A Distance Measure Based on Fuzzy D-implications: Application in Pattern Recognition

A new distance measure between fuzzy sets (FSs) based on fuzzy D-implications is introduced in this paper. The proposed measure uses a matrix representation of each set in order to encode its information, where matrix norms in conjunction with fuzzy D-implications can be applied to measure the distance between the two FSs. It is worth noting that the applied technique in deriving the proposed measure gives the flexibility to construct several distance measures by incorporating different fuzzy implications, extending its applicability to several applications where the most appropriate implication is used. Apart from the analysis in constructing a D-implication based distance measure, a detailed discussion of its main properties is also presented. Moreover, an appropriate set of experiments has taken place in order to examine the performance of the proposed distance compared to well-known fuzzy implications, in some pattern classification problems from the literature. The corresponding results are promising and show that the proposed measure can classify the patterns correctly and with high degree of confidence.