A Fully Fuzzy Method of Network Data Envelopment Analysis for Assessing Revenue Efficiency Based on Ranking Functions

Document Type: بنیادی - نظری


1 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran

2 Department of mathematics, kerman Branch, Islamic azad university, kerman.

3 Department of mathematics, zahedan branch, Islamic azad university, zahedan.



The purpose of this paper is to evaluate the revenue efficiency in the fuzzy network data envelopment analysis‎. ‎Precision measurements in real-world data are not practically possible‎, ‎so assuming that data is crisp in solving problems is not a valid assumption‎. ‎One way to deal with imprecise data is fuzzy data‎. ‎In this paper‎, ‎linear ranking functions are used to transform the full fuzzy efficiency model into a precise linear programming problem and‎, ‎assuming triangular fuzzy numbers‎, ‎the fuzzy revenue efficiency of decision makers is measured‎. ‎In the end‎, ‎a numerical example shows the proposed method.


bibitem{1} Aghayi‎, ‎N.‎, ‎``Revenue efficiency measurement with undesirable data in fuzzy DEA"‎, ‎$7^{th}$ International Conference on Intelligent systems‎, ‎Modelling and Simulation‎, ‎2016‎.

‎bibitem{2} Banihashemi‎. ‎S.‎, ‎Tohidi G.‎, ‎2013‎. ‎``Allocation efficiency in the network DEA"‎, ‎International Journal of Data Envelopment Analysis‎, ‎1 (2)‎, ‎85-97‎.

‎bibitem{3} Charnes‎, ‎A.‎, ‎Cooper‎, ‎W.W.‎, ‎Rhodes‎, ‎E.‎, ‎1978‎. ‎``Measuring the efficiency of decision making units"‎, ‎European Journal of Operational Research‎, ‎2‎, ‎429–444‎.

‎bibitem{4} Chen‎, ‎S.M.‎, ‎1994‎. ‎``Fuzzy system reliability analysis using fuzzy number arithmetic operations"‎, ‎Fuzzy Sets and Systems‎, ‎66‎, ‎31-38‎.

‎bibitem{5} Coelli‎, ‎T.‎, ‎Rao‎, ‎D.S.P‎. ‎and Battese‎, ‎G.‎, ‎``An introduction to efficiency and productivity analysis (2nd Edition)"‎, ‎Springer US( 2005)‎.

‎bibitem{6} Cooper‎, ‎W.W.‎, ‎Seiford‎, ‎L.M.‎, ‎Tone‎, ‎K.‎, ‎``Data envelopment analysis‎: ‎a comprehensive text with models‎, ‎applications‎, ‎references and DEA-solver software"‎, ‎2nd edn‎. ‎Springer‎, ‎New York (2007)‎.

‎bibitem{7}Fare‎. ‎R.‎, ‎Grosskopf‎. ‎S.‎, ‎``Intertemporal production frontiers‎: ‎with Dynamic DEA"‎, ‎Kulwer Academic publishers‎, ‎Boston‎, ‎2000‎.

‎bibitem{8} Kordrostami‎, ‎S.‎, ‎Jahani S‎. ‎N.‎, ‎2019‎, ‎``Fuzzy revenue efficiency in sustainable supply chains"‎, ‎International Journal of Applied Operation Research‎, ‎9(1)‎, ‎63-70‎.

‎bibitem{9} Lewis‎. ‎H‎. ‎F.‎, ‎Sexton‎. ‎T‎. ‎R.‎, ‎2004‎. ‎``Network DEA‎: ‎Performance analysis of a organization with a comprehensive internal structure"‎, ‎Computers & Operations Research‎, ‎31‎, ‎1365-1410‎.

‎bibitem{10} Maleki‎, ‎H.R.‎, ‎2002‎. ‎``Ranking functions and their applications to fuzzy linear programming"‎, ‎Far East Journal of Mathematical Sciences‎, ‎4‎, ‎283-301‎.

‎bibitem{11} Nasseri‎, ‎S.H.‎, ‎Behmanesh‎, ‎E.‎, ‎Taleshian‎, ‎F.‎, ‎Abdolalipoor‎, ‎M.‎, ‎Taghi-Nezhad‎, ‎N.A‎ ., ‎2013.`` Fully fuzzy linear programming with inequality constraints"‎, ‎International Journal of Industrial Mathematics‎, ‎5 (4)‎, ‎309-316‎.

‎bibitem{12} Paryab‎, ‎K.‎, ‎Tavana‎, ‎M.‎, ‎Shiraz‎, ‎R.K.‎, ‎2014‎. ‎``Convex and non-convex approaches for cost-efficiency models with fuzzy data"‎, ‎International Journal of Data Mining Modeling and Management (in press)‎.

‎bibitem{13} Puri‎, ‎J.‎, ‎Yadav‎, ‎SP.‎, ‎2016‎. ‎``A fully fuzzy‎, ‎DEA approach for cost and revenue efficiency measurements in the presence of undesirable outputs and its application to the banking sector in india"‎, ‎International Journal of Fuzzy Systems‎, ‎18 (2)‎, ‎212-226‎.

‎bibitem{14} Sexton‎. ‎T‎. ‎R‎. ‎Lewis‎. ‎H‎. ‎F.‎, ‎2003‎. ‎``Two stage DEA‎: ‎An application to major league baseball"‎, ‎Journal of Productivity Analysis‎, ‎19‎, ‎227-249‎.

‎bibitem{15} Tone‎, ‎K.‎, ‎2002‎. ‎``A strange case of cost and allocation efficiencies in DEA"‎, ‎Journal of the Operational Research Society‎, ‎53 (11)‎, ‎1225-1231‎.

‎bibitem{16} Tone‎, ‎K.‎, ‎Tsutsui‎. ‎M.‎, ‎2009‎. ‎``Network DEA‎: ‎A slacks-based measure approach"‎, ‎European Journal of Operational Research‎, ‎197‎, ‎243-252‎.

‎bibitem{17} Zadeh‎, ‎L.A.‎, ‎1965‎. ‎``Fuzzy sets"‎, ‎Information and Control‎, ‎8‎, ‎338-353‎.


‎bibitem{18} Zimmermann‎, ‎H.J.‎, ‎``Fuzzy set theory and its applications"‎, ‎3rd edn‎. ‎Kluwer-Nijhoff Publishing‎, ‎Boston‎, ‎1996‎.