Nonlinear Assignment-Based Methods for Interval-Valued Intuitionistic Fuzzy Multi-Criteria Decision Analysis with Incomplete Preference Information

In the context of interval-valued intuitionistic fuzzy sets, this paper develops nonlinear assignment-based methods to manage imprecise and uncertain subjective ratings under incomplete preference structures and thereby determines the optimal ranking order of the alternatives for multiple criteria decision analysis. By comparing each interval-valued intuitionistic fuzzy number's score function, accuracy function, membership uncertainty index, and hesitation uncertainty index, a ranking procedure is employed to identify criterion-wise preference of alternatives. Based on the criterion-wise rankings and a set of known but incomplete information about criterion weights, a nonlinear assignment model is constructed to estimate criterion weights and to order the priority of various alternatives. Considering multiple criteria evaluation problems with preference conflict about criterion importance, an integrated nonlinear programming model is further established with regard to incomplete and inconsistent weight information. These proposed nonlinear assignment-based methods can obtain an aggregate ranking that effectively combines the relative performance of each alternative in each criterion. In addition, this overall ranking most closely agrees with the criterion-wise rankings. Finally, the feasibility of the proposed method is illustrated by a practical example of selecting a suitable bridge construction method.