TESTING STATISTICAL HYPOTHESES UNDER FUZZY DATA AND BASED ON A NEW SIGNED DISTANCE

[1] M. Gh. Akbari and A. Rezaei, Bootstrap testing fuzzy hypotheses and observations on fuzzy
statistic, Expert Systems with Applications, 37 (2010), 5782{5787.
[2] T. Allahviranloo, S. Abbasbandy, and R. Saneifard, A method for ranking of fuzzy numbers
using new weighed distance, Mathematical and Computational Applications, 16 (2011), 359{
369.
[3] M. Arefi and S. M. Taheri, A fuzzy-based approach to testing statistical hypotheses, Interna-
tional Journal of Intelligent Technologies and Applied Statistics, 4(1) (2011), 109{132.
[4] M. Arefi and S. M. Taheri, Testing fuzzy hypotheses using fuzzy data based on fuzzy test
statistic, Journal of Uncertain Systems, 5(1) (2011), 45{61.
[5] M. Arefi and S. M. Taheri, A new approach for testing fuzzy hypotheses based on fuzzy data,
International Journal of Computational Intelligence Systems, 6(2) (2013), 318{327.
[6] B. F. Arnold, An approach to fuzzy hypothesis testing, Metrika, 44 (1996), 119{126.
[7] B. F. Arnold, Testing fuzzy hypotheses with crisp data, Fuzzy Sets and Systems 94 (1998),
323{333.
[8] C. Bertoluzza, N. Corall, and A. Salas, On a new class of dictances between fuzzy numbers,
Mathware & Soft Computing, 2 (1995), 71{84.
[9] P. P. Bonissone, Soft computing: the convergence of emerging reasoning technologies, Soft
Computing, 1 (1997), 6{18.
[10] J. J. Buckley, Fuzzy statistics: hypothesis testing, Soft Computing, 9 (2004), 512{518.
[11] M. R. Casals, and M. A. Gil, A note on the operativeness of Neyman-Pearson tests with
fuzzy information, Fuzzy Sets and Systems, 30 (1989), 215{220.
[12] M. R. Casals, M. A. Gil, and P. Gil, The fuzzy decision problem: an approach to the prob-
lem of testing statistical hypotheses with fuzzy information, European Journal of Operation
Research, 27 (1986), 371{382.
[13] J. Chachi, S. M. Taheri, and R. Viertl, Testing statistical hypotheses based on fuzzy confidence
intervals, Austrian Journal of Statistics, 41(4)(2012), 267{286.
[14] S. H. Chen and CH Hsieh, Representation, ranking, distance, and similarity of L-R type fuzzy
number and application, Australian Journal of Intelligent Information Processing Systems,
6(4) (2000), 217{229.
[15] I. Couso, L. Sanchez, Defuzzification of fuzzy p-values, In: Soft Methods for Handling Vari-
ability and Imprecision, D. Dubois et al. (Eds.), Advances in Soft Computing, Springer,
(2008), 126{132.
[16] M. Delgado, J. L. Verdegay, and M. A. Vila, Testing fuzzy hypotheses: A Bayesian approach,
In: Approximate Reasoningin Expert Systems, M. M. Gupta, A. Kandel, W. Bandlery, J. B.
Kiszka (Eds.), North-Holland, (1985), 307{316.
[17] J. G. Dijkman, H. Van Haeringen and S. J. De Lange, Fuzzy numbers, Journal of Mathemat-
ical Analysis and Applications, 92(2) (1983), 301{341.
[18] P. Filzmoser and R. Viertl, Testing hypotheses with fuzzy data: the fuzzy p-value, Metrika,
59 (2004), 21{29.
[19] P. Grzegorzewski, Testing fuzzy hypotheses with vague data, In: Statistical Modeling, Analysis
and Management of Fuzzy Data, C. Bertoluzza et al. (Eds.), Springer, Heidelberg, (2002),
213{225.
[20] P. Grzegorzewski, Testing statistical hypotheses with vague data, Fuzzy Sets and Systems,
112 (2000), 501{510.
[21] C. Kahraman, C. E. Bozdag, D. Ruan and A. F. Ozok, Fuzzy sets approaches to statistical
parametric and nonparametric tests, International Journal of Intelligent Systems, 19 (2004),
1{19.

[22] G. J. Klir and B. Yuan, Fuzzy Sets and Fuzzy Logic Theory and Applications, Prentic-Hall,
Englewood Cliffs, NJ, 1995.
[23] R. Kruse and K. D. Meyer, Statistics with Vague Data, D. Reidel Publishing Company,
Dortrecht, Boston, 1987.
[24] X. Li and B. Liu, On distance between fuzzy variables, Journal of Intelligent and Fuzzy
Systems, 19(3) (2008), 197{204.
[25] J. Liu, L. Martinez, H. Wang, R. M. Rodriguez and V. Novozhilov, Computing with words in
risk assessment, International Journal of Computational Intelligence Systems, 3(4) (2010),
396{419.
[26] L. Magdalena, What is Soft Computing? Revisiting possible answers, International Journal
of Computational Intelligence Systems, 3(2) (2010), 148{159.
[27] A. Parchami, S. M. Taheri and M. Mashinchi, Fuzzy p-value in testing fuzzy hypotheses with
crisp data, Statistical Papers, 51 (2010), 209{226.
[28] A. Parchami, S. M. Taheri and M. Mashinchi, Testing fuzzy hypotheses based on vague ob-
servations: a p-value approach, Statistical Papers, 53(2) (2012), 469{484.
[29] D. Richards, Advanced Mathematical Methods with Maple, Cambridge University Press, New
York, 2002.
[30] R. Seising, What is Soft Computing? - Bridging gaps for 21st Century science!, International
Journal of Computational Intelligence Systems, 3(2) (2010), 160{175.
[31] S. M. Taheri Trends in fuzzy statistics, Austrian Journal of Statistics, 32 (2003), 239{257.
[32] S. M. Taheri and M. Arefi, Testing fuzzy hypotheses based on fuzzy test statistic, Soft Com-
puting, 13 (2009), 617{625.
[33] S. M. Taheri and J. Behboodian, Neyman-Pearson Lemma for fuzzy hypothesis testing,
Metrika, 49 (1999), 3{17.
[34] S. M. Taheri and J. Behboodian, A Bayesian approach to fuzzy hypotheses testing, Fuzzy
Sets and Systems, 123 (2001), 39{48.
[35] S. M. Taheri and J. Behboodian, On Bayesian approach to fuzzy testing hypothesis with fuzzy
data, Italian Journal of Pure and Applied Mathematics, 19 (2006), 139{154.
[36] S. M. Taheri and G. Hesamian A generalization of the Wilcoxon signed-rank test and its
applications, Statistical Papers, 54(2) (2013), 457{470.
[37] S. M. Taheri and G. Hesamian, Goodman-Kruskal measure of association for fuzzy-
categorized variables, Kybernetika, 47(1) (2011), 110{122.
[38] H. Torabi, J. Behboodian, and S. M. Taheri Neyman-Pearson Lemma for fuzzy hypotheses
testing with vague data, Metrika, 64 (2006), 289{304.
[39] W. Trutschnig, G. Gonzalez-Rodriguez, A. Colubi, and M. A. Gil, A new family of metrics for
compact, convex (fuzzy) sets based on a generalized concept of mid and spread, Information
Sciences, 179 (2009), 3964{3972.
[40] R. Viertl, Fuzzy models for precision measurements, Mathematics and Computers in Simu-
lation, 79 (2008), 874{878.
[41] R. Viertl, Statistical Methods for Fuzzy Data, J. Wiley, Chichester, 2011.
[42] J. S. Yao and K. M. Wu, Ranking fuzzy numbers based on decomposition principle and signed
distance, Fuzzy Sets and Systems, 116 (2000), 275{288.
[43] Sh. Yosefi, M. Arefi, and M. Gh. Akbari, A new approach for testing fuzzy hypotheses based
on likelihood ratio statistic, Statistical Papers, 57 (2016), 665{688.
[44] L. A. Zadeh, From computing with numbers to computing with words - from manipulation of
measurements to manipulation of perceptions, IEEE Transactions on Circuits and Systems-1:
Fundamental Theory and Applications, 46(1) (1999), 105{119.
[45] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338{353.