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Indirect membership function assignment based on ordinal regression

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  • Qing Li

Abstract

In many fuzzy sets applications, fuzzy membership functions are commonly developed based on empirical or expert knowledge. The equation of a membership function is usually determined somewhat arbitrarily. This paper explores a novel membership function design method based on ordinal regression analysis. The estimated thresholds between ordinal measurement categories are applied to calculate the intersection points between fuzzy sets. These intersection points are further applied to determine the equations of the membership functions. Information distortion due to empirical guess can thus be reduced and more latent information in the fuzzy responses can therefore be captured. A case study investigating the relationship between foster mothers’ satisfaction and the foster time and information provided has been conducted in this research. The applicability and effectiveness of the proposed membership function assignment approach have been demonstrated through several case studies.

Suggested Citation

  • Qing Li, 2016. "Indirect membership function assignment based on ordinal regression," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(3), pages 441-460, March.
    • Handle: RePEc:taf:japsta:v:43:y:2016:i:3:p:441-460
    DOI: 10.1080/02664763.2015.1070802
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    References listed on IDEAS

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    1. Jay Verkuilen, 2005. "Assigning Membership in a Fuzzy Set Analysis," Sociological Methods & Research, , vol. 33(4), pages 462-496, May.
    2. Phillis, Yannis A. & Andriantiatsaholiniaina, Luc A., 2001. "Sustainability: an ill-defined concept and its assessment using fuzzy logic," Ecological Economics, Elsevier, vol. 37(3), pages 435-456, June.
    3. Michelle Lalla & Gisella Facchinetti & Giovanni Mastroleo, 2005. "Ordinal scales and fuzzy set systems to measure agreement: An application to the evaluation of teaching activity," Quality & Quantity: International Journal of Methodology, Springer, vol. 38(5), pages 577-601, January.
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    1. Niccolò Cao & Antonio Calcagnì, 2022. "Jointly Modeling Rating Responses and Times with Fuzzy Numbers: An Application to Psychometric Data," Mathematics, MDPI, vol. 10(7), pages 1-11, March.

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