Subscribe to our Newsletter and get informed about new publication regulary and special discounts for subscribers!

BMSA > BMSA Volume 14 > Statistical Hypothesis Test in Three Factor ANOVA...
< Back to Volume

Statistical Hypothesis Test in Three Factor ANOVA Model under Fuzzy Environments Using Trapezoidal Fuzzy Numbers

Full Text PDF


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.


Bulletin of Mathematical Sciences and Applications (Volume 14)
S. Parthiban and P. Gajivaradhan, "Statistical Hypothesis Test in Three Factor ANOVA Model under Fuzzy Environments Using Trapezoidal Fuzzy Numbers", Bulletin of Mathematical Sciences and Applications, Vol. 14, pp. 23-42, 2016
Online since:
February 2016

[1] S. Abbasbandy, B. Asady, The nearest trapezoidal fuzzy number to a fuzzy quantity, Appl. Math. Comput., 156 (2004) 381-386.


[2] S. Abbasbandy, M. Amirfakhrian, The nearest approximation of a fuzzy quantity in parametric form, Appl. Math. Comput., 172 (2006) 624-632.


[3] S. Abbasbandy, M. Amirfakhrian, The nearest trapezoidal form of generalized left right fuzzy number, Internat. J. Approx. Reason., 43 (2006) 166-178.


[4] S. Abbasbandy, T. Hajjari, Weighted trapezoidal approximation-preserving cores of a fuzzy number, Computers and Mathematics with Applications, 59 (2010) 3066-3077.


[5] E. Baloui Jamkhaneh and A. Nadi Ghara, Testing statistical hypotheses for compare means with vague data, International Mathematical Forum, 5 (2010) 615-620.


[6] S. Bodjanova, Median value and median interval of a fuzzy number, Inform. Sci. 172 (2005) 73-89.


[7] J. J. Buckley, Fuzzy statistics, Springer-Verlag, New York, (2005).

[8] J. Chachi, S. M. Taheri and R. Viertl, Testing statistical hypotheses based on fuzzy confidence intervals, Forschungsbericht SM-2012-2, Technische Universitat Wien, Austria, (2012).

[9] D. Dubois and H. Prade, Operations on fuzzy numbers, Int. J. Syst. Sci., 9 (1978) 613-626.

[10] S. C. Gupta, V. K. Kapoor, Fundamentals of mathematical statistics, Sultan Chand & Sons, New Delhi, India.

[11] R. R. Hocking, Methods and applications of linear models: regression and the analysis of variance, New York: John Wiley & Sons, (1996).

[12] Iuliana Carmen BĂRBĂCIORU, Statistical Hypothesis Testing Using Fuzzy Linguistic Variables, Fiabilitatesi Durabilitate-Fiability & Durability, Supplement, 1 (2012) Editura Academica Brȃncusi, Tȃrgu Jiu, ISSN 1844-640X.

[13] George J. Klir and Bo Yuan, Fuzzy sets and fuzzy logic, Theory and Applications, Prentice- Hall, New Jersey, (2008).

[14] T. S. Liou and M. J. Wang, Ranking Fuzzy Numbers with Integral Value, Fuzzy Sets and Systems, 50 (1992) 247-225.


[15] Mikihiko Konishi, Tetsuji Okuda and Kiyoji Asai, Analysis of variance based on Fuzzy interval data using moment correction method, International Journal of Innovative Computing, Information and Control, 2 (2006) 83-99.

[16] S. Parthiban, and P. Gajivaradhan, One-factor ANOVA model using trapezoidal fuzzy numbers through alpha cut interval method, Annals of Pure and Applied Mathematics, 11(1) (2016) 45-61.

[17] S. Parthiban, and P. Gajivaradhan, A comparative study of two factor ANOVA model under fuzzy environments using trapezoidal fuzzy numbers, Int. J. of Fuzzy Mathematical Archive, 10(1) (2016) 1-25.


[18] S. Salahsour, S. Abbasbandy and T. Allahviranloo, Ranking Fuzzy Numbers using Fuzzy Maximizing-Minimizing points, EUSFLAT-LFA: July 2011, Aix-les-Bains, France.


[19] Salim Rezvani and Mohammad Molani, Representation of trapezoidal fuzzy numbers with shape function, to appear in Annals of Fuzzy mathematics and Informatics.

[20] Salim Rezvani, Ranking Generalized Trapezoidal Fuzzy Numbers with Euclidean Distance by the Incentre of Centroids, Mathematica Aeterna, 3 (2) (2013) 103-114.

[21] Y. L. P. Thorani, et al., Ordering Generalized Trapezoidal Fuzzy Numbers, Int. J. Contemp. Math. Sciences, 7(12) (2012) 555-573.

[22] T. Veerarajan, Probability, statistics and random process, Tata McGraw Hill Education Pvt. Ltd., New Delhi, India.

[23] R. Viertl, Statistical methods for fuzzy data, John Wiley and Sons, Chichester, (2011).

[24] R. Viertl, Univariate statistical analysis with fuzzy data, Computational Statistics and Data Analysis, 51 (2006) 33-147.


[25] Y. M. Wang et al., On the centroids of fuzzy numbers, Fuzzy Sets and Systems, 157 (2006) 919-926.

[26] H. C. Wu, Analysis of variance for fuzzy data, International Journal of Systems Science, 38 (2007) 235-246.

[27] H. C. Wu, Statistical confidence intervals for fuzzy data, Expert Systems with Applications, 36 (2009) 2670-2676.


[28] H. C. Wu, Statistical hypotheses testing for fuzzy data, Information Sciences, 175 (2005) 30-56.

[29] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965) 338-353.

Show More Hide
Cited By:

[1] S. Parthiban, P. Gajivaradhan, "Statistical Hypothesis Test in Three Factor ANOVA Model under Fuzzy Environments Using Trapezoidal Fuzzy Numbers", Bulletin of Mathematical Sciences and Applications, Vol. 14, p. 23, 2016