A novel parameter similarity measure between interval-valued picture fuzzy sets with its application in pattern recognition

As an extension of picture fuzzy sets (PFSs), interval-valued picture fuzzy sets (IVPFSs) can better model and handle incomplete, indeterminate and inconsistent information in some practical applications. One of the important topics in IVPFSs is the similarity measure of IVPFSs, for which few studies have been proposed within the literature. Moreover, some existing similarity measures cannot adequately meet the conditions of similarity measure with some counterintuitive cases. In this work, we devise a novel similarity measure between IVPFSs based on the effect of the margin of the degree of refusal membership. First, the interval-valued picture fuzzy numbers will be transformed into two right-angled triangular-based pyramids in a spatial rectangular coordinate system. Then, a new parameter distance measure for IVPFSs is defined to assess the similarity between IVPFNs according to the centers of gravity of their corresponding right-angled triangular-based pyramids. Meanwhile, a comparison between different similarity measures is performed to illustrate that the proposed similarity measure can overcome the deficiencies of other extant measures. Finally, we apply it to handle pattern recognition problems. The comparison results indicate that the proposed algorithm can adequately meet the conditions of similarity measure, produce more reasonable and creditable results and perform well in complex contexts.