Anestis G. Hatzimichailidis

Distance and similarity measures for fuzzy operators

We introduce and study a new family of normalized distance measures between binary fuzzy operators, along with its dual family of similarity measures. Both are based on matrix norms and arise from the study of the aggregate plausibility of set-operations. We also suggest a new family of normalized distance measures between fuzzy sets, based on binary operators and matrix norms, and discuss its qualitative and quantitative features. All measures proposed are intended for applications and may be customized according to the needs and intuition of the user.

L-fuzzy Sets and Intuitionistic Fuzzy Sets

In this article we firstly summarize some notions on L−fuzzy sets, where L denotes a complete lattice. We then study a special case of L−fuzzy sets, namely the “intuitionistic fuzzy sets”. The importance of these sets comes from the fact that the negation is being defined independently from the fuzzy membership function. The latter implies both flexibility and effectiveness in fuzzy inference applications. We additionally show several practical applications on intuitionistic fuzzy sets, in the context of computational intelligence.

A novel distance measure of intuitionistic fuzzy sets and its application to pattern recognition problems

A novel distance measure between two intuitionistic fuzzy sets (IFSs) is proposed in this paper. The introduced measure formulates the information of each set in matrix structure, where matrix norms in conjunction with fuzzy implications can be applied to measure the distance between the IFSs. The advantage of this novel distance measure is its flexibility, which permits different fuzzy implications to be incorporated by extending its applicability to several applications where the most appropriate implication is used. Moreover, the proposed distance might be expressed equivalently by using either intuitionistic fuzzy sets or interval‐valued fuzzy sets. Appropriate experimental configurations have taken place to compare the proposed distance measure with similar distance measures from the literature, by applying them to several pattern recognition problems. The results are very promising because the performance of the new distance measure outperforms the corresponding performance of well‐known IFSs measures, by recognizing the patterns correctly and with high degree of confidence.

An Implication in Fuzzy Sets

In this paper we introduce a fuzzy implication. The proposed fuzzy implication does not belong in one of the well known three general classes of fuzzy implications (S-implications, R-implications and QL-implications). Also we give an extended model of this fuzzy implication in intuitionistic fuzzy set and/or interval-valued fuzzy sets.