Interval-valued intuitionistic fuzzy QUALIFLEX method with a likelihood-based comparison approach for multiple criteria decision analysis

QUALIFLEX (i.e., QUALItative FLEXible multiple criteria method) is a useful outranking method used for multiple criteria decision analysis. This paper uses the main structure of QUALIFLEX to develop an interval-valued intuitionistic fuzzy QUALIFLEX outranking method with a likelihood-based comparison approach for handling multiple criteria decision-making problems within a decision environment of interval-valued intuitionistic fuzzy sets. We propose the concept of using the likelihood of fuzzy preference relations to compare interval-valued intuitionistic fuzzy numbers. To address diversiform preference types, we represent the decision-maker's various forms of preference structures and assess the criterion weights using incomplete information. Using a criterion-wise preference of alternatives via comparison of the likelihoods, we develop a new QUALIFLEX-based model to measure the level of concordance of the complete preference order for managing multiple criteria decisions. The feasibility and applicability of the proposed methods are illustrated using a practical example, namely, the selection of a suitable bridge construction method. A comparative analysis with other relevant methods is conducted to validate the effectiveness of the proposed methodology.