Novel Intuitionistic-Based Interval Type-2 Fuzzy Similarity Measures With Application to Clustering

Similarity measures have been widely used in applications dealing with reasoning, classification, and information retrieval. In this article, we first propose three new interval type-2 fuzzy similarity measures (IT-2 FSMs) as a dual concept of some semimetric distances between intuitionistic fuzzy sets (IFSs). We also prove that the extended IT-2 FSMs satisfy many common properties (i.e., reflexivity, transivity, symmetry, and overlapping). Experiments are carried out on a variety of datasets including UCI learning machine and real data. Comparative studies between the proposed IT-2 FSMs and the other well-known existing similarity measures (Gorzalczany, Bustince, Mitchell, Zeng, and Li as well as VSM and Jaccard) are performed. Obviously, the best results are obtained with the IT-2 FSMs being resilient to the high levels of uncertainty noise. We also prove that our IT-2 FSMs can overcome the drawbacks of some existing similarity measures based on the accuracy rate measure. In addition, the proposed IT-2 FSMs are joined with fuzzy C-means algorithm as a clustering method and the proposed system is compared against the existing clustering algorithms (type-1 fuzzy k-means, type-1, and type-2 fuzzy C-means, cluster forest, bagged clustering, evidence accumulation, and random projection). Relying on the clustering quality parameters R and C (equivalent to the standard classification accuracy), the advanced IT-2FSMs show higher classification accuracy of about 86% which outperforms nearly the other classifiers.

Automated summary

This article proposes three new interval type-2 fuzzy similarity measures and proves their common properties. The experiments show that these measures are resilient to high levels of uncertainty noise and can overcome the drawbacks of existing similarity measures. The application of these measures in clustering algorithms also achieves good results.