Similarity measure on incomplete imprecise interval information and its applications

The concept of fuzzy numbers has been generalized to intuitionistic fuzzy interval numbers (IFINs) to solve problems with imprecision in the information modeling. Similarity measure is an important tool to measure the degree of resemblance between any two objects in real-life situations and is applied in many areas such as decision making, image processing, pattern recognition, etc. In this paper, a new distance-based similarity measure between IFINs is proposed using which a similarity measure on incomplete imprecise interval information is attempted. Some properties of the proposed distance measure and similarity measure are studied using illustrative examples. The nominal decreasing and increasing properties based on the proposed distance measure and similarity measure are proved. Further, the superiority of the proposed similarity measure over familiar existing methods is shown by different numerical examples and the proposed measure is applied to technique for order preference by similarity to ideal solution method under interval-valued intuitionistic fuzzy environment. Finally, the applicability of the proposed method in pattern recognition problems is illustrated.