The purpose of this paper is to define the fuzzy quotient group by using some special fuzzy relation which is defined in this study and to prove some basic properties. c ©2003 Yang’s Scientific Research Institute, LLC. All rights reserved.

The aim of this paper is to introduce the concepts of fuzzy strong h-ideals and fuzzy congruences of hemirings. The quotient hemirings via fuzzy strong h-ideals are investigated. The relationships between fuzzy congruences and fuzzy strong h-ideals of hemirings are discussed. Pay attention to an open question on fuzzy congruences. Finally, the normal fuzzy strong h-ideals of hemirings are explo...

Bresar in 1993 proved that each biderivation on a noncommutative prime ring is a multiple of a commutatot. A result of it is a characterization of commuting additive mappings, because each commuting additive map give rise to a biderivation. Then in 1995, he investigated biderivations, generalized biderivations and sigma-biderivations on a prime ring and generalized the results of derivations fo...

Let $R$ be a prime ring of characteristic not equal to $2$, $U$ the Utumi quotient and $C$ extended centroid $R$. $G$ $F$ two generalized derivations on $L$ non-central Lie ideal If $F\Big(G(u)\Big)u = G(u^{2})$ for all $u \in L$, then one following holds: (1) $G=0$. (2) There exist $p,q U$ such that $G(x)=p x$, $F(x)=qx$ $x R$ with $qp=p$. (3) satisfies $s_4$.

using the notion of “belongingness ($epsilon$)” and “quasi-coincidence (q)” of fuzzy points with fuzzy sets, we introduce the concept of an ($ alpha, beta$)- fuzzyhv-ideal of an hv-ring, where , are any two of {$epsilon$, q,$epsilon$ $vee$ q, $epsilon$ $wedge$ q} with $ alpha$ $neq$ $epsilon$ $wedge$ q. since the concept of ($epsilon$, $epsilon$ $vee$ q)-fuzzy hv-ideals is an important and ...

In [17] Lee and Shiue showed that if R is a non-commutative prime ring, I a nonzero left ideal of R and d is a derivation of R such that [d(x)x, x]k = 0 for all x ∈ I, where k,m, n, r are fixed positive integers, then d = 0 unless R ∼= M2(GF (2)). Later in [1] Argaç and Demir proved the following result: Let R be a non-commutative prime ring, I a nonzero left ideal of R and k,m, n, r fixed posi...

in this paper, for a complete lattice l, we introduce interval-valued l-fuzzy ideal (prime ideal) of a near-ring which is an extended notion of fuzzy ideal (prime ideal) of a near-ring. some characterization and properties are discussed.

Starting from a unified treatment of uncertainty by combining probability and fuzzy set theory [1], Goodman [2] put forward the equivalence between a fuzzy set and a class of random sets. Falling shadow representation theory was established based on the collection of Wang and Sanchez [3], which is directly related to the concept of probabilistic fuzzy set membership function. The theory shows t...

Let D be an integral domain with quotient field K. The Nagata ring D(X) and the Kronecker function ring Kr(D) are both subrings of the field of rational functions K(X) containing as a subring the ring D[X] of polynomials in the variable X. Both of these function rings have been extensively studied and generalized. The principal interest in these two extensions ofD lies in the reflection of vari...