The concept of assurance region (AR) was proposed in Data Envelopment Analysis (DEA) literature to restrict the ratio of any two weights within a given lower and upper bounds so as to overcome the difficulty of ignoring or relying too much on any of the input or output while calculating the efficiency. Further, AR approach was extended to handle fuzzy input/output data. But, available information is not always sufficient to define the impreciseness in the input/output data using classical fuzzy sets. Intuitionistic Fuzzy Set (IFS) is a generalized fuzzy set to characterize the impreciseness by taking into account degree of hesitation also. In this paper, intuitionistic fuzzy DEA/AR approach has been proposed to evaluate the efficiency where input/output data are represented as intuitionistic fuzzy. Based on the expected value approach, classical cross efficiency has also been generalized to rank the DMUs for the case of intuitionistic fuzzy data. To the best of my knowledge, this is the first attempt to propose assurance region approach (DEA/AR) in DEA with intuitionistic fuzzy input/output data. This approach is useful for the experts and decision makers when they are hesitant about defining the degree of membership/non-membership of fuzzy data. Results have been illustrated and validated using a case of flexible manufacturing systems (FMS).
Accepté le :
DOI : 10.1051/ro/2017081
Mots-clés : DEA fuzzy, DEA assurance region, intuitionistic fuzzy sets, fuzzy sets
@article{RO_2018__52_1_241_0,
author = {Singh, Sanjeet},
title = {Intuitionistic fuzzy {DEA/AR} and its application to flexible manufacturing systems},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {241--257},
publisher = {EDP-Sciences},
volume = {52},
number = {1},
year = {2018},
doi = {10.1051/ro/2017081},
mrnumber = {3812479},
zbl = {1403.90663},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ro/2017081/}
}
TY - JOUR AU - Singh, Sanjeet TI - Intuitionistic fuzzy DEA/AR and its application to flexible manufacturing systems JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2018 SP - 241 EP - 257 VL - 52 IS - 1 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ro/2017081/ DO - 10.1051/ro/2017081 LA - en ID - RO_2018__52_1_241_0 ER -
%0 Journal Article %A Singh, Sanjeet %T Intuitionistic fuzzy DEA/AR and its application to flexible manufacturing systems %J RAIRO - Operations Research - Recherche Opérationnelle %D 2018 %P 241-257 %V 52 %N 1 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ro/2017081/ %R 10.1051/ro/2017081 %G en %F RO_2018__52_1_241_0
Singh, Sanjeet. Intuitionistic fuzzy DEA/AR and its application to flexible manufacturing systems. RAIRO - Operations Research - Recherche Opérationnelle, Tome 52 (2018) no. 1, pp. 241-257. doi : 10.1051/ro/2017081. http://archive.numdam.org/articles/10.1051/ro/2017081/
[1] , and , Measuring the efficiency of decision making units. Eur. J. Oper. Res. 2 (1978) 429–444 | DOI | MR | Zbl
[2] , The Measurement of Productive Efficiency. J. R. Statis. Soc. Series A (General) 120 (1957) 253–290 | DOI
[3] , and Data envelopment analysis: A comprehensive text with models. Applications, references and DEA-solver software: 2nd edition. (2007) | Zbl
[4] , and , Evaluation of research in efficiency and productivity: A survey and analysis of the first 30 years of scholarly literature in DEA. Socio-Econ. Plan. Sci. 42 (2008) 151–157 | DOI
[5] , and , A survey of data envelopment analysis in energy and environmental studies. Eur. J. Oper. Res. 189 (2008) 1–18 | DOI | MR | Zbl
[6] and , Data envelopment analysis (DEA) – Thirty years on. Eur. J. Oper. Res. 192 (2009) 1–17 | DOI | MR | Zbl
[7] , Measuring the Performance of Teams in the Indian Premier League. Am. J. Oper. Res. 1 (2011) 180–184
[8] and , Efficiency analysis of non-homogeneous parallel sub-unit systems for the performance measurement of higher education. Ann. Oper. Res. (2017) 1–26
[9] , and , Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis. Manag. Sci. 30 (1984) 1078–1092 | DOI | Zbl
[10] Quantitative Models for Performance Evaluation and Benchmarking: Data Envelopment Analysis with Spreadsheets, 3rdEd. Springer International Publishing Switzerland (2014) | MR | Zbl
[11] , , and , Comparative Site Evaluations for Locating a High-Energy Physics Lab in Texas. Interfaces 16 (1986) 35–49 | DOI
[12] , , , and , The role of multiplier bounds in efficiency analysis with application to Kansas farming. J. Econ. 46 (1990) 93–108 | DOI
[13] , Measuring the industrial performance of Chinese cities by data envelopment analysis. Socio-Econ. Plan. Sci. 26 (1992) 75–88 | DOI
[14] , , , and , DEA/Assurance Region SBDC Efficiency and Unique Projections. Oper. Res. 44 (1996) 533–542 | DOI | Zbl
[15] , , and , DEA/AR efficiency and profitability of Mexican banks a total income model. Eur. J. Oper. Res. 98 (1997) 346–363 | DOI | Zbl
[16] and , Determination of bounds in DEA assurance region method: Its application to evaluation of baseball players and chemical companies. J. Oper. Res. Soc. Japan 52 (2009) 453–467 | MR
[17] , and , Assurance region context-dependent DEA with an application to Taiwanese hotel industry, Int. J. Oper. Res. 8 (2010) 292–312 | DOI
[18] , Measuring efficiency by a fuzzy statistical approach. Fuzzy Sets Syst. 46 (1992) 73–80 | DOI
[19] , A fuzzy systems approach in data envelopment analysis. Comput. Math. Appl. 24 (1992) 259–266 | DOI | MR | Zbl
[20] , Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst. 1 (1978) 3–28 | DOI | MR | Zbl
[21] Fuzzy Set Theory and Its Applications. Springer (2001) | DOI | MR | Zbl
[22] and , A mathematical programming approach for measuring technical efficiency in a fuzzy environment. J. Product. Anal. 10 (1998) 85–102 | DOI
[23] , Data envelopment analysis in fuzzy environment. Int. J. Inf. Manag. Sci. 12 (2001) 51–65 | MR | Zbl
[24] and , Fuzzy DEA: a perceptual evaluation method. Fuzzy Sets Syst. 119 (2001) 149–160 | DOI | MR
[25] and , Fuzzy efficiency measures in data envelopment analysis. Fuzzy Sets Syst. 113 (2000) 427–437 | DOI | Zbl
[26] , Fuzzy data envelopment analysis and its application to location problems. Inf. Sci. (Ny). 179 (2009) 820–829 | DOI | MR | Zbl
[27] and , A flexible deterministic, stochastic and fuzzy Data Envelopment Analysis approach for supply chain risk and vendor selection problem: Simulation analysis. Expert Syst. Appl. 37 (2010) 7438–7448 | DOI
[28] , and , Measuring Transport Systems Efficiency Under Uncertainty by Fuzzy Sets Theory Based Data Envelopment Analysis: Theoretical and Practical Comparison with Traditional DEA Model. Transp. Res. Procedia 5 (2015) 186–200 | DOI
[29] , and , A Technique for Supply Chain Network Design under Uncertainty using Cross-Efficiency Fuzzy Data Envelopment Analysis. IFAC-PapersOnLine 48 (2015) 634–639 | DOI
[30] , and , Assessing productive efficiency of banks using integrated Fuzzy-DEA and bootstrapping: A case of Mozambican banks. Eur. J. Oper. Res. 249 (2016) 378–389 | DOI | Zbl
[31] , and , The State of the Art in Fuzzy Data Envelopment Analysis (2014) 1–45
[32] , Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20 (1986) 87–96 | DOI | MR | Zbl
[33] , and , An application of intuitionistic fuzzy sets in medical diagnosis. Fuzzy Sets Syst. 117 (2001) 209–213 | DOI | Zbl
[34] and , New similarity measures of intuitionistic fuzzy sets and application to pattern recognitions, Pattern Recognit. Lett. 23 (2002) 221–225 | DOI | Zbl
[35] , and , A group MADM method for personnel selection problem using Delphi technique based on intuitionistic fuzzy sets. J. Mil. Inf. Sci. 1 (2013) 1–13
[36] , , , , and , IFSJSP: A novel methodology for the Job-Shop Scheduling Problem based on intuitionistic fuzzy sets. Int. J. Prod. Res. 51 (2013) 5100–5119 | DOI
[37] and , Multiplicative consistency of intuitionistic reciprocal preference relations and its application to missing values estimation and consensus building. Knowledge-Based Syst. 71 (2014) 187–200 | DOI
[38] , A new knowledge-based measure for intuitionistic fuzzy sets and its application in multiple attribute group decision making. Expert Syst. Appl. 42 (2015) 8766–8774 | DOI
[39] The DEA and Intuitionistic Fuzzy TOPSIS Approach to Departments’ Performances: A Pilot Study. J.Appl. Math. 2011 (2011) 1–16 | DOI | Zbl
[40] , and , Sorting of decision making units in data envelopment analysis with intuitionistic fuzzy weighted entropy. D.C. Wyld al. Adv. Comput. Sci. Eng. Appl., AISC 166 (2012) 567–576
[41] , , and , An intuitionistic fuzzy data envelopment analysis for efficiency evaluation under uncertainty: case of a finance and credit institution. E+M Ekon. Manag. 1 (2013) 128–137
[42] and , Intuitionistic fuzzy data envelopment analysis: An application to the banking sector in India. Expert Syst. Appl. 42 (2015) 4982–4998 | DOI
[43] and , Intuitionistic Fuzzy Number and Its Arithmetic Operation with Application on System Failure. J. Uncertain Syst. 7 (2013) 92–107
[44] and , A unified framework for the selection of a Flexible Manufacturing System. Eur. J. Oper. Res. 85 (1995) 297–315 | DOI | Zbl
[45] , A fuzzy DEA/AR approach to the selection of flexible manufacturing systems. Comput. Ind. Eng. 54 (2008) 66–76 | DOI
[46] , Distances and orderings in a family of intuitionistic fuzzy numbers. EUSFLAT Confere. 5 (2003) 223–227
[47] and , A New Approach on Solving Intuitionistic Fuzzy Linear Programming Problem. Appl. Math. Sci. 6 (2012) 3467–3474 | MR | Zbl
[48] and , The non-archimedean CCR ratio for efficiency analysis: A rejoinder to Boyd and Fare. Eur. J. Oper. Res. 15 (1984) 333–334 | DOI
[49] and , Programming with linear fractional functionals. Nav. Res. Logist. Q. 9 (1962) 181–186 | DOI | MR | Zbl
[50] , and , Review of ranking methods in the data envelopment analysis context. Eur. J. Oper. Res. 140 (2002) 249–265 | DOI | MR | Zbl
[51] , and , Data envelopment analysis: Critique and extensions. New Dir. Progr. Eval. 1986 (1986) 73–105
[52] and , Efficiency and Cross-Efficiency in DEA: Derivations, Meanings and Uses. J. Oper. Res. Soc. 45 (1994) 567 | DOI | Zbl
[53] , and , Preference voting and project ranking using DEA and cross-evaluation. Eur. J. Oper. Res. 90 (1996) 461–472 | DOI | Zbl
[54] and , A performance benchmarking study of Indian Railway zones. Benchmarking An Int. J. 15 (2008) 599–617 | DOI
[55] , Evaluation of world’s largest social welfare scheme: An assessment using non-parametric approach. Eval. Program Plan. 57 (2016) 16–29 | DOI
[56] An assessment of technical efficiency and cross-efficiency in Taiwan’s electricity distribution sector. Eur. J. Oper. Res. 137 (2002) 421–433 | DOI | Zbl
[57] , and , DEA game cross-efficiency approach to Olympic rankings. Omega 37 (2009) 909–918 | DOI
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