A Variable Precision Covering-Based Rough Set Model Based on Functions

Abstract

Classical rough set theory is a technique of granular computing for handling the uncertainty, vagueness, and granularity in information systems. Covering-based rough sets are proposed to generalize this theory for dealing with covering data. By introducing a concept of misclassification rate functions, an extended variable precision covering-based rough set model is proposed in this paper. In addition, we define the f-lower and f-upper approximations in terms of neighborhoods in the extended model and study their properties. Particularly, two coverings with the same reductions are proved to generate the same f-lower and f-upper approximations. Finally, we discuss the relationships between the new model and some other variable precision rough set models.

Reliability Evolution of Elevators Based on the Rough Set and the Improved TOPSIS Method

“…Therefore, in the process of evaluating the reliability of elevator equipment, we need to fully consider the interacting factors among indicators, clarify the interrelation among indicators, and build the figure of interrelation among the indicators of the reliability of elevators, which is shown in Figure 1. [6][7][8] Definition 1. Let = ( , , , ) be a knowledge expressing system, where is the universe, is the attribute set, is the attribute-values set, and is the information function.…”

Lattice Structure of Variable Precision Rough Sets

“…Some researchers extended this concept to variable precision covering based rough set model [16][17]. Algebraic properties of rough set have been widely studied by researchers [18][19][20][21][22][23][24]. Algebraic properties of variable precision rough set is discussed in this paper and it could be shown that for different classification error the set of variable precision rough sets have a lattice structure.…”