Some novel Dice similarity measures for picture fuzzy sets and their applications

The similarity measures, as an important tool for assessing the similarity between picture fuzzy sets, have attracted the attention of numerous scholars and achieved rich achievements. Although existing similarity measures have exhibited their unique research contributions, they still fail to distinguish between highly similar but different picture fuzzy sets. This phenomenon poses a major challenge in applications, limiting our ability to make accurate judgments in scenarios that necessitate meticulous differentiation of picture fuzzy sets. Furthermore, the current research focuses on proposing individual and specific calculation formulas, particularly in the realm of Dice similarity measures. However, the systematic, uniform construction of Dice similarity measures remains mostly untapped. The main objective of this article is to propose a method for constructing Dice similarity measures. Through this approach, we can not only integrate existing Dice similarity measures into a unified framework, but also generate novel similarity measures. Firstly, we introduce a function that satisfies specific conditions as the basis for constructing Dice similarity measures. Secondly, by selecting different functions, we obtain various similarity measures. Finally, we propose the pattern recognition algorithm, the face recognition algorithm and the cluster analysis algorithm, all based on the proposed similarity measures. These algorithms are then applied to various fields, including pattern recognition, face recognition, and clustering analysis. Experimental results demonstrate that the proposed similarity measures not only compensate for the shortcomings of existing similarity measures but also exhibit high reliability and practicality, offering a powerful new tool for research and applications in related fields.