Soft Classes and Soft Rough Classes with Applications in Decision Making

Abstract

Rough set was defined by Pawlak in 1982. Concept of soft set was proposed as a mathematical tool to cope with uncertainty and vagueness by Molodtsov in 1999. Soft sets were combined with rough sets by Feng et al. in 2011. Feng et al. investigated relationships between a subset of initial universe of soft set and a soft set. Feng et al. defined the upper and lower approximations of a subset of initial universe over a soft set. In this study, we firstly define concept of soft class and soft class operations such as union, intersection, and complement. Then we give some properties of soft class operations. Based on definition and operations of soft classes, we define lower and upper approximations of a soft set. Subsequently, we introduce concept of soft rough class and investigate some properties of soft rough classes. Moreover, we give a novel decision making method based on soft class and present an example related to novel method.