A fuzzy set theory solution to combining Likert items into a single overall scale (or subscales)

Quality and Quantity

Volumn 49, Issue 2, 2015, Pages 739-762

  Symeonaki, Maria ^a   Michalopoulou, Catherine ^a   Kazani, Aggeliki ^a  

^a PANTEION UNIVERSITY   (Greece)

Author keywords

Construct validity; Exploratory factor analysis; Fuzzy inference systems; Fuzzy set theory; Likert scales; Reliability

Indexed keywords

EID: 84944443757     PISSN: 00335177     EISSN: 15737845     Source Type: Journal    
DOI: 10.1007/s11135-014-0021-z     Document Type: Article

References (41)

1. Anagnostopoulos, F., Yfantopoulos, J., Moustaki, I., Niakas, D.: Psychometric and factor analytic evaluation of the 15D health-related quality of life instrument: the case of Greece. Qual. Life Res. 22(8), 1973–1986 (2013)
2. Aydin, O., Pakdil, F.: Fuzzy SERVQUAL analysis in airlines services. Organizacija 41, 108–115 (2008)
3. Bartholomew, D.J., Steele, F., Moustaki, I., Galbraith, J.: Analysis of Multivariate Social Science Data. Chapman and Hall/CRC, London (2008)
4. Betti, G., D’Adostino, A., Neri, L.: Educational mismatch of graduates: a multidimensional and fuzzy indicator. Soc. Indic. Res. 103, 465–480 (2011)
5. Clarkand, L.A., Watson, D.: Constructing validity: basic issues in objective scale development. Psychol. Assess. 7(2), 309–319 (1995)
6. De la Rosa, S., Gil, M.A., López, M.T., Lubiano, M.A.: Fuzzy rating vs. fuzzy conversion scales: an empirical comparison through the MSE. In: Kruze, R., Berthold, M., Moewes, C., Gil, M.A., Grzegorzewski, P., Hryniewicz, O. (eds.) Synergies of Soft Computing and Statistics for Intelligent Data Analysis, Advanced in Intelligent Systems and Computing, vol. 190, pp. 135–143. Springer, Berlin (2013)
7. DiStefano, C., Zhu, M., Mîndrilă, D.: Understanding and using factor scores: considerations for the applied researcher. Pract. Assess. Res. Eval. 14(20), 1–11 (2009)
8. Dubois, D., Prade, H.: The three semantics of fuzzy sets. Fuzzy Sets Syst. 90, 141–150 (1997)
9. Eurobarometer: Racism and Xenophobia. Commission of the European Communities, Brussels (1989)
10. Fabrigar, L., Wegener, D., MacCallum, R., Strahan, E.: Evaluating the use of exploratory factor analysis in psychological research. Psychol. Methods 4(3), 272–299 (1999)
11. Gacto, M.J., Alcalá, R., Herrera, F.: A double axis classification of interpretability measures for linguistic fuzzy rule-based systems. In: Fanelli, A.M., Pedrycz, W., Petrosino, A. (eds.) Fuzzy Logic Applications, pp. 99–106. Springer, Berlin (2011)
12. Gil, M.A., Gil, G.-R.: Fuzzy vs. Likert scale in statistics. Comb. Exp. Theory Stud. Fuzziness Soft Comput. 271, 407–420 (2012)
13. Gil, M.A., de Saa, S., López, M.T., Lubiano, M.A.: Comparing Likert and Fuzzy Scales Through Some Atatistical Tools. ERCIM, London (2011)
14. Hartley, J., Betts, L.R.: Four layouts and a finding: the effects of changes in the order of the verbal labels and numerical values on Likert-type scales. Int. J. Soc. Res. Methodol. 13, 17–27 (2009)
15. Hesketh, T., Hesketh, B.: Computerised fuzzy ratings: the concept of a fuzzy class. Behav. Res. Methods Instrum. Comput. 26(3), 272–277 (1994)
16. Hesketh, T., Pryor, R., Hesketh, B.: An application of a computerized fuzzy graphic rating scale to the psychological measurement of individual differences. Int. J. Man-Mach. Stud. 29(1), 21–35 (1988)
17. Klir, G.J., Yuan, B.: Fuzzy Sets and Fuzzy Logic Theory and Applications, 1st edn. Prentice Hall, New York (1995)
18. Lalla, M., Facchinetti, G., Mastroleo, G.: Ordinal scales and fuzzy set systems to measure agreement: an application to the evaluation of teaching activity. Qual. Quant. 38, 577–601 (2005)
19. Lazim, A., Abu Osman, M.T.: Measuring teacher’s beliefs about Mathematics: a fuzzy set approach. Int. J. Soc. Humanit. Sci. Eng. 8(1), 39–43 (2009)
20. Lazim, A., Abu Osman, M.T.: Fuzzy set conjoint model in describing student’s perceptions on computer algebra system learning environment. Int. J. Comput. Sci. Issues 8(2), 92–97 (2011)
21. Likert, R.: A technique for the measurement of attitudes. Arch. Psychol. 140, 1–55 (1932)
22. Lozano, L.M., García-Cueto, E., Muñiz, J.: Effect of the number of response categories on the reliability and validity of rating scales. Methodology 4, 73–79 (2008)
23. Michalopoulou, C., Tsartas, P., Giannisopoulou, M., Kafetzis, P., Manologlou, E.: Macedonia and the Balkans: xenophobia and development, in Greek. National Centre for Social Research-Alexandria, Athens, Greece (Abridged English edition 1999) (1998)
24. Mogharreban, N., Dilalla, L.: Fuzzy inference in the analysis of non-interval data. In: Proceedings of the WSEAS International Conference on Simulation, Modeling and Optimization, Lisbon, Portugal, pp. 22–24 (2006)
25. Moser, C., Kalton, G.: Survey Methods in Social Investigation. Heineman Educational Books, London (1971)
26. Nunnally, J.C., Bernstein, I.H.: Psychometric Theory, 3rd edn. McGraw-Hill, New York (1994)
27. O’Connor, B.P.: SPSS and SAS programs for determining the number of components using parallel analysis and Velicer’s MAP test. Behav. Res. Methods Instrum. Comput. 32, 396–402 (2000)
28. Reuse, S., Waller, N., Comrey, A.: Factor analysis and scale revision. Psychol. Assess. 12(3), 287–297 (2000)
29. Revelle, W., Zinbarg, R.E.: Coefficients alpha, beta, omega, and the glb: comments on Sijtsma. Psychometrika 74(1), 145–154 (2009)
30. Sah, M., Degtiarev, K.: Forecasting enrolment model based on first-order fuzzy time series. In: Proceedings of the World Academy of Science, Engineering and Technology I, pp. 132–135 (2005)
31. Song, Q., Chissom, B.: Forecasting enrolments with fuzzy time series: part II. Fuzzy Sets Syst. 62, 1–8 (1994)
32. Stamou, G., Tzafestas, S.: Fuzzy relation equations and fuzzy inference systems: an inside approach. IEEE Trans. Syst. Man Cybern. 99(6), 694–702 (1999)
33. Stephan, F.F., McCarthy, P.J.: Sampling Opinions: An Analysis of Survey Procedure. Greenwood, Westport (1974)
34. Steiner, D.L., Norman, G.R.: Health Measurement Scales: A Practical Guide to Their Development and Use, 4th edn. Oxford University Press, Oxford (2008)
35. Stevens, J.: Applied Multivariate Statistics for the Social Sciences, 4th edn. Lawrence Erbaum Associates, Mahwah (2002)
36. Symeonaki, M., Kalamatianou, A.: Markov systems with fuzzy states for the description of students’ educational progress in Greek Universities. Proceedings of the 58th World Statistics Congress ISI, Dublin, Ireland (2011)
37. Symeonaki, M., Kazani, A.: Developing a Fuzzy Likert Scale for Measuring Xenophobia in Greece. ASMDA, Rome (2011)
38. Tabachnick, B.G., Fidell, L.S.: Using Multivariate Statistics. Pearson Allyn and Bacon, Upper Saddle River (2007)
39. Thompson, B.: Exploratory and Confirmatory Factor Analysis: Understanding Concepts and Applications. The American Psychological Association, Washington, DC (2005)
40. Turksen, I.B., Willson, I.A.: A fuzzy set preference model for consumer choice. Fuzzy Sets Syst. 68, 253–266 (1994)
41. Zadeh, L.A.: Fuzzy sets. Inf Control 8(3), 338–353 (1965)