A Certain Structure of Bipolar Fuzzy Subrings

The role of symmetry in ring theory is universally recognized. The most directly definable universal relation in a symmetric set theory is isomorphism. This article develops a certain structure of bipolar fuzzy subrings, including bipolar fuzzy quotient ring, bipolar fuzzy ring homomorphism, and bipolar fuzzy ring isomorphism. We define (α,β)-cut of bipolar fuzzy set and investigate the algebraic attributions of this phenomenon. We also define the support set of bipolar fuzzy set and prove various important properties relating to this concept. Additionally, we define bipolar fuzzy homomorphism by using the notion of natural ring homomorphism. We also establish a bipolar fuzzy homomorphism between bipolar fuzzy subring of the quotient ring and bipolar fuzzy subring of this ring. We constituted a significant relationship between two bipolar fuzzy subrings of quotient rings under a given bipolar fuzzy surjective homomorphism. We present the construction of an induced bipolar fuzzy isomorphism between two related bipolar fuzzy subrings. Moreover, to discuss the symmetry between two bipolar fuzzy subrings, we present three fundamental theorems of bipolar fuzzy isomorphism.

Dual Pairs of Matroids with Coefficients in Finitary Fuzzy Rings of Arbitrary Rank

Infinite matroids have been defined by Reinhard Diestel and coauthors in such a way that this class is (together with the finite matroids) closed under dualization and taking minors. On the other hand, Andreas Dress introduced a theory of matroids with coefficients in a fuzzy ring which is – from a combinatorial point of view – less general, because within this theory every circuit has a finite intersection with every cocircuit. Within the present paper, we extend the theory of matroids with coefficients to more general classes of matroids, if the underlying fuzzy ring has certain properties to be specified.

OPERATOR ⊞A and ⊠A ON INTUITIONISTIC FUZZY RING

Intuitionistic fuzzy sets is a sets that are characterized by membership and non-membership function which sum is less than one. When applied to ring theory, it will called intuitionistic fuzzy rings. The fuzzy set operator is a mapping between the membership function and the interval [0,1]. In this study, we will describe properties of operator and in intuitionistic fuzzy rings. The characteristics that will be studied include the structure of and if A is an intuitive and fuzzy ring and vice versa.

STRUKTUR IMAGE DAN PRE-IMAGE HOMOMORFISMA PADA TRANSLASI RING FUZZY INTUITIONISTIK

A set that is characterized by membership function and a non-membership function with the sum of both at intervals of 0 to 1 is called intuitionistik fuzzy set.. When it’s applied in ring’s theory, it will called intuitionistic fuzzy ring. In this research,if the topics is membership fuction and non-membership function then there are translates operator. This operator only changes the values of the membership and non-membership function while the properties are fixed. This journal discussed the structure of image ad pre-image homomorphism of translates on intuitionistic fuzzy rings. The result obtained that the structure of image and pre-image is also intuitionistic fuzzy rings. Full Article

Some Results on Fuzzy Topological Modules and Fuzzy Topological Submodules

In this paper, we bring together the structure of fuzzy topological space ,fuzzy module and that of fuzzy ring to form a combined structure, that of a fuzzy topological R-module. Properties of fuzzy topological R-module ,topological R-submodule and its Properties are also briefly examined. we proved many theorems and corollaries as results shown in this paper.

FUZZY RINGS AND ITS PROPERTIES

One of algebraic structure that involves a binary operation is a group that is defined an un empty set (classical) with an associative binary operation, it has identity elements and each element has an inverse. In the structure of the group known as the term subgroup, normal subgroup, subgroup and factor group homomorphism and its properties. Classical algebraic structure is developed to algebraic structure fuzzy by the researchers as an example semi group fuzzy and fuzzy group after fuzzy sets is introduced by L. A. Zadeh at 1965. It is inspired of writing about semi group fuzzy and group of fuzzy, a research on the algebraic structure of the ring is held with reviewing ring fuzzy, ideal ring fuzzy, homomorphism ring fuzzy and quotient ring fuzzy with its properties. The results of this study are obtained fuzzy properties of the ring, ring ideal properties fuzzy, properties of fuzzy ring homomorphism and properties of fuzzy quotient ring by utilizing a subset of a subset level and strong level as well as image and pre-image homomorphism fuzzy ring. Keywords: fuzzy ring, subset level, homomorphism fuzzy ring, fuzzy quotient ring

P-F Fuzzy Rings and Normal Fuzzy Ring

In 1965, Zadeh introduced the concept of fuzzy subset. Since that time many papers were introduced in different mathematical scopes of theoretical and practical applications. In 1982, Liuformulated the term of fuzzy ring and fuzzy ideal of a ring R. In 2004, Hadi and Abou-Draeb, introduced and studied P-F fuzzy rings and normal fuzzy rings and now we are complete it. In this chapter, the concepts P-F fuzzy rings and normal fuzzy rings have been investigated. Several basic results related to these concepts have given and studied. The relationship between them has also been given. Moreover, some properties of t-pure fuzzy ideal of a fuzzy ring have been given which need it later.