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Efficiency Measurement in Data Envelopment Analysis with Fuzzy Data

  • Chiang Kao
Chapter
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 221)

Abstract

Conventional data envelopment analysis (DEA) requires the data to have crisp values, which can be measured precisely. However, there are cases where data is missing and has to be estimated, or the situation has not occurred yet and the data has to be predicted. There are also cases where the factors are qualitative, and thus the data cannot be measured precisely. In these cases, fuzzy numbers can be used to represent the imprecise values, and this paper discusses the corresponding measurement of efficiency. Based on the extension principle, two approaches are proposed; one views the membership function of the fuzzy data vertically, and the results are represented by membership grades. The other views it horizontally, and the results are represented by α-cuts. The former approach is easier to understand, yet is applicable only to very simple problems. The latter, in contrast, can be applied to all problems, and is easier to implement. An example explains the development and implementation of these two approaches.

Keywords

Data envelopment analysis Fuzzy data Two-level programming Extension principle 

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of Industrial and Information ManagementNational Cheng Kung UniversityTainanTaiwan

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