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

Abstract

The main objective of the present study is to point to the 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 (i.e., between true and false) or unknown. This extension of soft set approach allows a more intuitive and clearer representation of various decision-making problems involving incomplete or uncertain information. In other words, it is a viable approach to analyze soft-set-based multi-criteria-group decision-making problems in the absence of adequate information resulting from the inability to determine the data. In this regard, this study introduced the concept of three-valued soft set and some of its operations and products. In addition, the formulas required to calculate all possible choice values were proposed for each object in the (weighted) three-valued soft sets and their respective decision values were calculated. Both Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) and ELimination Et Choice Translating REality (ELECTRE) methods were modified to deal with multi-criteria group decision problems and then, three-valued soft-set-based decision-making algorithms were constructed. To demonstrate the practicality of these algorithms, the examples adopted from the decision problems in real life were addressed. Lastly, some aspects of the efficiency of the proposed algorithms were discussed using computational experiments.