Generalized entropy optimization methods with fuzzy data analysis

In this thesis, it is defined Maximum Fuzzy Entropy (Max(F)Ent) problem for fuzzy data analysis and in order to solve this problem Generalized Maximum Fuzzy Entropy (GMax(F)Ent) methods in the form of MinMax(F)Ent and MaxMax(F)Ent methods are developed. Then, the existence of solution of Max(F)Ent problem is proved by Lagrange multipliers method. Solutions of Max(F)Ent problem obtained by GMax(F)Ent methods in the form of distributions of (MinMax(F)Ent)_m, (MaxMax(F)Ent)_m are taken into account in detail and compared with each other in the sense of data modelling in the different application fields. The performances of distributions of (MinMax(F)Ent)_m ve (MaxMax(F)Ent)_m are determined by Maximum Fuzzy Entropy measure, Chi – Square criteria, RMSE criteria. Additionally, while the moment constraints are increased, the effects of (MinMax(F)Ent)_m and (MaxMax(F)Ent)_m distributions on the data modeling are observed. The results are acquired by using statistical software MATLAB 7.10.0 (R2010a). The obtained results show that (MinMax(F)Ent)_m and (MaxMax(F)Ent)_m distributions give significant results in the data modeling for fuzzy data analysis.