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A Statistical Hypothesis Testing of Analysis of Variance for Two Way Classification in Fuzzy Environments

A. Mariappan, M. Pachamuthu


The Analysis of Variance (ANOVA) is the most popular technique for testing of significance. ANOVA for one way classification model is a series of observations distributed over the different levels at single factor and the two-way classification model is the set of observations distributed over different levels of two simultaneous factors. In real-life situations, most of the observations cannot be recorded or collected precisely. A fuzzy environment is the decision-making process in which the goals and the constraints, but not necessarily the system under control, are fuzzy in nature. The two-way classification model is the collection of observations of two simultaneous variables distributed over challenging levels without the h-level concept of Trapezoidal Fuzzy Numbers (TZFNs). In this paper a statistical hypothesis testing of ANOVA two way classification with fuzzy environments through an numerical examples.

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C. Barbacioru; Statistical Hypothesis Testing Using Fuzzy Linguistic

Variables, Fiability & Durability/Fiabilitate si Durabilitate (2012).

D. Dubois; H. Prade; Operations on fuzzy numbers, International Journal of

systems science, 9(6)613-626 (1978).

D. Kalpanapriya; P. Pandian; Fuzzy hypothesis testing of ANOVA model with

fuzzy data. International Journal of Modern Engineering Research, 2(4) 2951-2956 (2012).

H. C. Wu; Analysis of variance for fuzzy data, International Journal of Systems

Science, 38(3) 235-246 (2007).

J. de Andres-Sanchez; Claim reserving with fuzzy regression and the two ways of

ANOVA, Applied Soft Computing, 12(8) 2435-2441 (2012).

J. J. Buckley; Fuzzy probability and statistics Heidelberg: Springer, 85-93 (2006).

J. K. George; Y. Bo; Fuzzy sets and fuzzy logic: theory and applications, PHI New

Delhi, 443-455 (1995).

L. A. Zadeh; Information and control, Fuzzy sets, 8(3) 338-353 (1965).

P. Pandian; D. Kalpanapriya; Two-factor ANOVA technique for fuzzy data

having membership grades, Research Journal of Pharmacy and Technology, 9(12) 2394-


R. R. Hocking; Methods and applications of linear models: regression and the

analysis of variance, John Wiley & Sons, (2013).

R. Viertl; Statistical methods for fuzzy data, John Wiley & Sons,( (2011).

S. Abbasbandy; B. Asady; The nearest trapezoidal fuzzy number to a fuzzy

quantity. Applied mathematics and computation, 156(2) 381-386 (2004).

S. Abbasbandy; M. Amirfakhrian; The nearest approximation of a fuzzy quantity

in parametric form, Applied Mathematics and Computation, 172(1) 624-632 (2006).

S. Abbasbandy; M. Amirfakhrian; The nearest trapezoidal form of a generalized

left right fuzzy number, International Journal of Approximate Reasoning, 43(2) 166-178 (2006).

S. C. Gupta; V.K. Kapoor; Fundamentals of applied statistics, edition 11,

published by Sultan chand & Sons. New Delhi, India( 2007).

S. Parthiban; P. Gajivaradhan; A comparative study of two factor ANOVA

model under fuzzy environments using trapezoidal fuzzy numbers, International Journal of Fuzzy

Mathematical Archive, 10(1) 1-25(2016).

T. Nakama; A. Colubi; M. A. Lubiano; Two-way analysis of variance for

interval-valued data. In Combining soft computing and statistical methods in data

analysis (pp. 475-482). Springer, Berlin, Heidelberg (2010).


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