An integrated interval type-2 fuzzy rough technique for emergency decision making

Abstract

This paper aims to develop a hybrid emergency decision-making (EDM) method by combining best–worst method (BWM), multi-attributive border approximation area comparison (MABAC) and prospect theory (PT) in trapezoidal interval type-2 fuzzy rough (TrIT2FR) environment. In this hybrid method, the decision information is represented by trapezoidal interval type-2 fuzzy rough numbers (TrIT2FRNs). Firstly, this paper defines the TrIT2FRN and analyzes its desirable properties. Then, the TrIT2FR-BWM is developed to determine criteria weights. To develop the TrIT2FR-BWM, this paper completes the following three core issues: (i) propose an effective theorem to normalize the TrIT2FR weights; (ii) build a crisp programming model to transform the minmax objective of weight-determining model for the TrIT2FR-BWM; (iii) design a consistency ratio for the TrIT2FR-BWM to check the reliability of the determined criteria weights. Afterwards, this paper extends the classical MABAC into TrIT2FR environment to calculate the border approximation area (BAA). Subsequently, the PT is used to rank the alternatives, in which the calculated BAA is selected as the reference point. Lastly, the validity of the proposed method is certificated with a real site selection case of makeshift hospitals on COVID-19. Sensitivity analysis and comparative analyses are conducted to illustrate the robustness and superiorities of the proposed method. Some valuable results are summarized as follows: (i) the best alternative determined by the proposed method conforms with the actual selection result, (ii) the proposed models in the TrIT2FR-BWM have strong robustness, (iii) PT is helpful to improve the decision quality of EDM.