### Abstract

Conventional data envelopment analysis (DEA) treats a system as a whole unit when measuring efficiency, ignoring the operations of the component processes. Network DEA, on the other hand, takes the component processes into consideration, with results that are more representative and can be used to identify inefficient components. This paper discusses network DEA for fuzzy observations. Two approaches, the membership grade and the α-cut, are proposed for measuring the system and process efficiencies via two-level mathematical programming. The model associated with the latter approach is transformed into a conventional one-level program so that the existing solution methods can be applied. Since the data is fuzzy, the measured efficiencies are also fuzzy. The property of the system efficiency slack being the sum of the process efficiency slacks, which holds in the deterministic case, was found to hold for the fuzzy case as well. A simple network system with three processes is used to illustrate the proposed idea.

Original language | English |
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Title of host publication | Performance Measurement with Fuzzy Data Envelopment Analysis |

Publisher | Springer Verlag |

Pages | 191-206 |

Number of pages | 16 |

ISBN (Print) | 9783642413711 |

DOIs | |

Publication status | Published - 2014 Jan 1 |

### Publication series

Name | Studies in Fuzziness and Soft Computing |
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Volume | 309 |

ISSN (Print) | 1434-9922 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Computer Science (miscellaneous)
- Computational Mathematics

### Cite this

*Performance Measurement with Fuzzy Data Envelopment Analysis*(pp. 191-206). (Studies in Fuzziness and Soft Computing; Vol. 309). Springer Verlag. https://doi.org/10.1007/978-3-642-41372-8_9

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*Performance Measurement with Fuzzy Data Envelopment Analysis.*Studies in Fuzziness and Soft Computing, vol. 309, Springer Verlag, pp. 191-206. https://doi.org/10.1007/978-3-642-41372-8_9

**Network data envelopment analysis with fuzzy data.** / Kao, Chiang.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

TY - CHAP

T1 - Network data envelopment analysis with fuzzy data

AU - Kao, Chiang

PY - 2014/1/1

Y1 - 2014/1/1

N2 - Conventional data envelopment analysis (DEA) treats a system as a whole unit when measuring efficiency, ignoring the operations of the component processes. Network DEA, on the other hand, takes the component processes into consideration, with results that are more representative and can be used to identify inefficient components. This paper discusses network DEA for fuzzy observations. Two approaches, the membership grade and the α-cut, are proposed for measuring the system and process efficiencies via two-level mathematical programming. The model associated with the latter approach is transformed into a conventional one-level program so that the existing solution methods can be applied. Since the data is fuzzy, the measured efficiencies are also fuzzy. The property of the system efficiency slack being the sum of the process efficiency slacks, which holds in the deterministic case, was found to hold for the fuzzy case as well. A simple network system with three processes is used to illustrate the proposed idea.

AB - Conventional data envelopment analysis (DEA) treats a system as a whole unit when measuring efficiency, ignoring the operations of the component processes. Network DEA, on the other hand, takes the component processes into consideration, with results that are more representative and can be used to identify inefficient components. This paper discusses network DEA for fuzzy observations. Two approaches, the membership grade and the α-cut, are proposed for measuring the system and process efficiencies via two-level mathematical programming. The model associated with the latter approach is transformed into a conventional one-level program so that the existing solution methods can be applied. Since the data is fuzzy, the measured efficiencies are also fuzzy. The property of the system efficiency slack being the sum of the process efficiency slacks, which holds in the deterministic case, was found to hold for the fuzzy case as well. A simple network system with three processes is used to illustrate the proposed idea.

UR - http://www.scopus.com/inward/record.url?scp=84958529322&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84958529322&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-41372-8_9

DO - 10.1007/978-3-642-41372-8_9

M3 - Chapter

AN - SCOPUS:84958529322

SN - 9783642413711

T3 - Studies in Fuzziness and Soft Computing

SP - 191

EP - 206

BT - Performance Measurement with Fuzzy Data Envelopment Analysis

PB - Springer Verlag

ER -