Abstract
Likert scales or associated codings are often used in connection with opinions/valuations/ratings, and especially with questionnaires with a pre-specified response format.A guideline to design questionnaires allowing free fuzzy-numbered response format is now given, the fuzzy numbers scale being very rich and expressive and enabling to describe in a friendly way the usual answers in this context. A review of some techniques for the statistical analysis of the obtained responses is enclosed and a real-life example is used to illustrate the application.
This paper has been written as a tribute to Professor Ebrahim Mamdani. We have had the great opportunity of meeting a unique outstanding person, during last years mainly because of him being a member of the Scientific Committee of the European Centre for Soft Computing. We have learned a lot from his lectures and conversations, and have enjoyed with the fruitful discussions around, so we will feel always indebted to him.
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References
Bertoluzza, C., Corral, N., Salas, A.: On a new class of distances between fuzzy numbers. Math. & Soft Comput. 2, 71–84 (1995)
Bharadwaj, B.: Development of a fuzzy Likert scale for the WHO ICF to include categorical definitions on the basis of a continuum. ETD Collection for Wayne State University. Paper AAI1442894 (2007), http://digitalcommons.wayne.edu/dissertations/AAI1442894
Eshragh, F., Mamdani, E.H.: A general approach to linguistic approximation. Int. J. Man-Machine Studies 11, 501–519 (1979)
Gil, M.A., Lubiano, M.A., Montenegro, M., López-García, M.T.: Least squares fitting of an affine function and strength of association for interval data. Metrika 56, 97–111 (2002)
Giné, E., Zinn, J.: Bootstrapping general empirical measures. Ann. Probab. 18, 851–869 (1990)
González-Rodríguez, G., Colubi, A., Gil, M.A.: Fuzzy data treated as functional data. A one-way ANOVA test approach. Comp. Statist Data Anal. (2011) (in press) doi:10.1016/j.csda.2010.06.013
González-Rodríguez, G., Montenegro, M., Colubi, A., Gil, M.A.: Bootstrap techniques and fuzzy random variables: Synergy in hypothesis testing with fuzzy data. Fuzzy Sets and Systems 157, 2608–2613 (2006)
van Laerhoven, H., van der Zaag-Loonen, H.J., Derkx, B.H.F.: A comparison of Likert scale and visual analogue scales as response options in childrens questionnaires. Acta Pædiatr 93, 830–835 (2004)
Lalla, M., Facchinetti, G., Mastroleo, G.: Ordinal scales and fuzzy set systems to measure agreement: an application to the evaluation of teaching activity. Quality & Quantity 38, 577–601 (2004)
Lazim, M.A., Osman, M.T.A.: Measuring teachers’ beliefs about Mathematics: a fuzzy set approach. Int. J. Soc. Sci. 4(1), 39–43 (2009)
Lubiano, M.A., Gil, M.A.: Estimating the expected value of fuzzy random variables in random samplings from finite populations. Statistical Papers 40(3), 277–295 (1999)
Lubiano, M.A., Gil, M.A., López-Díaz, M., López, M.T.: The lambda-mean squared dispersion associated with a fuzzy random variable. Fuzzy Sets and Systems 111(3), 307–317 (2000)
Körner, R.: An asymptotic α-test for the expectation of random fuzzy variables. J. Stat. Plann Infer. 83, 331–346 (2000)
Körner, R., Näther, W.: On the variance of random fuzzy variables. In: Bertoluzza, C., Gil, M.A., Ralescu, D.A. (eds.) Statistical Modeling, Analysis and Management of Fuzzy Data, pp. 22–39. Physica-Verlag, Heidelberg (2002)
Montenegro, M., Casals, M.R., Lubiano, M.A., Gil, M.A.: Two-sample hypothesis tests of means of a fuzzy random variable. Information Sciences 133(1-2), 89–100 (2001)
Montenegro, M., Colubi, A., Casals, M.R., Gil, M.A.: Asymptotic and Bootstrap techniques for testing the expected value of a fuzzy random variable. Metrika 59, 31–49 (2004)
Nguyen, H.T.: A note on the extension principle for fuzzy sets. J. Math. Anal. Appl. 64, 369–380 (1978)
Puri, M.L., Ralescu, D.A.: The concept of normality for fuzzy random variables. Ann. Probab. 11, 1373–1379 (1985)
Puri, M.L., Ralescu, D.A.: Fuzzy random variables. J. Math. Anal. Appl. 114, 409–422 (1986)
Ramos-Guajardo, A.B., Colubi, A., González-Rodríguez, G., Gil, M.A.: One sample tests for a generalized Fréchet variance of a fuzzy random variable. Metrika 71(2), 185–202 (2010)
Trutschnig, W., González-Rodríguez, G., Colubi, A., Gil, M.: A new family of metrics for compact. Sets Based on a Generalized Concept of Mid and Spread Inform. Sci. 179, 3964–3972 (2009)
Wu, C.-H.: An empirical study on the transformations of Likert-scale data to numerical scores. Appl. Math. Sci. 58(1), 2851–2862 (2007)
Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning. Part 1. Inform. Sci. 8, 199–249 (1975); ; Part 2. Inform. Sci. 8, 301–353; Part 3. Inform. Sci. 9, 43–80
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Gil, M.Á., González-Rodríguez, G. (2012). Fuzzy vs. Likert Scale in Statistics. In: Trillas, E., Bonissone, P., Magdalena, L., Kacprzyk, J. (eds) Combining Experimentation and Theory. Studies in Fuzziness and Soft Computing, vol 271. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24666-1_27
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