Possibility Degree Research Articles

Q-ROF-SIR methods and their applications to multiple attribute decision making

q-rung orthopair fuzzy set (q-ROFS) is a useful tool to express uncertain information. With the parameter q increasing, q-ROFSs have broader space for describing uncertain information than intuitionistic fuzzy sets (IFSs) and Pythagorean fuzzy sets (PFSs). This paper extends the superiority and inferiority ranking (SIR) methods to solve multiple attribute decision making (MADM) problems within the q-ROF environment, named q-ROF-SIR methods. In the q-ROF-SIR methods, the possibility degree (PD) for q-rung orthopair fuzzy numbers (q-ROFNs) is introduced to improve the preference intensity. Further, the q-ROF entropy weight (q-ROF-EW) method is constructed to determine the attribute weights suppose the weights of attribute are unknown. Finally, the effectiveness and applicability of the q-ROF-SIR methods are verified.

2-Dimension linguistic PROMETHEE methods for multiple attribute decision making

In multiple attribute decision making (MADM) problems, 2-dimension linguistic term set (2DLTS) is useful for modelling both the linguistic evaluations on alternatives and the decision makers’ self-assessments. This paper extends the preference ranking organization method for enrichment evaluations (PROMETHEE) methods to solve 2-dimension linguistic MADM problems. The extended PROMETHEE methods with 2DLTSs are mainly based on the improvement of the preference functions. For measuring two 2-dimension linguistic elements (2DLEs) in the improved preference functions, the possibility degree (PD) for 2DLEs is proposed to describe the PD of one 2DLE no less than another. It is shown that the PD for 2DLEs can measure the PD between two incomparable 2DLEs as well as two comparable 2DLEs. Furthermore, two examples are given to illustrate the effectiveness and flexibility of the proposed methods in solving the MADM problems evaluated by 2DLEs.