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Hypothesis testing for means in connection with fuzzy rating scale-based data: algorithms and applications

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  • Lubiano, María Asunción
  • Montenegro, Manuel
  • Sinova, Beatriz
  • de la Rosa de Sáa, Sara
  • Gil, María Ángeles

Abstract

The fuzzy rating scale was introduced as a tool to measure intrinsically ill-defined/ imprecisely-valued attributes in a free way. Thus, users do not have to choose a value from a class of prefixed ones (like it happens when a fuzzy semantic representation of a linguistic term set is considered), but just to draw the fuzzy number that better represents their valuation or measurement. The freedom inherent to the fuzzy rating scale process allows users to collect data with a high level of richness, accuracy, expressiveness, diversity and subjectivity, what is especially valuable for statistical purposes.

Suggested Citation

  • Lubiano, María Asunción & Montenegro, Manuel & Sinova, Beatriz & de la Rosa de Sáa, Sara & Gil, María Ángeles, 2016. "Hypothesis testing for means in connection with fuzzy rating scale-based data: algorithms and applications," European Journal of Operational Research, Elsevier, vol. 251(3), pages 918-929.
    • Handle: RePEc:eee:ejores:v:251:y:2016:i:3:p:918-929
    DOI: 10.1016/j.ejor.2015.11.016
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    References listed on IDEAS

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    1. Manuel Montenegro & Ana Colubi & María Rosa Casals & María Ángeles Gil, 2004. "Asymptotic and Bootstrap techniques for testing the expected value of a fuzzy random variable," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 59(1), pages 31-49, February.
    2. Yan, Hong-Bin & Ma, Tieju, 2015. "A group decision-making approach to uncertain quality function deployment based on fuzzy preference relation and fuzzy majority," European Journal of Operational Research, Elsevier, vol. 241(3), pages 815-829.
    3. Gil, Maria Angeles & Montenegro, Manuel & Gonzalez-Rodriguez, Gil & Colubi, Ana & Rosa Casals, Maria, 2006. "Bootstrap approach to the multi-sample test of means with imprecise data," Computational Statistics & Data Analysis, Elsevier, vol. 51(1), pages 148-162, November.
    4. Haelermans, Carla & De Witte, Kristof, 2012. "The role of innovations in secondary school performance – Evidence from a conditional efficiency model," European Journal of Operational Research, Elsevier, vol. 223(2), pages 541-549.
    5. Nikolaidis, Yiannis & Dimitriadis, Sotirios G., 2014. "On the student evaluation of university courses and faculty members’ teaching performance," European Journal of Operational Research, Elsevier, vol. 238(1), pages 199-207.
    6. Roszkowska, Ewa & Wachowicz, Tomasz, 2015. "Application of fuzzy TOPSIS to scoring the negotiation offers in ill-structured negotiation problems," European Journal of Operational Research, Elsevier, vol. 242(3), pages 920-932.
    7. P. Filzmoser & R. Viertl, 2004. "Testing hypotheses with fuzzy data: The fuzzy p-value," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 59(1), pages 21-29, February.
    8. González-Rodríguez, Gil & Colubi, Ana & Gil, María Ángeles, 2012. "Fuzzy data treated as functional data: A one-way ANOVA test approach," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 943-955.
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    Cited by:

    1. Ana M. Castaño & M. Asunción Lubiano & Antonio L. García-Izquierdo, 2020. "Gendered Beliefs in STEM Undergraduates: A Comparative Analysis of Fuzzy Rating versus Likert Scales," Sustainability, MDPI, vol. 12(15), pages 1-17, August.
    2. Beatriz Sinova & Stefan Van Aelst & Pedro Terán, 2021. "M-estimators and trimmed means: from Hilbert-valued to fuzzy set-valued data," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 15(2), pages 267-288, June.

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