Novel Similarity Measure Based on the Transformed Right-Angled Triangles Between Intuitionistic Fuzzy Sets and its Applications

Intuitionistic fuzzy set (IFS) is one of the most robust and trustworthy tools for portraying the imprecise information with the help of the membership degrees. Similarity measure, one of the information measures, plays an important role in treating imperfect and ambiguous information to reach the final decision by determining the degree of similarity between the pairs of the numbers. Motivated by these, this paper aims to present a novel distance/ similarity among the IFSs based on the transformation techniques with their characteristics. To explore the study, the given IFSs are transformed into the right-angled triangle over a unit square area, and hence based on the intersection of the triangles, novel distance and similarity measures are proposed. An algorithm to solve the decision-making problems with the proposed similarity measure is developed and implemented to execute their performance over the numerous examples such as pattern recognition and clustering analysis. The reliability of the developed measure is investigated by applying it in clustering and the pattern recognition problems and their results are compared with some prevailing studies. From the investigation, we conclude that several existing measures fail to give classification results under the different instances such as division by zero problems or counter-intuitive cases while the proposed measure successfully overcomes this drawback.

Automated summary

The paper presents a novel distance/similarity measure among IFSs based on transformation techniques and characteristics. It proposes new distance and similarity measures based on right-angled triangles over a unit square area, and an algorithm for decision-making problems, demonstrating improved performance compared to existing measures. The reliability of the developed measure is verified through clustering and pattern recognition problems, showing successful classification results where existing measures fail.