Analysis of variance based on fuzzy observations

Analysis of variance (ANOVA) is an important method in exploratory and confirmatory data analysis. The simplest type of ANOVA is one-way ANOVA for comparison among means of several populations. In this article, we extend one-way ANOVA to a case where observed data are fuzzy observations rather than real numbers. Two real-data examples are given to show the performance of this method.

[1]  Peter R. Nelson,et al.  Design and Analysis of Experiments, 3rd Ed. , 1991 .

[2]  Hung T. Nguyen,et al.  A First Course in Fuzzy Logic , 1996 .

[3]  Ana Colubi,et al.  Introduction to ANOVA with Fuzzy Random Variables , 2004 .

[4]  María Angeles Gil,et al.  Fuzzy random variables , 2001, Inf. Sci..

[5]  Ana Colubi,et al.  Computational Statistics and Data Analysis Fuzzy Data Treated as Functional Data: a One-way Anova Test Approach , 2022 .

[6]  Lotfi A. Zadeh,et al.  The Concepts of a Linguistic Variable and its Application to Approximate Reasoning , 1975 .

[7]  Michael Hanss,et al.  Applied Fuzzy Arithmetic: An Introduction with Engineering Applications , 2004 .

[8]  Reinhard Viertl,et al.  Statistical Methods for Fuzzy Data: Viertl/Statistical Methods for Fuzzy Data , 2011 .

[9]  R. Viertl.  Statistical Methods for Fuzzy Data , 2011 .

[10]  William G. Cochran,et al.  Experimental Designs, 2nd Edition , 1950 .

[11]  Seyed Mahmoud Taheri,et al.  Testing fuzzy hypotheses based on fuzzy test statistic , 2009, Soft Comput..

[12]  BEHAVIOUR OF FUZZY ANOVA , 1987 .

[13]  Ana Colubi,et al.  Bootstrap approach to the multi-sample test of means with imprecise data , 2006, Comput. Stat. Data Anal..

[14]  Ana Colubi,et al.  Asymptotic and Bootstrap techniques for testing the expected value of a fuzzy random variable , 2004 .

[15]  R. Viertl,et al.  Testing hypotheses with fuzzy data: The fuzzy p-value , 2004 .

[16]  Ricardo Fraiman,et al.  An anova test for functional data , 2004, Comput. Stat. Data Anal..

[17]  A. Kaufmann,et al.  Introduction to fuzzy arithmetic : theory and applications , 1986 .

[18]  R. R. Hocking.  Methods and Applications of Linear Models: Regression and the Analysis of Variance , 2003 .

[19]  Hsien-Chung Wu,et al.  Analysis of variance for fuzzy data , 2007, Int. J. Syst. Sci..

[20]  Maria L. Rizzo,et al.  Statistical Computing with R , 2007 .

[21]  Margaret J. Robertson,et al.  Design and Analysis of Experiments , 2006, Handbook of statistics.

[22]  Didier Dubois,et al.  Fuzzy sets and systems ' . Theory and applications , 2007 .