Abstract
Interval-valued fuzzy soft decision making problems have obtained great popularity recently. Most of the current methods depend on level soft set that provide choice value of alternatives to be ranked. Such choice value always encounter the equal condition that the optimal alternative can’t be gained. Most important of all, the current decision making procedure is not in accordance with the way that the decision makers think about the decision making problems. In this paper, we initiate a new axiomatic definition of interval-valued fuzzy distance measure and similarity measure, which is expressed by interval-valued fuzzy number (IVFN) that will reduce the information loss and keep more original information. Later, the objective weights of various parameters are determined via grey system theory, meanwhile, we develop the combined weights, which can show both the subjective information and the objective information. Then, we present three algorithms to solve interval-valued fuzzy soft decision making problems by Multi-Attributive Border Approximation area Comparison (MABAC), Evaluation based on Distance from Average Solution (EDAS) and new similarity measure. Three approaches solve some unreasonable conditions and promote the development of decision making methods. Finally, the effectiveness and feasibility of approaches are demonstrated by some numerical examples.