An inclusion comparison approach for multiple criteria decision analysis based on interval-valued intuitionistic fuzzy sets

Abstract: The theory of interval-valued intuitionistic fuzzy sets provides an intuitive and feasible way of addressing uncertain and ambiguous properties. Many useful models and methods have been developed for multiple criteria decision analysis within the interval-valued intuitionistic fuzzy environment. In contrast to the elaborate existing methods, this paper establishes a simple and effective method for managing the sophisticated data expressed by interval-valued intuitionistic fuzzy sets. An inclusion comparison possibility defined on interval-valued intuitionistic fuzzy sets is proposed, and some important properties are investigated. Then, an inclusion-based index that considers positive and negative ideals is offered. Considering the maximal comprehensive inclusion-based indices, this paper constructs a linear programming model (for consistent information) and an integrated, nonlinear programming model (for inconsistent information) to estimate the criterion weights and the optimal ranking order of the alternatives under an incomplete preference structure. The feasibility of the proposed method is illustrated by a practical example of selecting a suitable bridge construction method, and a comparative analysis with other relevant methods is conducted to validate the effectiveness and applicability of the proposed methodology.