The Generalized Dice Similarity Measures for Picture Fuzzy Sets and Their Applications

The picture fuzzy set is characterized by three functions expressing the degree of membership, the degree of neutral membership and the degree of non-membership. It was proposed as a generalization of an intuitionistic fuzzy set in order to deal with indeterminate and inconsistent information. In this work, we shall present some novel Dice similarity measures of picture fuzzy sets and the generalized Dice similarity measures of picture fuzzy sets and indicate that the Dice similarity measures and asymmetric measures (projection measures) are the special cases of the generalized Dice similarity measures in some parameter values. Then, we propose the generalized Dice similarity measures-based patterns recognition models with picture fuzzy information. Then, we apply the generalized Dice similarity measures between picture fuzzy sets to building material recognition. Finally, an illustrative example is given to demonstrate the efficiency of the similarity measures for building material recognition.