Developing a TOPSIS algorithm for Q-rung orthopair Z-numbers with applications in decision making

No decision can be made without first taking the decision-making process into consideration. Multi-criteria decision-making (MCDM) seeks to identify the optimal option by taking into account multiple criteria during the selection process. Numerous tools and techniques from MCDM can be used in a variety of sectors, including engi-neering design and finance. Recently, because of the general-ization ability and more flexibility of Q-rung orthopair fuzzy sets (Q-ROFS), it has been used widely to solve MCDM problems. However, under uncertainty, evaluating an alter-native in the form of Q-ROFS with a full reliability is not always possible. Therefore, in this paper, we have defined the notion of Q-rung orthopair Z-numbers, in which the reli-abilities of an evaluated Q-ROFS have also been considered to make decision-making more comprehensive regarding the uncertainty. Mathematically, a Q-rung orthopair Z-number ZQ=(CQ,RQ) defined on a non-empty finite set X is a pair of two Q-ROFS, where CQ is Q-ROFS defined on X and RQis the reliability of the CQ in the form of Q-ROFS. Further, arithmetic operations on these Z-numbers have been intro-duced. Moreover, a series of dice similarity measures have been defined for Q-rung orthopair Z-numbers. To solve the MCDM problems, a TOPSIS method based on these dis-tance measures has also been discussed. Further, an appli-cation of the proposed method has been studied to solve an industrial problem. Furthermore, a sensitivity analysis of the involved parameters has been done to illustrate the stability and efficiency of the proposed approach. Finally, a case study has been conducted investigating the allocation of healthcare resources, along with a comparative analysis of the outcomes attained using the proposed technique. This analysis intends to demonstrate the proposed method's valid-ity and superiority. Further, it has been shown by numerical experiments that decision-making with Q-ROZN is more suitable since it gives the decision-maker additional freedom in terms of the reliabilities of evaluated Q-ROFS.