Analysis of variance based on fuzzy observations

References

• Cochran , WG and Cox , GM . 1957 . Experimental Designs , 2nd , New York : Wiley .
   Google Scholar
• Cuevas , A , Febrero , M and Fraiman , R . 2004 . An ANOVA Test for Functional Data . Computer Statistics and Data Analysis , 47 : 111 – 122 .
   Web of Science ®Google Scholar
• Dean , A and Voss , D . 1999 . Design and Analysis of Experiments , New York : Springer-Verlag .
   Google Scholar
• Degaribay , VG . 1987 . Behaviour of Fuzzy ANOVA . Kybernetes , 16 : 107 – 112 .
   Web of Science ®Google Scholar
• Dubois , D and Prade , H . 1980 . Fuzzy Sets and Systems: Theory and Application , New York : Academic .
   Google Scholar
• Filzmoser , P and Viertl , R . 2009 . Testing Hypotheses with Fuzzy Data: The Fuzzy p-value . Metrika , 59 : 21 – 29 .
   Web of Science ®Google Scholar
• Gil , MA , Montenegro , M , González-Rodríguez , G , Colubi , A and Casals , MR . 2006 . Bootstrap Approach to the Multi-sample Test of Means with Imprecise Data . Computer Statistics and Data Analysis , 51 : 148 – 162 .
   Web of Science ®Google Scholar
• González-Rodríguez , G . Colubi, A., and Gil, M.A. (2011), ‘Fuzzy Data Treated as Functional Data: A One-way ANOVA Test Approach’, Computational Statistics and Data Analysis, doi:10.1016/j.csda.2010.06.013
   Google Scholar
• Hanss , M . 2005 . Applied Fuzzy Arithmetic: An Introduction with Engineering Applications , Heidelberg, Berlin : Springer-Verlag .
   Google Scholar
• Hocking , RR . 1996 . Methods and Applications of Linear Models: Regression and the Analysis of Variance , New York : John Wiley & Sons .
   Google Scholar
• Kaufmann , A and Gupta , MM . 1985 . Introduction to Fuzzy Arithmetic: Theory and Applications , New York : Van Nostrand .
   Google Scholar
• Konishi , M , Okuda , T and Asai , K . 2006 . Analysis of Variance Based on Fuzzy Interval Data Using Moment Correction Method . International Journal of Innovative Computing, Information and Control , 2 : 83 – 99 .
   Web of Science ®Google Scholar
• Montenegro , M , Colubi , A , Casals , MR and Gil , MA . 2004 . Asymptotic and Bootstrap Techniques for Testing the Expected Value of a Fuzzy Random Variable . Metrika , 59 : 31 – 49 .
   Web of Science ®Google Scholar
• Montenegro , M , González-Rodríguez , G , Gil , MA , Colubi , A and Casals , MR . 2004 . “ Introduction to ANOVA with Fuzzy Random Variables ” . In Soft Methodology and Random Information Systems , Edited by: Lopez-Diaz , M , Gil , MA , Grzegorzewski , P , Hryniewicz , O and Lawry , J . 487 – 494 . Berlin : Springer .
   Google Scholar
• Montgomery , DC . 1991 . Design and Analysis of Experiments , (3rd , New York : John Wiley & Sons .
   Google Scholar
• Nguyen , HT and Walker , EA . 2005 . A First Course in Fuzzy Logic , 3rd , Paris : Chapman Hall/CRC .
   Google Scholar
• Puri , ML and Ralescu , DA . 1986 . Fuzzy Random Variables . Journal of Mathematical Analysis and Applications , 114 : 409 – 422 .
   Web of Science ®Google Scholar
• Rizzo , ML . 2008 . Statistical Computing with R , Paris : Chapman Hall/CRC .
   Google Scholar
• Taheri , SM and Arefi , M . 2009 . Testing Hypotheses Based on Fuzzy Test Statistic . Soft Computing , 13 : 617 – 625 .
   Web of Science ®Google Scholar
• Viertl , R . 2011 . Statistical Methods for Fuzzy Data , New York : John Wiley & Sons .
   Google Scholar
• Wu , HC . 2007 . Analysis of Variance for Fuzzy Data . International Journal of Systems Science , 38 : 235 – 246 .
   Web of Science ®Google Scholar
• Zadeh , LA . 1965 . Fuzzy Sets . Information and Control , 8 : 338 – 359 .
   Web of Science ®Google Scholar
• Zadeh , LA . 1975 . The Concept of a Linguistic Variable and Its Application to Approximate Reasoning . Information Sciences , 8 : 199 – 249 .
   Web of Science ®Google Scholar