A two-stage acceptable hesitancy based goal programming framework to evaluating missing values of incomplete intuitionistic reciprocal preference relations

- Propose geometric consistency of incomplete intuitionistic reciprocal preference relations (IRPRs).
- Develop a goal programming model by minimizing inconsistency of the completed IRPRs.
- Develop a goal programming model to find the most fitting optimal solution.
- Devise a weighted cross ratio uninorm based method to aggregate individual IRPRs.

There exist two main types of uncertainty for an intuitionistic reciprocal preference relation (IRPR). One is inconsistency among pairwise intuitionistic judgments, and the other is vagueness and incompleteness of judgments. It is important to capture and control uncertainty or hesitancy of the obtained results for evaluating missing values of incomplete IRPRs. In this paper, we put forward geometric consistency of incomplete IRPRs. A two-stage procedure comprising two goal programming models is developed to evaluate missing values of an incomplete IRPR. The first goal programming model is devised to minimize the inconsistency level of the resulting complete IRPR and control ratio-based hesitation indices of the evaluated intuitionistic judgments within a given acceptable threshold. The second goal programming model aims to seek the most fitting evaluation values in the sense of maintaining the inconsistency level derived by the first model. By applying the developed evaluation model and introducing a weighted AND-like representable Cross Ratio uninorm-based aggregation method, a procedure is then presented for solving group decision making problems with incomplete IRPRs. Three numerical examples including a comparative study are examined to illustrate the advantage and applicability of the developed framework.