A graph based group decision making approach with intuitionistic fuzzy preference relations

- Design an algorithm to rank criteria and identify the best and worst criteria.
- Give three new definitions of consistency to check the consistency of the IFPRs.
- Construct some optimization models to derive the weights of the criteria.
- Propose a consistency ratio to evaluate the reliability of the derived weights.
- Provide a decision-making procedure of the IF-BWM.

Intuitionistic fuzzy preference relation (IFPR) is an efficient tool in tackling comprehensive multi-criteria group decision making (MCGDM) problems via pairwise comparisons. Based on the intuitionistic fuzzy analytic hierarchy process (IFAHP) and the best-worst method (BWM), this paper aims to put forward a novel graph-based group decision making approach called the intuitionistic fuzzy best-worst method (IF-BWM) for MCGDM. To achieve this goal, we first aggregate the individual IFPRs provided by the decision makers into a collective IFPR by the intuitionistic fuzzy weighted averaging (IFWA) operator. Afterwards, we draw the directed network according to the collective IFPR, and then design an algorithm to identify the best and worst criteria through computing the out-degrees and in-degrees of the directed network. Furthermore, to derive the weights of criteria, some mathematical models corresponding to the different definitions of consistent IFPR are developed. Finally, the procedure of the IF-BWM is proposed for practical applications and three numerical examples are given to illustrate the approach.

113