Picture Hesitant Fuzzy Generalized Dice Similarity Measures and Their Application in Pattern Recognition

Abstract

The idea of picture hesitant fuzzy set (PHFS) is the combination of picture fuzzy set (PFS) and hesitant fuzzy set (HFS), which is characterized by three functions representing the degree of membership, the degree of abstinence and the degree of non-membership are the form of subsets of unit interval. The idea of PHFS is an important  tool to deal with abstinence and inconsistence information in real life problems. Motivations of this manuscript, we presented some new dice similarity measures (DSMs) for PHFSs, generalization dice similarity measures (GDSMs) for PHFSs and specify that the DSM and asymmetric measures (projection measures) are the particular case of the GDSM in some parameter values. Next, we investigated the GDSM based patterns recognition models with picture hesitant fuzzy information (PHFI). Then, with the help of GDSM for PHFSs to developed the application in building material recognition. Moreover, we evaluate the numerical example to show the effectiveness and flexibility of the similarity measures (SMs) in the environment of building metrical recognitions. In last, we will discuss the comparison between proposed methods with existing methods with the help of some examples, which shown the flexibility and effectiveness of the proposed methods.