Multiset rough approximations and their generated topologies

Abstract

In this paper, we introduce a generalized framework for multiset neighborhoods, extending the previously defined structures into eight distinct types. Based on these generalized neighborhoods, we define corresponding multiset approximations and construct eight new topologies derived from them. Additionally, we extend six classical types of rough set approximations to the multiset context and investigate their properties in detail. These developments offer a unified and expanded perspective on approximation theory within multiset environments.