Abstract
This paper deals with the problem of three factor ANOVA model (Latin Square Design-LSD) test using Trapezoidal Fuzzy Numbers (tfns.). The proposed test is analysed under various types of trapezoidal fuzzy models such as Alpha Cut Interval, Membership Function, Ranking Function, Total Integral Value and Graded Mean Integration Representation. Finally a comparative view of the conclusions obtained from various test is given. Moreover, two numerical examples having different conclusions have been given for a concrete comparative study.
Highlights
Fuzzy set theory [29] has been applied to many areas which need to manage uncertain and vague data
Gajivaradhan and Parthiban analysed one-way ANOVA test using alpha cut interval method for trapezoidal fuzzy numbers [16] and they presented a comparative study of 2-factor ANOVA test under fuzzy environments using various methods [17]
We propose a new statistical fuzzy hypothesis testing of ANOVA for three factors of classifications (Latin Square Design-LSD) in which the designated samples are in terms of fuzzy data
Summary
Fuzzy set theory [29] has been applied to many areas which need to manage uncertain and vague data Such areas include approximate reasoning, decision making, optimization, control and so on. Hypothesis testing of one factor ANOVA model for fuzzy data was proposed by Wu [26, 28] using the h-level set and the notions of pessimistic degree and optimistic degree by solving optimization problems. Liou and Wang proposed the Total Integral Value of the trapezoidal fuzzy number with the index of optimism and pessimism [14]. We propose a new statistical fuzzy hypothesis testing of ANOVA for three factors of classifications (Latin Square Design-LSD) in which the designated samples are in terms of fuzzy (trapezoidal fuzzy numbers) data. We use the centroid/ranking grades of trapezoidal fuzzy numbers (tfns.) in hypothesis testing. The same concept can be used when we have samples in terms of triangular fuzzy numbers [5, 26]
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