Algorithms for interval-valued fuzzy soft sets in stochastic multi-criteria decision making based on regret theory and prospect theory with combined weight

This paper presents two novel interval-valued fuzzy soft set approaches. First, we initiate a new axiomatic definition of interval-valued fuzzy distance measure, which is expressed by interval-valued fuzzy number (IVFN) that will reduce the information loss and remain more original information. Then, the objective weights of various parameters are determined via normal distribution. Combining objective weights with subjective weights, we present the combined weights, which can reflect both the subjective considerations of the decision maker and the objective information. Later, we propose two algorithms to solve stochastic multi-criteria decision making problem, which take regret aversion and prospect preference of decision makers into consideration in the decision process. Finally, the effectiveness and feasibility of two approaches are demonstrated by two numerical examples.