On methods of defuzzification of parametrically represented fuzzy numbers

A comparative analysis of such methods of defuzzification of fuzzy numbers as WABL (Weighted Averaging Based on Levels), centroid, and mean of maxima (MOM) is presented in the study. Analytic formulas are presented for calculating the defuzzification values for parametrically represented fuzzy numbers of triangular and trapezoidal form.     

A fuzzy ID3 induction for linguistic data sets

In real life, humans communicate by means of words. Computing with words enables flexibility via fuzzy logic to reach more informative results for the classification and decision‐making. Fuzzy logic handles the imprecise information. In our paper, we propose a novel fuzzy ID3 algorithm for the classification on linguistic data set, where data can be given as linguistic variables. Linguistic variables are defined by using triangular fuzzy numbers given as LR (left‐right) fuzzy numbers. And weighted averaging based on levels (WABL) method is used as the defuzzification method for each data. Then, fuzzy c‐means algorithm is performed to handle the membership degrees for each variable given in each data set used in an experimental study. At last, the fuzzy ID3 algorithm is applied. The rules are generated, and the reasoning is done by different T‐operators. Our study is encouraged by (using) statistical analysis. In conclusion, it is seen that our algorithm proposed for linguistic data is as good as the proposed approach for numeric data. Also, it is shown that the proposed linguistic approach by using different T‐operators on linguistic data gives better results than numerical approach on some data sets.     

Fuzzy least squares regression model based of weighted distance between fuzzy numbers

A new distance ND1 between fuzzy numbers based on an averaged representative of a fuzzy number (Weighting Average Based on Levels, WABL) is proposed. Based on this distance a new least squares regression model is proposed. The proposed model is studied for a broad class of fuzzy numbers and class of functions the membership of which is formed on the basis of the template μ_[.](x) = max(0.1 ? |x|^s).