2016/01/12 by Waqas Mahmood, Mahmood, Waqas
Computer Science · Mathematics · #08Axx #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Group Theory (math.GR) #Rough Sets and Fuzzy Logic
paper · pdf · doi:10.48550/arxiv.1602.08012
openalex publication_date 2016/01/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The theory of rough sets was firstly introduced by Pawlak (see \citep). Many Mathematician has been studied the relations between rough sets and algebraic systems such as groups, rings and modules. In this paper we will introduce the lower and upper approximations in a quotient group. We will discuss several properties of the lower and upper approximations. Moreover under some additional assumptions we are able to show that the lower approximation is a normal subgroup of the quotient group but this property fails for the upper approximation. At the end we will develop several homomorphisms between lower approximations.