ideal of fuzzy ring, uniform fuzzy ring and semiuniform fuzzy ring. Where a fuzzy ideal A of a fuzzy ring X is semiessential if I  P  (0) for any prime fuzzy ideal P of X. A fuzzy ring X is called uniform (semiuniform) if every fuzzy ideal of X is essential (semiessential) respectively. In S.1, some basic definitions and results are collected. In S.2, we study semiesential fuzzy ideals of fuzzy ring, we give some basic properties about this concept. In S.3, we study the notion of uniform fuzzy rings and semiuniform fuzzy rings. Several properties about them are given. Throughout this paper, R is commutative ring with unity, and X(0) = 1, for any fuzzy ring.
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.
Let
be an
module, and let
be a set, let
be a soft set over
. Then
is said to be a fuzzy soft module over
iff
,
is a fuzzy submodule of
. In this paper, we introduce the concept of fuzzy soft modules over fuzzy soft rings and some of its properties and we define the concepts of quotient module, product and coproduct operations in the category of
modules.
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.
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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.
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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.
In this paper, we introduce the concept of almost Quasi-Frobcnius fuzzy ring as a " " of Quasi-Frobenius ring. We give some properties about this concept with qoutient fuzzy ring. Also, we study the fuzzy external direct sum of fuzzy rings.
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.
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.