On Parametric Picture Fuzzy Information Measure in Pattern Recognition Problem

Various similarity/distance information measures for the extensions of fuzzy sets have been proposed and utilized in different fields such as data science, clustering techniques, medical diagnosis, econometrics, decision-making, etc. In the present communication, we propose a new kind of parametric distance measure for the picture fuzzy sets and study various set-theoretic binary operations and properties related to the measure along with their mathematical validation. The parametrization feature of this measure provides additional flexibility in processing the information. Further, for a given unknown pattern, based on the proposed parametric picture fuzzy distance measure and the methodology of minimum discriminant information, we classify it into a set of known patterns. A numerical example to show the implementation has also been provided for clarity and better readability.