A Comparative Study of Chi-Square Goodness-of-Fit Under Fuzzy Environments

Abstract

Testing goodness-of-fit plays a vital role in data analysis.  This problem seems to be much more complicated in the presence of vague data.  In this paper, the chi-square goodness-of-fit under trapezoidal fuzzy numbers (tfns.) is proposed using alpha cut interval method.  And the ranking grades of tfns. are also used to compute the chi-square test statistic.  The proposed technique is illustrated with two different numerical examples along with different methods of ranking grades for a concrete comparative study.

Keywords: Chi-square Test, Fuzzy Sets, Trapezoidal Fuzzy Numbers, Alpha Cut, Ranking Function, Graded Mean Integration Representation.