Linguistic value soft set-based approach to multiple criteria group decision-making

Molodtsov's soft set theory provides a general mathematical tool for dealing with uncertainty in decision-making. In the past few years, a large number of generalized soft set concepts and approaches to decision-making have been studied by many researchers. This paper considers a new generalization of Molodtsov's soft set concept, named linguistic value soft set, by introducing a linguistic variable to the definition of soft set theory. Then, the information in several soft sets can be saved in one linguistic value soft set. We define basic notions such as the equality of two linguistic value soft sets, and the subsets and complement of a linguistic soft set. Next, we present the binary operations for linguistic value soft set theory. Then, we discuss the properties of linguistic value soft set for the basic notions and binary operations. Further, we define the concept of linguistic value soft matrix and choice value matrix of a linguistic value soft set, and we discuss the operation laws. By using these new definitions of linguistic value soft set theory, we establish a new approach to multiple criteria group decision-making problems with linguistic value information. We present a detailed description of the decision-making problem and the decision steps. Finally, the validity of the proposed decision-making method is tested by a numerical example with the background of an evaluation decision problem for automobiles. The main contribution of this paper is twofold. One is to propose the concept of linguistic value soft set and establish the main results of the theoretical aspect for the new generalization form. Another is to present a new approach to multiple attribute group decision-making based on linguistic value soft set.