Two-criteria method for comparing real-valued and interval-valued intuitionistic fuzzy values

•Two-criteria method for comparison real valued intuitionistic fuzzy values.•Two-criteria method for comparison and interval valued intuitionistic fuzzy values.•Multiple criteria decision making in the intuitionistic fuzzy setting.

This paper presents a new approach to comparing real-valued and interval-valued intuitionistic fuzzy values. The score and accuracy functions are used to build the “net profit” and “risk” local criteria. These criteria are aggregated in a generalized criterion taking into account their weights, which depend on the risk aversion of a decision maker. In the case of interval-valued intuitionistic fuzzy values, conventional interval arithmetic rules are used and as a result, the interval score and accuracy functions are obtained and used to get an interval estimate of a degree to which an interval-valued intuitionistic fuzzy value is greater/lesser than another one. As opposed to the known methods, a new approach makes it possible to estimate the strength of relations between real-valued and interval-valued intuitionistic fuzzy values. Using some numerical examples, it is shown that the proposed approach provides intuitively clear results. The advantages of proposed method are shown using the realistic example of multiple criteria decision making problem in interval-valued intuitionistic fuzzy environment.