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Modeling qualitative data in data envelopment analysis for composite indicators

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Abstract

Composite indicators (CIs) are useful tools for performance evaluation in policy analysis and public communication. Among various performance evaluation methodologies, data envelopment analysis (DEA) has recently received considerable attention in the construction of CIs. In basic DEA-based CI models, obtainment of measurable and quantitative indicators is commonly the prerequisite of the evaluation. However, it becomes more and more difficult to be guaranteed in today’s complex performance evaluation activities, because the natural uncertainty of reality often leads up to the imprecision and vagueness inherent in the information that can only be represented by means of qualitative data. In this study, we investigate two approaches within the DEA framework for modeling both quantitative and qualitative data in the context of composite indicators construction. They are imprecise DEA (IDEA) and fuzzy DEA (FDEA), respectively. Based on their principle, we propose two new models of IDEA-based CIs and FDEA-based CIs in road safety management evaluation by creating a composite road safety policy performance index for 25 European countries. The results verify the robustness of the index scores computed from both models, and further imply the effectiveness and reliability of the proposed two approaches for modeling qualitative data.

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Notes

  1. If (u*, v*) is an optimal solution, then (au*, av*) is also optimal for a > 0 (Cooper et al. 2004).

  2. ɛ is a small number used to reflect the minimum allowable gap between the values associated with y ik and yik+1, which can have a certain impact on the final index scores. In real situations, different ɛ values can be used for different ordinal indicators, or other discrimination intensity functions can be employed. See also (Cook and Kress 1990).

  3. \( \sum\nolimits_{r = 1}^{s} {u_{r} \left( {y_{lrj} - a_{rj} L^{*} (h)} \right)} \le 1 \) is always satisfied when \( \sum\nolimits_{r = 1}^{s} {u_{r} \left( {y_{urj} + b_{rj} R^{*} (h)} \right)} \le 1 \).

  4. The common 4-point scale ordinal values are used for all the five indicators, which provide no loss of generality.

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Authors and Affiliations

  1. Transportation Research Institute (IMOB), Hasselt University, Wetenschapspark 5 bus 6, 3590, Diepenbeek, Belgium

    Yongjun Shen, Da Ruan, Elke Hermans, Tom Brijs, Geert Wets & Koen Vanhoof

  2. Belgian Nuclear Research Centre (SCK·CEN), Boeretang 200, 2400, Mol, Belgium

    Da Ruan

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  1. Yongjun Shen
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  2. Da Ruan
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  3. Elke Hermans
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  4. Tom Brijs
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  5. Geert Wets
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  6. Koen Vanhoof
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Correspondence to Yongjun Shen.

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Shen, Y., Ruan, D., Hermans, E. et al. Modeling qualitative data in data envelopment analysis for composite indicators. Int J Syst Assur Eng Manag 2, 21–30 (2011). https://doi.org/10.1007/s13198-011-0051-z

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