A multi-attribute group decision-making algorithm based on soft intervals that considers the priority rankings of group members on attributes of objects, along with some applications

There are a considerable number of studies involving soft sets, the most significant ones focusing on decision-making. In this study, we have developed decision-making algorithms using soft intervals on soft sets, which accounted for the priority order of individuals in situations where multiple people were involved. Soft sets can be considered as a parameterized family of subsets of the universal set; for this reason, soft sets provide an effective tool for evaluating the multiple attributes of objects in decision-making problems. In this study, the parameter set of the soft set was used for the attributes of the objects, while the universal set of the soft set was used for the objects being selected. A soft interval can be considered as a soft set that includes all parameterized subsets of the universal set within the specified boundaries determined by the order on the soft set. In this study, soft intervals were generated from the orderings on a soft set which were based on the users rankings of object attributes. The first algorithm enabled us to obtain the choice object based on the ranking of decision makers with equal influence on the decision, while the second algorithm achieved this for rankings of those with different influences. Both of these seeked to find the most appropriate object by considering the priority rankings of users in scenarios where a joint decision was required and the optimal decision objects were subsequently ranked. The novelty of the proposed algorithm lied in utilizing the new theory of soft sets to select the most suitable object for a group from multi-attribute objects, considering each member's ranking of attributes of objects.