Similarity measure for intuitionistic fuzzy sets and its applications in pattern recognition and multimodal medical image fusion.

Intuitionistic fuzzy similarity measures (IFSMs) play a significant role in applications involving complex decision-making, pattern recognition, and image processing. Several researchers have introduced different methods of IFSMs, yet these IFSMs fail to provide rational decisions. Therefore, in this research, we present a novel IFSM by considering the global maximum and the minimum differences in membership, non-membership, and hesitancy degrees between two intuitionistic fuzzy sets (IFSs). We show that the proposed IFSM meets the fundamental properties and provide numerical examples to prove its superiority. We implement it to solve pattern recognition problems and demonstrate its applicability and feasibility by using the parameter 'degree of confidence' as a performance index. Additionally, an image fusion method using the proposed IFSM is developed in this work. To construct an image fusion algorithm, initially, we employ a two-layer decomposition method based on Gaussian filtering to the source images of different modalities to decompose them into the base subimages and the detailed subimages. Then, we use the proposed IFSM to extract the features of base subimages and define two fusion rules to fuse the base subimages and detailed subimages. Then, we show the applicability of this method by conducting extensive experiments using three different types of medical image datasets. We evaluated the effectiveness of the proposed image fusion method using six metrics: Mean, Standard Deviation, feature mutual information, Spatial Frequency, Average Gradient, and Xydeas. Experimental results reveal that the proposed IFSM and fusion approach achieve superior performance compared to most existing methods.