Operational Research

, Volume 17, Issue 3, pp 697–714 | Cite as

Environmental efficiency evaluation with left–right fuzzy numbers

  • Ma-Lin Song
  • Yuan-Xiang Zhou
  • Rong-Rong Zhang
  • Ron Fisher
Original Paper


Undesirable outputs such as waste and smoke pollution are often produced along with desirable outputs in the production processes of many enterprises. Therefore, when evaluating production efficiency, both desirable and undesirable outputs should be considered simultaneously. Based on the previous data envelopment analysis model, we present a fuzzy slacks-based measure model incorporating a confidence coefficient on the postulation that inputs and outputs are left–right (L–R) fuzzy numbers. In this paper, the model not only solves the input slacks when presetting the confidence coefficient but also solves efficiency evaluation problems when undesirable output exists, thereby expanding the range of applications for environmental efficiency evaluation. Furthermore, it provides a basis for decision making in a wider range of situations to reduce undesirable outputs, control the quantities of pollutants discharged, and improve the environment. To provide an example of this last point, the proposed model is applied to perform an analysis of the industrial environmental performance of 31 provinces in China.


Environmental efficiency Undesirable outputs Fuzzy sets Confidence coefficient Fuzzy slacks-based measure 



This work was supported by Major Projects in Philosophy and Social Science Research of the Ministry of Education of China under Grant No. 14JZD031; the Program of Post-Graduate Scientific Research Innovation Fund by Anhui University of Finance and Economics under Grant No. CXJJ2014069; the Program for New Century Excellent Talents in University under Grant No. NCET-12-0595; the National Natural Science Foundation of China under Grant Nos. 71171001 and 71471001; and Key Projects in Philosophy and Social Science of Anhui, China under Grant No. AHSKZ2014D01.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Ma-Lin Song
    • 1
  • Yuan-Xiang Zhou
    • 1
  • Rong-Rong Zhang
    • 1
  • Ron Fisher
    • 2
  1. 1.School of Statistics and Applied MathematicsAnhui University of Finance and EconomicsBengbuPeople’s Republic of China
  2. 2.Griffith Business SchoolGriffith UniversityGold CoastAustralia

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