Interval-valued intuitionistic fuzzy best-worst method with additive consistency

Best-worst method (BWM) has received extensive attention because of its fewer pairwise comparisons and maintenance of consistency. Extending it to various fuzzy environments has become a hot research spot. This paper initiates a new interval-valued intuitionistic fuzzy (IVIF) BWM with additive consistency. Firstly, an IVIF fuzzy preference relation (IVIFPR) is viewed as a directed graph with IVIF weights. An approach is offered to distinguish the best and worst criteria by the defined score out-degree and accuracy out-degree of criteria. The concept of IVIF reference comparisons is introduced. The additive consistency of IVIF reference comparisons is acquired by that of IVIFPR using its left and right intuitionistic fuzzy preference relations. We derive the rela-tionship between the IVIF reference comparisons and the IVIF priority weight vector. Based on this relationship, a linear goal programming model is constructed to generate the IVIF priority weights. Two consistency indexes are analytically obtained and the consistency ratio is then defined to check the consistency of IVIF reference com-parisons. For the unacceptably additive consistency, a new approach is put forward to enhance the consistency. Thereby, the proposed IVIF BWM is summarized step by step. Three examples of applications are furnished to demonstrate its effectiveness and validation.