Exponential Function-Based Similarity Measures for q-Rung Linear Diophantine Fuzzy Sets and Their Application to Clustering Problem

Abstract

The q-rung linear Diophantine fuzzy set is a recently developed tool to handle with uncertain and vague information in real-life issues and can be applied for reference parameter-based opinions. Similarity measures determine distance with dimensions that represent features of the objects. Despite the importance of exponential function-based similarity measures, there is no satisfactory formulation for q-rung linear Diophantine fuzzy sets in the literature. This paper proposes similarity measures based on exponential function for q-rung linear Diophantine fuzzy sets and thus presents the first formulas for calculating the similarity coefficient between two q-rung linear Diophantine fuzzy sets. The salient features of the new similarity measures are axiomatically addressed to ensure their good performance. Also, they are applied to the clustering problem and the results are analyzed. A comparative study is established and thus several advantages of the proposed similarity measures are discussed.