Measures of separation for interval-valued intuitionistic fuzzy sets and their applications

The interval-valued intuitionistic fuzzy set (IVIFS), which is an extension of the intuitionistic fuzzy set (IFS), characterizes the membership and non-membership degree with the number of intervals. This paper begins with an introduce to order relation, which is embedding. Based on the embedding, we have proposed a separation measure for intervals, and used the coimplication function and interval width to construct it. Then, considering epistemic interpretation of IVIFSs, we generalized the measure of the interval values to IVIFS, and obtained the IVI-separation measure, which can compare the accuracy of two elements on IVIFSs. At the same time, a special construction method was provided based on aggregate functions. Finally, we studied the separation measure of intersection, union, and complement operations on IVIFSs.