The aim of this article is to lay a foundation for providing a soft algebraic tool in considering many problems that contain uncertainties. In order to provide these soft algebraic structures, the notion of union-soft sets is introduced, and its application to BCK/BCI-algebras is considered. The notions of union-soft algebras, union-soft (commutative) ideals and closed union-soft ideals are int...

In this paper, we introduce the concept of interval valued fuzzy weak bi-ideals of $Gamma$-near-rings, which is a generalized concept of fuzzy weak bi-ideals of $Gamma$- near-rings. We also characterize some properties and examples of interval valued fuzzy weak bi-ideals of $Gamma$-near-rings.

Processing of the certain information, especially inferences based on certain information. Is based on classical two-valued logic. Due to strict and complete logical foundation (classical logic), making inference levels. Thus, it is natural and necessary to attempt to establish some rational logic system as the logical foundation for uncertain information processing. It is evident that this kin...

The purpose of this paper is to construct a weak hyper semi-quantale as a generalization of the concept of semi-quantale and used it as an appropriate hyperlattice-theoretic basis to formulate new lattice-valued topological theories. Based on such weak hyper semi-quantale, we aim to construct the notion of a weak hypervalued-topology as a generalized form of the so-called lattice-valued t...

Many authors studied the graph theory in connection with commutative semigroups and commutative and noncommutative rings as we can refer to references. For example, Beck 1 associated to any commutative ring R its zero-divisor graph G R whose vertices are the zero-divisors of R including 0 , with two vertices a, b joined by an edge in case ab 0. Also, DeMeyer et al. 2 defined the zero-divisor gr...

Seok-Zun Song 1,* ID , Florentin Smarandache 2 and Young Bae Jun 3 1 Department of Mathematics, Jeju National University, Jeju 63243, Korea 2 Department of Mathematics & Science, University of New Mexico, 705 Gurley Ave., Gallup, NM 87301, USA; [email protected] 3 Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea; [email protected] * Correspondence: sz...