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Measuring quality of life with fuzzy numbers: in the perspectives of reliability, validity, measurement invariance, and feasibility

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Abstract

Purpose

Fuzzy set theory (FST) can improve various aspects of measurement with questionnaires. However, very little is known about how to use FST to measure quality of life (QOL). The main purpose of our study was to find an appropriate fuzzy measure for QOL that, while demonstrating the advantages of FST, can also be compared with mainstream QOL measures, most of which use traditional Likert-type scales.

Methods

Referring to the literature on fuzzy scoring methods, we first revised the measurement scale and scoring method of the traditional WHOQOL-BREF (i.e., a five-point Likert-type scale) to create three versions of a fuzzy WHOQOL-BREF. Then, we examined the psychometric relationships of these three fuzzy measures and the traditional WHOQOL-BREF in a within-subject design.

Results

Our results show that a fuzzy-scales weighted-by-membership (FSWM) version of the WHOQOL-BREF is comparable to the traditional WHOQOL-BREF in that it accepts strong invariance and shows almost perfect agreement. It also demonstrates higher reliability and face validity than the traditional WHOQOL-BREF.

Conclusion

We recommend that future studies examine the use of FSWM to measure QOL.

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References

  1. Neisser, U. (1967). Cognitive psychology. New York: Aooletion-Centry-Crofts.

    Google Scholar 

  2. Rabius, P. V., & Black, B. S. (2007). Measuring quality of life in dementia: Purposes, goals, challenges and progress. International Psychogeriatrics, 19(3), 401–407.

    Article  Google Scholar 

  3. Schneider, S. (2001). In search of realistic optimism: Meaning, knowledge, and warm fuzziness. American Psychologist, 56, 250–263.

    Article  CAS  PubMed  Google Scholar 

  4. Smithson, M. (1987). Fuzzy set analysis for behavior and social science. New York: Springer.

    Book  Google Scholar 

  5. Brown, S. J., & Morley, A. M. (2007). Risk perception, fuzzy representations and comparative optimism. British Journal of Psychology, 98, 578–587.

    Article  Google Scholar 

  6. Matt, G. E., Turingan, M. R., Dinh, Q. T., Felsch, J. A., Hovell, M. F., & Gehrman, C. (2003). Improving self-reports of drug-use: Numeric estimates as fuzzy sets. Addiction, 98, 1239–1247.

    Article  PubMed  Google Scholar 

  7. Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8, 338–352.

    Article  Google Scholar 

  8. Yu, S. C., & Yu, M. M. (2007). Fuzzy partial credit scaling: A more valid approach to scoring beck depression inventory II. Social Behavior and Personality, 35(9), 1163–1172.

    Article  Google Scholar 

  9. Pryor, R. G., Hesketh, B., & Gleitzman, M. (1989). Making things clearer by making them fuzzy: Counseling illustrations of a fuzzy graphic rating scale. The Career Development Quarterly, 38(2), 136–147.

    Article  Google Scholar 

  10. Higginson, I. J., & Carr, A. J. (2001). Using quality of life measures in the clinical setting. British Medical Journal, 322(7297), 1297–1300.

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  11. Schwartz, C. E., & Rapkin, B. D. (2004). Reconsidering the psychometrics of quality of life assessment in light of response shift and appraisal. Health and Quality of Life Outcomes, 2, 16–27.

    Article  PubMed Central  PubMed  Google Scholar 

  12. O’Leary, T. E., Diller, L., & Recklitis, C. J. (2007). The effects of response bias on self-reported quality of life among childhood cancer survivors. Quality of Life Research, 16, 1211–1220.

    Article  PubMed  Google Scholar 

  13. Hesketh, B., Pryor, R., & Gleitzman, M., & Hesketh, T. (1988). Practical applications and psychometric evaluation of a computerized fuzzy graphic ration scale. In: T. Zetenyi (Eds.), Fuzzy Sets in Psychology (pp. 425–454). Amsterdam: Elsevier, North-Holland.

  14. Lin, Y. H. (2002). The construction of fuzzy linguistics numbers for questionnaire and its empirical study. Survey Research-Method and Application, 11, 31–68.

    Google Scholar 

  15. Costas, C. S. L., Maranon, P. P., & Cabrera, J. A. H. (1994). Application of diffuse measurement to the evaluation of psychological structures. Quality and Quantity, 28(3), 305–313.

    Article  Google Scholar 

  16. The WHOQOL-Taiwan Group. (2005). The User’s Manual of the Development of the WHOQOL-BREF Taiwan Version (2nd ed.). Taipei: Taiwan WHOQOL Group.

    Google Scholar 

  17. Muthen, L. K., & Muthen, B. O. (2002). How to use a Monte Carlo study to decide on sample size and determine power. Structural Equation Modeling, 4, 599–620.

    Article  Google Scholar 

  18. Beauducel, A., & Herzberg, P. Y. (2006). On the performance of maximum likelihood versus means and variance adjusted weighted least squares estimation in CFA. Structural Equation Modeling, 13(2), 186–203.

    Article  Google Scholar 

  19. Rhemtulla, M., Brosseau-Liard, P. É., & Savalei, V. (2012). When can categorical variables be treated as continuous? A comparison of robust continuous and categorical SEM estimation methods under suboptimal conditions. Psychological Methods, 17(3), 354–373.

    Article  PubMed  Google Scholar 

  20. Meade, A. W., & Kroustalis, C. M. (2006). Problem with item parceling for confirmatory factor analytic tests of measurement invariance. Organizational Research Methods, 9(3), 369–403.

    Article  Google Scholar 

  21. Hollen, P. J., Gralla, R. J., Kris, M. G., McCoy, S., Donaldson, D. W., & Moinpour, C. M. (2005). A comparison of visual analogue and numerical rating scale formats for the Lung Cancer Symptom Scale (LCSS): Does format affect patient ratings of symptoms and quality of life? Quality of Life Research, 14(3), 837–847.

    Article  CAS  PubMed  Google Scholar 

  22. Muthen, B., & Asparouhov, T. (2013). BSEM Measurement Invariance Analysis. Mplus Web Notes, http://www.statmodel.com/examples/webnotes/webnote17.pdf.

  23. Revelle, W., & Zinbarg, R. E. (2009). Coefficients alpha, beta, omega and the glb: Comments on Sijtsma. Psychometrika, 74(1), 145–154.

    Article  Google Scholar 

  24. Cheung, G. W., & Rensvold, R. B. (2002). Evaluating goodness-of-fit indexes for testing measurement invariance. Structural Equation Modeling, 9(2), 233–255.

    Article  Google Scholar 

  25. Little, T. D. (1997). Mean and covariance structures (MACS) analyses of cross-cultural data: Practical and theoretical issues. Multivariate Behavioral Research, 32, 53–76.

    Article  Google Scholar 

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Acknowledgments

The authors gratefully acknowledge the financial support of the National Science Council (NSC 96-2413-H-002-011-MY3, NSC 99-2410-H-002-085-MY2). Our thanks also go to Dr. Yuan-Horng Lin and Dr. Sen-Chi Yu for their invaluable suggestions on the article. Last, we have to thank all of our participants and the Department of Psychology at National Taiwan University for their support.

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Authors and Affiliations

  1. Department of Psychology, University of Kansas, 1415 Jayhawk Blvd.Fraser Hall, Room 426, Lawrence, KS, 66045-7556, USA

    Po-Yi Chen

  2. Department of Psychology, National Taiwan University, 1, Sec. 4, Roosevelt RD., Taipei, Taiwan

    Grace Yao

Authors
  1. Po-Yi Chen
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  2. Grace Yao
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Correspondence to Grace Yao.

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Chen, PY., Yao, G. Measuring quality of life with fuzzy numbers: in the perspectives of reliability, validity, measurement invariance, and feasibility. Qual Life Res 24, 781–785 (2015). https://doi.org/10.1007/s11136-014-0816-3

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  • DOI: https://doi.org/10.1007/s11136-014-0816-3

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