A Distance Measure for Intuitionistic Fuzzy Sets and Its Application to Pattern Classification Problems

As a generation of fuzzy sets, intuitionistic fuzzy sets (IFSs) have a more powerful ability to represent and address the uncertainty of information. Therefore, IFSs have been used in many areas. However, the distance measure between the IFSs indicating the difference or discrepancy grade is still an open question that has attracted considerable attention over the past few decades. Although various measurement methods have been developed, some problems still exist regarding the unsatisfactory axioms of distance measure or that lack discernment and cause counterintuitive cases. To address the above issues, in this article, we propose a new distance measure between IFSs based on the Jensen-Shannon divergence. This new IFS distance measure can not only satisfy the axiomatic definition of distance measure but also has nonlinear characteristics. As a result, it can better discriminate the discrepancies between IFSs, and it generates more reasonable results than do other existing measure methods; these advantages are illustrated by several numerical examples. Based on these qualities, an algorithm for pattern classification is designed that provides a promising solution for addressing inference problems.

Automated summary

This article introduces a new distance measure between Intuitionistic Fuzzy Sets (IFSs) based on the Jensen-Shannon divergence, which not only meets the axiomatic definition of distance measure, but also possesses nonlinear characteristics, allowing for better discrimination between IFSs and producing more reasonable results compared to other existing methods. This new distance measure is illustrated through numerical examples and is further applied to pattern classification, offering a promising solution for solving inference problems.