A Method of Uncertainty Measurements for Multidimensional Z-number and Their Applications

Abstract

Z-number provides the reliability of evaluation information, and it is widely used in many fields. However, people usually describe things from various aspects, so multidimensional Z-number has more advantages over traditional Z-number in describing evaluation information. In view of the uncertainty of the multidimensional Z-number, the entropy of multidimensional Z-number is defined and an entropy formula of multidimensional Z-number is established. Furthermore, the entropy is used to construct an average operator of multidimensional Z-numbers. In addition, a novel distance measure is introduced to measure the distance between two multidimensional Z-numbers. Moreover, the group decision model in the multidimensional Z-number environment is constructed by combining the average operator with the TOPSIS decision-making method. Finally, an illustrative example is given to verify the feasibility and effectiveness of the proposed method.

A new decision making method based on Z-decision-making trial and evaluation laboratory and ordered weighted average and its application in renewable energy source investment

“…The uncertainty of information in the RES investment decision process attributes to the subjectivity of domain experts and the complexity of the evaluation objects. The existing methods for dealing with uncertain information are fuzzy set theory (Bilgili et al, 2022;Van Thanh, 2022;Saraswat and Digalwar, 2021), grey theory (Wang C.-N. et al, 2021;Almutairi et al, 2022), Dempster-Shafer (D-S) evidence theory (Deng and Jiang, 2020;Xiong et al, 2021;Xiao, 2021), Dnumber theory (Deng and Jiang, 2019b,a), and Z-number theory (Rathore et al, 2021;Tian and Kang, 2020;Li et al, 2020;Jiang et al, 2020). Among them, Z-number can represent the uncertainty and the reliability of evaluating information simultaneously (Hu and Lin, 2022;Cheng et al, 2022;Tian et al, 2021;Meng et al, 2022b), which is superior in the modeling of uncertainties in RES investment.…”