Likelihood-based assignment methods for multiple criteria decision analysis based on interval-valued intuitionistic fuzzy sets

The aim of this paper is to develop useful likelihood-based assignment methods for addressing multiple criteria decision-making problems within the environment of interval-valued intuitionistic fuzzy sets. Based on the likelihoods of interval-valued intuitionistic fuzzy preference relations, this paper determines the mean likelihoods of outranking relations and presents a mean likelihood determination method for generating a set of criterion-wise rankings of alternatives. By employing the concepts of rank frequency matrices and (ordinary) rank contribution matrices, this paper establishes a likelihood-based linear assignment model for multiple criteria decision analysis in the interval-valued intuitionistic fuzzy context. Additionally, this paper propounds two likelihood-based assignment models for handling incomplete and conflicting certain information of importance weights. These models can transform the criterion-wise ranks into the overall ranks for determining the optimal priority ranking of the alternatives. The feasibility and applicability of the proposed methods are illustrated with a practical problem of selecting a bridge construction method which involves various preference types. Finally, this paper conducts a comparative analysis with previous assignment-based methods in an interval-valued intuitionistic fuzzy setting to validate the effectiveness and advantages of the proposed methods.