TY - JOUR

T1 - Data envelopment analysis with missing data

T2 - An application to university libraries in Taiwan

AU - Kao, C.

AU - Liu, S. Tai

N1 - Funding Information:
Acknowledgements—This research is supported by the National Science Council of the Republic of China under contracts NSC87-2416-H006-022 and NSC86-2416-H006-003.

PY - 2000/8

Y1 - 2000/8

N2 - In measuring the relative efficiencies of a set of decision making units (DMUs) via data envelopment analysis (DEA), detailed inputs and outputs are usually involved. However, there are cases where some DMUs are unable to provide all the necessary data. This paper adopts the concept of a membership function used in fuzzy set theory for representing imprecise data. The smallest possible, most possible, and largest possible values of the missing data are derived from the observed data to construct a triangular membership function. With the membership function, a fuzzy DEA model can be utilized to calculate the efficiency scores. Since the efficiency scores are fuzzy numbers, they are more informative than crisp efficiency scores calculated by assuming crisp values for the missing data. As an illustration, the efficiency scores of the 24 University libraries in Taiwan, with three missing values, are calculated to show the extent that the actual amount of resources and services provided by each University is away from the technically efficient amount of resources and services. This methodology can also be applied to calculate the relative efficiencies of the DMUs with imprecise linguistic data.

AB - In measuring the relative efficiencies of a set of decision making units (DMUs) via data envelopment analysis (DEA), detailed inputs and outputs are usually involved. However, there are cases where some DMUs are unable to provide all the necessary data. This paper adopts the concept of a membership function used in fuzzy set theory for representing imprecise data. The smallest possible, most possible, and largest possible values of the missing data are derived from the observed data to construct a triangular membership function. With the membership function, a fuzzy DEA model can be utilized to calculate the efficiency scores. Since the efficiency scores are fuzzy numbers, they are more informative than crisp efficiency scores calculated by assuming crisp values for the missing data. As an illustration, the efficiency scores of the 24 University libraries in Taiwan, with three missing values, are calculated to show the extent that the actual amount of resources and services provided by each University is away from the technically efficient amount of resources and services. This methodology can also be applied to calculate the relative efficiencies of the DMUs with imprecise linguistic data.

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U2 - 10.1057/palgrave.jors.2600056

DO - 10.1057/palgrave.jors.2600056

M3 - Article

AN - SCOPUS:0034245894

VL - 51

SP - 897

EP - 905

JO - Journal of the Operational Research Society

JF - Journal of the Operational Research Society

SN - 0160-5682

IS - 8

ER -