Multiple criteria decision analysis using a likelihood-based outranking method based on interval-valued intuitionistic fuzzy sets

The purpose of this paper is to develop a likelihood-based outranking method for handling multiple criteria decision analysis problems based on interval-valued intuitionistic fuzzy sets. Using the concept of likelihood of the interval-valued intuitionistic fuzzy preference relations, this paper determines certain generalized criteria and the corresponding likelihood-based preference functions. Based on some useful concepts of comprehensive preference indices, concordance indices, counter-likelihood-based preference functions, and discordance indices, this paper conducts a concordance–discordance analysis with concordance and discordance outranking relationships to determine a global Boolean matrix and acquire partial ranking orders of the alternatives. Alternatively, this paper determines complete ranking orders of the alternatives using the concepts of net concordance indices, net discordance indices, and mean outranking values. The feasibility and applicability of the proposed method are illustrated with a practical multiple criteria decision-making application concerning the selection of a suitable bridge construction method. Finally, comparative discussions with different decision-making methods are conducted to verify the effectiveness and advantages of the proposed method in aiding decision making.