Three-valued soft set and its multi-criteria group decision making via TOPSIS and ELECTRE

The purpose of this paper is to introduce a generalization of Molodtsov's approach to soft sets obtained by passing from the classical two-valued logic underlying those sets to a three-valued logic, where the third truth value can usually be interpreted as either non-determined or unknown. This extension of soft set approach allows for more intuitive and clearer representation of various decision making problems involving incomplete or uncertain information. In other words, it is a useful way to analyze soft set based multi-criteria group decision making problems under the lack of information resulting from the inability to determine the data. In this paper, we introduce the concept of three-valued soft set and its some basic operations and products. We propose the formulas to calculate all possible choice values for each object in the (weighted) three-valued soft sets, and thus calculate their respective decision values. By modifying the TOPSIS and ELECTRE methods to deal with multi-criteria group decision problems, three-valued soft set based decision making algorithms are constructed. To demonstrate the practicality of these algorithms, we address the outstanding examples adapted from the decision problems in real-life. Lastly, some aspects of the efficiency of the proposed algorithms are discussed with computational experiments.