Statistical Characteristics of Distributions Obtained Using the Signed Distance Defuzzification Method Compared to Other Methods

Abstract

Having in mind the evaluation of linguistic questionnaires, we aim to present a comparison in terms of statistical measures between on one side a relative recent defuzzification method, known as the signed distance method, and on the other side, other well-known traditional methods. The distribution’s properties of data resulting from the defuzzification process are generally not given or investigated. By simulations, we intend to investigate the location, dispersion and symmetry characteristics of the estimated distributions. Our simulations for different cases of input distributions and membership functions show first that the computed statistical measures don’t depend on the sample sizes. This phenomenon is particularly remarkable in the case of the signed distance and the mean of the maximum methods. Second, the signed distance is the method tending the most to conserve the symmetry of the distributions while the smallest and largest of maximum are the worst in keeping the skewness property.

Appendix

See Table 2.

Table 2 Statistical measures of the output distributions using different membership function types for each defuzzification method in the case of 2 symmetric input distributions (Skewness=0)