Theory and Optimization of Generalized Maximum Intuitionistic Fuzzy Entropy Methods

The studying and formulating of the generalized maximum fuzzy entropy methods for Intuitionistic Fuzzy Entropy is the focus of this manuscript. The methods were constructed by finding two generalized maximum fuzzy entropy distributions as MinMaxFE and MaxMaxFE, which gives the least and the greatest values of the entropy based on membership function values. We define the optimization problem and study the existence of the solution subject to moment constraints through Lagrange multiplier method. Real life application of data sets in medical fields and in image processing is studied to show whether the developed method can be applied successfully in fuzzy data analysis, and the performance of these distributions is measured using chi-square, RMSE, MFE criteria.