Roughness in BO/BH/Z-ALGEBRA

TL;DR

This paper introduces rough extensions of BO/BH/Z-algebras, explores set-valued mappings and morphisms within these structures, and investigates generalized approximation concepts based on ideals.

Contribution

It extends classical BO/BH/Z-algebras to rough versions and studies set-valued morphisms and approximation properties within these new algebraic frameworks.

Findings

Defined rough BO/BH/Z-algebras and their properties

Analyzed set-valued BO/BH/Z-morphisms and their characteristics

Developed generalized approximation concepts using ideals

Abstract

The main goal of this paper, present the concepts of rough BO/BH/Z- Algebra as extended of the concept of BO/BH/Z-algebra respectively. The other goal is to consider the (strong) set-valued mapping in these algebraic structures. The concept of a (strong) set-valued BO/BH/Z-morphism in BO/BH/Z algebras is investigated with several properties. Using the concept of generalized approximation space and ideal of BO/BH/Z-algebra, we consider another type of generalized lower and upper approximations based on the ideal. In addition, some properties are studied.