A novel decision-making approach based on regret theory under bipolar Z-number information

Abstract This study introduces a new set theory called bipolar fuzzy Z-number set that makes it possible to express an information both bipolar from positive and negative perspectives, and with the reliability of it. Then, besides basic set-theoretical operations and the score function, a new distance measure is also presented. Furthermore, a decision method integrating with regret theory is proposed. Additionally, to compute the weights of criteria under bipolar Z-number information, a method in which objective and subjective criterion weights are considered simultaneously is introduced by combining the weights found by SWARA and MEREC. Also, a model with standard deviation is developed to obtain decision maker’s weights. Finally, the problem of selection of paper raw material is handled to demonstrate stability and advantage of the proposed method.