In this paper completely simple semigroups or generalized groups are considered. We characterize generalized groups which are normal generalized groups. Homomorphisms of generalized groups are considered. Equivalent conditions for the kernel of a homomorphism are deduced. We prove that the group components of a generalized group have the same cardinality. We also prove that if G is a finite nor...

athemat s.2012.1 Abstract Rough set theory is a powerful mathematical tool for dealing with inexact, uncertain or vague information. The core concept of rough set theory are information systems and approximation operators of approximation spaces. In this paper, we define and investigate three types of lower and upper multiset approximations of any multiset. These types based on the multiset bas...

A mathematical procedure used to convert an element in the universe of discourse into the membership value of the fuzzy set is termed as fuzzification. In this paper we propose a new technique Vague-Fuzzification to implement fuzzification using vague sets. The proposed technique is designed that is using two methods to implement the same. First method includes a positive ordered transforming f...

Various attempts have been made by researchers on the study of vagueness of data through intuitionistic fuzzy sets and vague sets, and also it was shown that vague sets are intuitionistic fuzzy sets. But there are algebraic and graphical differences between vague sets and intuitionistic fuzzy sets. In this paper an attempt is made to define the correlation coefficient of interval vague sets lyi...

advance a modern extension formation of cubic vague sets identified as interval (CIVSs). similarly describe the idea (ICIVSs) (ECIVSs) by examples debate their exciting properties, excluding ICIVSs ECIVSs - . Additionally, show ( ECIVSs) necessity not be an ICIVS (or ECIVS). apply (CIVS) to topological spaces and present spaces. Further, we introduce P-cubic space R-cubic space. We discuss basi...

In this paper, a general expression of the Shapley value for fuzzy games on vague sets is proposed, where the player participation levels are vague sets. The existence and uniqueness of the given Shapley value are showed by establishing axiomatic system. When the fuzzy games on vague sets are convex, the given Shapley value is a vague population monotonic allocation function (VPMAF) and an elem...

let $g$ be a finite $p$-soluble group‎, ‎and $p$ a sylow $p$-sub-group of $g$‎. ‎it is proved‎ ‎that if all elements of $p$ of order $p$ (or of order ${}leq 4$ for $p=2$) are‎ ‎contained in the $k$-th term of the upper central series of $p$‎, ‎then the $p$-length of‎ ‎$g$ is at most $2m+1$‎, ‎where $m$ is the greatest integer such that‎ $p^m-p^{m-1}leq k$‎, ‎and the exponent of the image of $p$...

In this paper, we introduce the notions of product vague graph, balanced product vague graph, irregularity and total irregularity of any irregular vague graphs and some results are presented. Also, density and balanced irregular vague graphs are discussed and some of their properties are established. Finally we give an application of vague digraphs.