Mustafa Uçkun

INTUITIONISTIC FUZZY SETS IN GAMMA-SEMIGROUPS

We consider the intuitionistic fuzzification of the concept of several -ideals in a -semigroup S, and investigate some properties of such -ideals.

ON PRIME GAMMA-NEAR-RINGS WITH DERIVATIONS

Abstract. Conditions for a i-near-ring to be commutative areinvestigated. 1. IntroductionFor preliminary deflnitions and results related to near-rings, we referto Pilz [11]. The notion of a i-ring, a concept more general than a ring,was deflned by Nobusawa [8]. Barnes [1] weakened the conditions slightlyin the deflnition of i-ring in the sense of Nobusawa. Barnes [1], Kyuno[6], Luh [7] and Ozturk˜ (together with Jun) [9] studied the structure of˜i-rings and obtained various generalizations analogous to correspond-ing parts in ring theory. As a generalization of near-rings, i-near-ringswere deflned by Satyanarayana [13]. Recently, Booth, Groenewald andSatyanarayana studied several aspects in i-near-rings (see [2], [3], [12],[13], [14]). Also the third author (together with Cho and Kim) intro-duced the notion of i-derivations in i-near-rings and investigated basicproperties (see [4], [5]). In this paper, we investigate some conditionsfor a i-near-ring to be commutative.2. PreliminariesAll near-rings considered in this paper are left distributive. A i-

Klee-Phelps convex groupoids

Abstract We prove that a pair of proximal Klee-Phelps convex groupoids A(∘), B(∘) in a finite-dimensional normed linear space E are normed proximal, i.e., A(∘) δ B(∘) if and only if the groupoids are normed proximal. In addition, we prove that the groupoid neighbourhood Nz(∘) ⊆ Sz(∘) is convex in E if and only if Nz(∘) = Sz(∘).

Near Groups of Weak Cosets on Nearness Approximation Spaces

In this paper, we consider the problem of how to establish algebraic structures of near sets on nearness approximation spaces. Essentially, our approach is define the near group of all weak cosets by considering an operation on the set of all weak cosets. Afterwards, our aim is to study near homomorphism theorems on near groups, and investigate some properties of near groups.