A novel approach to soft set theory in decision-making under uncertainty

Soft set is a generic mathematical tool for dealing with uncertainty. That is why, the soft set theory has drawn attention from many researchers particularly for dealing with uncertainty in decision-making problems. However, the fact that the membership degrees of the elements belonging to the universe set in the theory are expressed only with 0 or 1 makes it difficult to express the uncertainty in the most accurate way. In this study, in order to solve this problem, the concepts of relational membership function and inverse relational membership function were defined and some related properties were studied. In addition, using these new concepts in soft set theory, some new technical formulations have been given and algorithms for decision-making under uncertainty are proposed. Finally, these algorithms were analysed comparatively and the differences from previously proposed algorithms was clearly stated.