Soft Computing

, Volume 21, Issue 19, pp 5851–5857 | Cite as

Data envelopment analysis with non-L-R type fuzzy data

  • Cheng-Feng Hu
  • Fung-Bao Liu
Methodologies and Application


This work considers efficiency measures in data envelopment analysis with non-L-R type fuzzy data. It shows that the relative efficiencies of decision-making units with non-L-R type fuzzy inputs and outputs can be measured by solving an optimization problem on a mixed domain. The necessary and sufficient conditions for solving the resulting optimization problems are then investigated. This is the first attempt to measure fuzzy efficiency in data envelopment analysis in view of optimization problems on a mixed domain.


Data envelopment analysis Fuzzy decision-making Triangular norms Optimization 



The author would like to thank referees for their very constructive comments in revising this paper.

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interest related to this work.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of Applied MathematicsNational Chiayi UniversityChiayiTaiwan
  2. 2.Department of Mechanical and Automation EngineeringI-Shou UniversityKaohsiungTaiwan

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