A mathematical programming-based method for heterogeneous multicriteria group decision analysis with aspirations and incomplete preference information

- A descriptive MCGDM framework considering heterogeneous inputs and multiple preference information is presented.
- A bi-objective intuitionistic fuzzy programming model is developed to identify the importance and interaction of criteria.
- A parametric mix integer nonlinear programming model is proposed to aggregate the individual rankings into a group one.
- A sensitivity analysis and a comparison analysis are performed to demonstrate the advantages of the proposed method.

Aspirations, which serve as a performance target and simplify cognitive processes associated with decision making, are an important decision factor for individuals and organizations. However, this factor is usually ignored in traditional multicriteria decision making. This paper considers a multicriteria group decision making problem with aspirations and incomplete preference information, in which criteria values and aspirations accept multiple formats. To solve this problem, new consistency and inconsistency indices considering importance and interaction as well as aspirations of criteria are defined. Then, we propose a bi-objective intuitionistic fuzzy programming model to identify importance and interaction parameters, based on which, an individual ranking of alternatives can be elicited. Next, to elicit a group ranking of individuals, a flexible mix 0-1 nonlinear programming model of minimizing the inconsistencies between the group final ranking and the individual ranking is established by comprehensively considering both the majority and the minority principles. Finally, an example of selecting the best strategic freight forwarder is used to illustrate the feasibility of the proposed method, followed by a sensitivity analysis and a comparison analysis. The prominent advantages of the developed method are its ability to handle multiple preference information characterizing bounded rationality and nonadditive behaviors of decision makers as well as improve a cardinal inputs-based group decision making model.