American Institute of Mathematical Sciences

Advanced
  • Previous Article
    The optimal solution to a principal-agent problem with unknown agent ability
  • JIMO Home
  • This Issue
  • Next Article
    Robust equilibrium control-measure policy for a DC pension plan with state-dependent risk aversion under mean-variance criterion
doi: 10.3934/jimo.2020046

Network data envelopment analysis with fuzzy non-discretionary factors

Cheng-Kai Hu 1, , Fung-Bao Liu 2, , Hong-Ming Chen 3, and  Cheng-Feng Hu 4,,

1. 

Department of International Business, Kao Yuan University, Kaohsiung, 82151, Taiwan
2. 

Department of Mechanical and Automation Engineering, I-Shou University, Kaohsiung, 84001, Taiwan
3. 

Department of Applied Mathematics, Tunghai University, Taichung 40704, Taiwan
4. 

Department of Applied Mathematics, National Chiayi University, Chiayi, 60004, Taiwan

* Corresponding author: C.-F. Hu

Received  January 2019 Revised  September 2019 Published  March 2020

Network data envelopment analysis (DEA) concerns using the DEA technique to measure the relative efficiency of a system, taking into account its internal structure. The results are more meaningful and informative than those obtained from the conventional DEA models. This work proposed a new network DEA model based on the fuzzy concept even though the inputs and outputs data are crisp numbers. The model is then extended to investigate the network DEA with fuzzy non-discretionary variables. An illustrative application assessing the impact of information technology (IT) on firm performance is included. The results reveal that modeling the IT budget as a fuzzy non-discretionary factor improves the system performance of firms in a banking industry.

Keywords: Network DEA, non-discretionary, fuzzy decision making.
Mathematics Subject Classification: Primary: 90B50, 90C08; Secondary: 91B06.
Citation: Cheng-Kai Hu, Fung-Bao Liu, Hong-Ming Chen, Cheng-Feng Hu. Network data envelopment analysis with fuzzy non-discretionary factors. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2020046
References:
[1]

R. D. Banker and R. Morey, Efficiency analysis for exogenously fixed inputs and outputs, Oper. Res., 34 (1986), 501-653.  doi: 10.1287/opre.34.4.513.  Google Scholar

[2]

M. Barat, G. Tohidi and M. Sanei, DEA for nonhomogeneous mixed networks, Asia Pac. Manag. Rev., 24 (2018), 161-166.  doi: 10.1016/j.apmrv.2018.02.003.  Google Scholar

[3]

R. E. Bellman and L. A. Zadeh, Decision making in a fuzzy environment, Manag. Sci., 17 (1970), B141–B164. doi: 10.1287/mnsc.17.4.B141.  Google Scholar

[4]

L. Castelli, R. Pesenti and W. Ukovich, DEA-like models for the efficiency evaluation of hierarchically structured units, Eur. J. Oper. Res., 154 (2004), 465-476.  doi: 10.1016/S0377-2217(03)00182-6.  Google Scholar

[5]

J. Zhu, Data Envelopment Analysis: A Handbook of Modeling Internal Structures and Networks, International Series in Operations Research & Management Science, 238. Springer, New York, 2016. doi: 10.1007/978-1-4899-7684-0.  Google Scholar

[6]

J. M. Cordero-Ferrera, F. Pedraja-Chaparro and D. Santín-González, Enhancing the inclusion of non-discretionary inputs in DEA, J. Oper. Res. Soc., 61 (2010), 574-584.  doi: 10.1057/jors.2008.189.  Google Scholar

[7]

R. Färe and S. Grosskopf, Intertemporal Production Frontiers: With Dynamic DEA, Boston: Kluwer Academic Publishers, 1996. Google Scholar

[8]

R. Färe and S. Grosskopf, Network DEA, Socio. Econ. Plann. Sci., 4 (2000), 35-49.   Google Scholar

[9]

D. U. A. Galagedera, Modelling social responsibility in mutual fund performance appraisal: A two-stage data envelopment analysis model with non-discretionary first stage output, Eur. J. Oper. Res., 273 (2019), 376-389.  doi: 10.1016/j.ejor.2018.08.011.  Google Scholar

[10]

B. Golany and Y. Roll, Some extensions of techniques to handle non-discretionary factors in data envelopment analysis, J. Prod. Anal., 4 (1993), 419-432.  doi: 10.1007/BF01073549.  Google Scholar

[11]

C. Kao, Network data envelopment analysis: A review, Eur. J. Oper. Res., 239 (2014), 1-16.  doi: 10.1016/j.ejor.2014.02.039.  Google Scholar

[12]

C. Kao, Efficiency decomposition and aggregation in network data envelopment analysis, Eur. J. Oper. Res., 255 (2016), 778-786.  doi: 10.1016/j.ejor.2016.05.019.  Google Scholar

[13]

C. Kao and S.-N. Hwang, Efficiency measurement for network systems: IT impact on firm performance, Decis. Support Syst., 48 (2010), 437-446.  doi: 10.1016/j.dss.2009.06.002.  Google Scholar

[14]

R. J. Kauffman and P. Weill, An evaluative framework for research on the performance effects of information technology investment, Proceedings of the 10th International Conference on Information Systems, (1989), 377–388. doi: 10.1145/75034.75066.  Google Scholar

[15]

M. A. Muniz, J. Paradi, J. Ruggiero and Z. Yang, Evaluating alternative DEA models used to control for non-discretionary inputs, Comput. Oper. Res., 33 (2006), 1173-1183.   Google Scholar

[16]

L. Simar and P. W. Wilson, Estimation and inference in two-stage, semi-parametric models of production processes, J. Econom., 136 (1997), 31-64.  doi: 10.1016/j.jeconom.2005.07.009.  Google Scholar

[17]

M. Taleb, R. Ramli and R. Khalid, Developing a two-stage approach of super efficiency slack-based measure in the presence of non-discretionary factors and mixed integer-valued data envelopment analysis, Expert. Syst. Appl., 103 (2018), 14-24.  doi: 10.1016/j.eswa.2018.02.037.  Google Scholar

[18]

C. H. Wang, R. Gopal and S. Zionts, Use of data envelopment analysis in assessing information technology impact on firm performance, Ann. Oper. Res., 73 (1997), 191-213.   Google Scholar

[19]

M. Zerafat Angiz L and A. Mustafa, Fuzzy interpretation of efficiency in data envelopment analysis and its application in a non-discretionary model, Knowl.-Based Syst., 49 (2013), 145-151.   Google Scholar

show all references

References:
[1]

R. D. Banker and R. Morey, Efficiency analysis for exogenously fixed inputs and outputs, Oper. Res., 34 (1986), 501-653.  doi: 10.1287/opre.34.4.513.  Google Scholar

[2]

M. Barat, G. Tohidi and M. Sanei, DEA for nonhomogeneous mixed networks, Asia Pac. Manag. Rev., 24 (2018), 161-166.  doi: 10.1016/j.apmrv.2018.02.003.  Google Scholar

[3]

R. E. Bellman and L. A. Zadeh, Decision making in a fuzzy environment, Manag. Sci., 17 (1970), B141–B164. doi: 10.1287/mnsc.17.4.B141.  Google Scholar

[4]

L. Castelli, R. Pesenti and W. Ukovich, DEA-like models for the efficiency evaluation of hierarchically structured units, Eur. J. Oper. Res., 154 (2004), 465-476.  doi: 10.1016/S0377-2217(03)00182-6.  Google Scholar

[5]

J. Zhu, Data Envelopment Analysis: A Handbook of Modeling Internal Structures and Networks, International Series in Operations Research & Management Science, 238. Springer, New York, 2016. doi: 10.1007/978-1-4899-7684-0.  Google Scholar

[6]

J. M. Cordero-Ferrera, F. Pedraja-Chaparro and D. Santín-González, Enhancing the inclusion of non-discretionary inputs in DEA, J. Oper. Res. Soc., 61 (2010), 574-584.  doi: 10.1057/jors.2008.189.  Google Scholar

[7]

R. Färe and S. Grosskopf, Intertemporal Production Frontiers: With Dynamic DEA, Boston: Kluwer Academic Publishers, 1996. Google Scholar

[8]

R. Färe and S. Grosskopf, Network DEA, Socio. Econ. Plann. Sci., 4 (2000), 35-49.   Google Scholar

[9]

D. U. A. Galagedera, Modelling social responsibility in mutual fund performance appraisal: A two-stage data envelopment analysis model with non-discretionary first stage output, Eur. J. Oper. Res., 273 (2019), 376-389.  doi: 10.1016/j.ejor.2018.08.011.  Google Scholar

[10]

B. Golany and Y. Roll, Some extensions of techniques to handle non-discretionary factors in data envelopment analysis, J. Prod. Anal., 4 (1993), 419-432.  doi: 10.1007/BF01073549.  Google Scholar

[11]

C. Kao, Network data envelopment analysis: A review, Eur. J. Oper. Res., 239 (2014), 1-16.  doi: 10.1016/j.ejor.2014.02.039.  Google Scholar

[12]

C. Kao, Efficiency decomposition and aggregation in network data envelopment analysis, Eur. J. Oper. Res., 255 (2016), 778-786.  doi: 10.1016/j.ejor.2016.05.019.  Google Scholar

[13]

C. Kao and S.-N. Hwang, Efficiency measurement for network systems: IT impact on firm performance, Decis. Support Syst., 48 (2010), 437-446.  doi: 10.1016/j.dss.2009.06.002.  Google Scholar

[14]

R. J. Kauffman and P. Weill, An evaluative framework for research on the performance effects of information technology investment, Proceedings of the 10th International Conference on Information Systems, (1989), 377–388. doi: 10.1145/75034.75066.  Google Scholar

[15]

M. A. Muniz, J. Paradi, J. Ruggiero and Z. Yang, Evaluating alternative DEA models used to control for non-discretionary inputs, Comput. Oper. Res., 33 (2006), 1173-1183.   Google Scholar

[16]

L. Simar and P. W. Wilson, Estimation and inference in two-stage, semi-parametric models of production processes, J. Econom., 136 (1997), 31-64.  doi: 10.1016/j.jeconom.2005.07.009.  Google Scholar

[17]

M. Taleb, R. Ramli and R. Khalid, Developing a two-stage approach of super efficiency slack-based measure in the presence of non-discretionary factors and mixed integer-valued data envelopment analysis, Expert. Syst. Appl., 103 (2018), 14-24.  doi: 10.1016/j.eswa.2018.02.037.  Google Scholar

[18]

C. H. Wang, R. Gopal and S. Zionts, Use of data envelopment analysis in assessing information technology impact on firm performance, Ann. Oper. Res., 73 (1997), 191-213.   Google Scholar

[19]

M. Zerafat Angiz L and A. Mustafa, Fuzzy interpretation of efficiency in data envelopment analysis and its application in a non-discretionary model, Knowl.-Based Syst., 49 (2013), 145-151.   Google Scholar

Figure 1.  General network systems [12]
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 2.  Network system discussed in [18]
Figure Options

Download full-size image

Download as PowerPoint slide

Table 1.  Data set for assessing IT impact on firm performance
DMU
j		 IT Fixed No. of Deposits Profit Fraction
$ \rm {budget}$ $ {\mbox{assets}} $ $ {\mbox{employees }}$ of loans
$({＄ \ \mbox{billions})}$ $({＄ \ \mbox{billions})} $ $ ({＄ \ \mbox{billions})} $ $({＄ \ \mbox{billions})} $ $ ({＄ \ \mbox{billions})} $ ${\mbox{recovered}}$
$ X_1 $ $ X_2 $ $ X_3 $ $ Z $ $ Y_1$ $ Y_2 $
1 $ 0.150 $ $ 0.713 $ $ 13.3 $ $ 14.478 $ $ 0.232 $ $ 0.986 $
2 $ 0.170 $ $ 1.071 $ $ 16.9 $ $ 19.502 $ $ 0.340 $ $ 0.986 $
3 $ 0.235 $ $ 1.224 $ $ 24.0 $ $ 20.952 $ $ 0.363 $ $ 0.986 $
4 $ 0.211 $ $ 0.363 $ $ 15.6 $ $ 13.902 $ $ 0.211 $ $ 0.982 $
5 $ 0.133 $ $ 0.409 $ $ 18.485 $ $ 15.206 $ $ 0.237 $ $ 0.984 $
6 $ 0.497 $ $ 5.846 $ $ 56.42 $ $ 81.186 $ $ 1.103 $ $ 0.955 $
7 $ 0.060 $ $ 0.918 $ $ 56.42 $ $ 81.186 $ $ 1.103 $ $ 0.986 $
8 $ 0.071 $ $ 1.235 $ $ 12.0 $ $ 11.441 $ $ 0.199 $ $ 0.985 $
9 $ 1.500 $ $ 18.120 $ $ 89.51 $ $ 124.072 $ $ 1.858 $ $ 0.972 $
10 $ 0.120 $ $ 1.821 $ $ 19.8 $ $ 17.425 $ $ 0.274 $ $ 0.983 $
11 $ 0.120 $ $ 1.915 $ $ 19.8 $ $ 17.425 $ $ 0.274 $ $ 0.983 $
12 $ 0.050 $ $ 0.874 $ $ 13.1 $ $ 14.342 $ $ 0.177 $ $ 0.985 $
13 $ 0.370 $ $ 6.918 $ $ 12.5 $ $ 32.491 $ $ 0.648 $ $ 0.945 $
14 $ 0.440 $ $ 4.432 $ $ 41.9 $ $ 47.653 $ $ 0.639 $ $ 0.979 $
15 $ 0.431 $ $ 4.504 $ $ 41.1 $ $ 52.63 $ $ 0.741 $ $ 0.981 $
16 $ 0.110 $ $ 1.241 $ $ 14.4 $ $ 17.493 $ $ 0.243 $ $ 0.988 $
17 $ 0.053 $ $ 0.450 $ $ 7.6 $ $ 9.512 $ $ 0.067 $ $ 0.980 $
18 $ 0.345 $ $ 5.892 $ $ 15.5 $ $ 42.469 $ $ 1.002 $ $ 0.948 $
19 $ 0.128 $ $ 0.973 $ $ 12.6 $ $ 18.987 $ $ 0.243 $ $ 0.985 $
20 $ 0.055 $ $ 0.444 $ $ 5.9 $ $ 7.546 $ $ 0.153 $ $ 0.987 $
21 $ 0.057 $ $ 0.508 $ $ 5.7 $ $ 7.595 $ $ 0.123 $ $ 0.987 $
22 $ 0.098 $ $ 0.370 $ $ 14.1 $ $ 16.906 $ $ 0.233 $ $ 0.981 $
23 $ 0.104 $ $ 0.395 $ $ 14.6 $ $ 17.264 $ $ 0.263 $ $ 0.983 $
24 $ 0.206 $ $ 2.680 $ $ 19.6 $ $ 36.430 $ $ 0.601 $ $ 0.982 $
25 $ 0.067 $ $ 0.781 $ $ 10.5 $ $ 11.581 $ $ 0.120 $ $ 0.987 $
26 $ 0.100 $ $ 0.872 $ $ 12.1 $ $ 22.207 $ $ 0.248 $ $ 0.972 $
27 $ 0.0106 $ $ 1.757 $ $ 12.7 $ $ 20.670 $ $ 0.253 $ $ 0.988 $
Table Options

Download as excel

DMU
j		 IT Fixed No. of Deposits Profit Fraction
$ \rm {budget}$ $ {\mbox{assets}} $ $ {\mbox{employees }}$ of loans
$({＄ \ \mbox{billions})}$ $({＄ \ \mbox{billions})} $ $ ({＄ \ \mbox{billions})} $ $({＄ \ \mbox{billions})} $ $ ({＄ \ \mbox{billions})} $ ${\mbox{recovered}}$
$ X_1 $ $ X_2 $ $ X_3 $ $ Z $ $ Y_1$ $ Y_2 $
1 $ 0.150 $ $ 0.713 $ $ 13.3 $ $ 14.478 $ $ 0.232 $ $ 0.986 $
2 $ 0.170 $ $ 1.071 $ $ 16.9 $ $ 19.502 $ $ 0.340 $ $ 0.986 $
3 $ 0.235 $ $ 1.224 $ $ 24.0 $ $ 20.952 $ $ 0.363 $ $ 0.986 $
4 $ 0.211 $ $ 0.363 $ $ 15.6 $ $ 13.902 $ $ 0.211 $ $ 0.982 $
5 $ 0.133 $ $ 0.409 $ $ 18.485 $ $ 15.206 $ $ 0.237 $ $ 0.984 $
6 $ 0.497 $ $ 5.846 $ $ 56.42 $ $ 81.186 $ $ 1.103 $ $ 0.955 $
7 $ 0.060 $ $ 0.918 $ $ 56.42 $ $ 81.186 $ $ 1.103 $ $ 0.986 $
8 $ 0.071 $ $ 1.235 $ $ 12.0 $ $ 11.441 $ $ 0.199 $ $ 0.985 $
9 $ 1.500 $ $ 18.120 $ $ 89.51 $ $ 124.072 $ $ 1.858 $ $ 0.972 $
10 $ 0.120 $ $ 1.821 $ $ 19.8 $ $ 17.425 $ $ 0.274 $ $ 0.983 $
11 $ 0.120 $ $ 1.915 $ $ 19.8 $ $ 17.425 $ $ 0.274 $ $ 0.983 $
12 $ 0.050 $ $ 0.874 $ $ 13.1 $ $ 14.342 $ $ 0.177 $ $ 0.985 $
13 $ 0.370 $ $ 6.918 $ $ 12.5 $ $ 32.491 $ $ 0.648 $ $ 0.945 $
14 $ 0.440 $ $ 4.432 $ $ 41.9 $ $ 47.653 $ $ 0.639 $ $ 0.979 $
15 $ 0.431 $ $ 4.504 $ $ 41.1 $ $ 52.63 $ $ 0.741 $ $ 0.981 $
16 $ 0.110 $ $ 1.241 $ $ 14.4 $ $ 17.493 $ $ 0.243 $ $ 0.988 $
17 $ 0.053 $ $ 0.450 $ $ 7.6 $ $ 9.512 $ $ 0.067 $ $ 0.980 $
18 $ 0.345 $ $ 5.892 $ $ 15.5 $ $ 42.469 $ $ 1.002 $ $ 0.948 $
19 $ 0.128 $ $ 0.973 $ $ 12.6 $ $ 18.987 $ $ 0.243 $ $ 0.985 $
20 $ 0.055 $ $ 0.444 $ $ 5.9 $ $ 7.546 $ $ 0.153 $ $ 0.987 $
21 $ 0.057 $ $ 0.508 $ $ 5.7 $ $ 7.595 $ $ 0.123 $ $ 0.987 $
22 $ 0.098 $ $ 0.370 $ $ 14.1 $ $ 16.906 $ $ 0.233 $ $ 0.981 $
23 $ 0.104 $ $ 0.395 $ $ 14.6 $ $ 17.264 $ $ 0.263 $ $ 0.983 $
24 $ 0.206 $ $ 2.680 $ $ 19.6 $ $ 36.430 $ $ 0.601 $ $ 0.982 $
25 $ 0.067 $ $ 0.781 $ $ 10.5 $ $ 11.581 $ $ 0.120 $ $ 0.987 $
26 $ 0.100 $ $ 0.872 $ $ 12.1 $ $ 22.207 $ $ 0.248 $ $ 0.972 $
27 $ 0.0106 $ $ 1.757 $ $ 12.7 $ $ 20.670 $ $ 0.253 $ $ 0.988 $
Table 2.  The system efficiency, $ \theta_p^{\ast}, $ and the membership degree, $ \alpha_p, p = 1, 2, \cdots, 27. $
DMU
j		 Model (2)
$ \theta^{\ast} $		 ${ \text{Model (6)}}$ DMU
j		 Model (2)
$ \theta^{\ast} $		 $ { \text{Model (6)}}$
$\alpha^{\ast}$ $ 1-\alpha^{\ast}$ $ \alpha^{\ast} $ $ 1-\alpha^{\ast} $
$ 1 $ $ 0.6388 $ $ 0.3612 $$ 0.6388 $ $ 15 $ $ 0.6582 $ $ 0.3418 $$ 0.6582 $
$ 2 $ $ 0.6507 $ $ 0.3493 $ $ 0.6507 $ $ 16 $ $ 0.6646 $ $ 0.3354 $$ 0.6646 $
$ 3 $ $ 0.5179 $ $ 0.4821 $$ 0.5179 $ $ 17 $ $ 0.7177 $ $ 0.2823 $$ 0.7177 $
$ 4 $ $ 0.5986 $ $ 0.4014 $ $ 0.5986 $ $ 18 $ $ 1.0000 $ $ 0.0000 $$ 1.0000 $
$ 5 $ $ 0.5556 $ $ 0.4444 $ $ 0.5556 $ $ 19 $ $ 0.8144 $ $ 0.1856 $$ 0.8144 $
$ 6 $ $ 0.7599 $ $ 0.2401 $$ 0.7599 $ $ 20 $ $ 0.6940 $ $ 0.3060 $$ 0.6940 $
$ 7 $ $ 1.0000 $ $ 0.0000 $$ 1.0000 $ $ 21 $ $ 0.7067 $ $ 0.2933 $$ 0.7067 $
$ 8 $ $ 0.5352 $ $ 0.4648 $$ 0.5352 $ $ 22 $ $ 0.7942 $ $ 0.2058 $$ 0.7942 $
$ 9 $ $ 0.6249 $ $ 0.3751 $ $ 0.6249 $ $ 23 $ $ 0.7802 $ $ 0.2198 $$ 0.7802 $
$ 10 $ $ 0.4961 $ $ 0.5039 $ $ 0.4961 $ $ 24 $ $ 0.9300 $ $ 0.0700 $$ 0.9300 $
$ 11 $ $ 0.4945 $ $ 0.5055 $ $ 0.4945 $ $ 25 $ $ 0.6270 $ $ 0.3730 $$ 0.6270 $
$ 12 $ $ 0.6685 $ $ 0.3315 $ $ 0.6685 $ $ 26 $ $ 1.0000 $ $ 0.0000 $$ 1.0000 $
$ 13 $ $ 0.9487 $ $ 0.0513 $ $ 0.9487 $ $ 27 $ $ 1.0000 $ $ 0.0000 $$ 1.0000 $
$ 14 $ $ 0.5880 $ $ 0.4120 $$ 0.5880 $
Table Options

Download as excel

DMU
j		 Model (2)
$ \theta^{\ast} $		 ${ \text{Model (6)}}$ DMU
j		 Model (2)
$ \theta^{\ast} $		 $ { \text{Model (6)}}$
$\alpha^{\ast}$ $ 1-\alpha^{\ast}$ $ \alpha^{\ast} $ $ 1-\alpha^{\ast} $
$ 1 $ $ 0.6388 $ $ 0.3612 $$ 0.6388 $ $ 15 $ $ 0.6582 $ $ 0.3418 $$ 0.6582 $
$ 2 $ $ 0.6507 $ $ 0.3493 $ $ 0.6507 $ $ 16 $ $ 0.6646 $ $ 0.3354 $$ 0.6646 $
$ 3 $ $ 0.5179 $ $ 0.4821 $$ 0.5179 $ $ 17 $ $ 0.7177 $ $ 0.2823 $$ 0.7177 $
$ 4 $ $ 0.5986 $ $ 0.4014 $ $ 0.5986 $ $ 18 $ $ 1.0000 $ $ 0.0000 $$ 1.0000 $
$ 5 $ $ 0.5556 $ $ 0.4444 $ $ 0.5556 $ $ 19 $ $ 0.8144 $ $ 0.1856 $$ 0.8144 $
$ 6 $ $ 0.7599 $ $ 0.2401 $$ 0.7599 $ $ 20 $ $ 0.6940 $ $ 0.3060 $$ 0.6940 $
$ 7 $ $ 1.0000 $ $ 0.0000 $$ 1.0000 $ $ 21 $ $ 0.7067 $ $ 0.2933 $$ 0.7067 $
$ 8 $ $ 0.5352 $ $ 0.4648 $$ 0.5352 $ $ 22 $ $ 0.7942 $ $ 0.2058 $$ 0.7942 $
$ 9 $ $ 0.6249 $ $ 0.3751 $ $ 0.6249 $ $ 23 $ $ 0.7802 $ $ 0.2198 $$ 0.7802 $
$ 10 $ $ 0.4961 $ $ 0.5039 $ $ 0.4961 $ $ 24 $ $ 0.9300 $ $ 0.0700 $$ 0.9300 $
$ 11 $ $ 0.4945 $ $ 0.5055 $ $ 0.4945 $ $ 25 $ $ 0.6270 $ $ 0.3730 $$ 0.6270 $
$ 12 $ $ 0.6685 $ $ 0.3315 $ $ 0.6685 $ $ 26 $ $ 1.0000 $ $ 0.0000 $$ 1.0000 $
$ 13 $ $ 0.9487 $ $ 0.0513 $ $ 0.9487 $ $ 27 $ $ 1.0000 $ $ 0.0000 $$ 1.0000 $
$ 14 $ $ 0.5880 $ $ 0.4120 $$ 0.5880 $
Table 3.  The results of solving the proposed fuzzy non-discretionary Model (14)
$ \begin{array}{c} \mbox{DMU}\\ j \end{array} $Fuzzy non-discretionary input
$ \bar{X}_{1j}^{\ast} $ $ \bar{X}_{2j}^{\ast} $ $ \bar{X}_{3j}^{\ast} $ $ \alpha^{\ast} $ $ 1-\alpha^{\ast} $Rank
10.11020.52369.63350.26540.734618
20.12600.772312.42590.25890.741117
30.15860.807916.13280.32530.674725
40.15060.256410.90130.28640.713621
50.09210.279311.21650.30770.692323
60.40084.634245.42890.19360.806410
70.06000.918056.42000.00001.00001
80.04850.76778.09880.31730.682724
91.090813.147164.85290.27280.727220
100.07981.071512.82950.33510.664926
110.07971.099712.74160.33580.664227
120.03760.65449.78830.24900.751014
130.35195.329111.89000.04880.95125
140.31163.104729.59290.29180.708222
150.32123.277230.49690.25470.745316
160.08240.894310.77290.25120.748815
170.04130.35095.88710.22020.779811
180.34505.892015.50000.00001.00001
190.10800.815410.61510.15650.84357
200.04210.33494.49480.23430.765713
210.04410.39044.36860.22680.773212
220.08130.304311.67750.17070.82938
230.08530.321611.95540.18020.81989
240.19252.412518.31760.06540.93466
250.04880.54487.53420.27170.728319
260.10000.872012.10000.00001.00001
270.01061.757012.70000.00001.00001
Table Options

Download as excel

$ \begin{array}{c} \mbox{DMU}\\ j \end{array} $Fuzzy non-discretionary input
$ \bar{X}_{1j}^{\ast} $ $ \bar{X}_{2j}^{\ast} $ $ \bar{X}_{3j}^{\ast} $ $ \alpha^{\ast} $ $ 1-\alpha^{\ast} $Rank
10.11020.52369.63350.26540.734618
20.12600.772312.42590.25890.741117
30.15860.807916.13280.32530.674725
40.15060.256410.90130.28640.713621
50.09210.279311.21650.30770.692323
60.40084.634245.42890.19360.806410
70.06000.918056.42000.00001.00001
80.04850.76778.09880.31730.682724
91.090813.147164.85290.27280.727220
100.07981.071512.82950.33510.664926
110.07971.099712.74160.33580.664227
120.03760.65449.78830.24900.751014
130.35195.329111.89000.04880.95125
140.31163.104729.59290.29180.708222
150.32123.277230.49690.25470.745316
160.08240.894310.77290.25120.748815
170.04130.35095.88710.22020.779811
180.34505.892015.50000.00001.00001
190.10800.815410.61510.15650.84357
200.04210.33494.49480.23430.765713
210.04410.39044.36860.22680.773212
220.08130.304311.67750.17070.82938
230.08530.321611.95540.18020.81989
240.19252.412518.31760.06540.93466
250.04880.54487.53420.27170.728319
260.10000.872012.10000.00001.00001
270.01061.757012.70000.00001.00001
[1]

Zhen Ming Ma, Ze Shui Xu, Wei Yang. Approach to the consistency and consensus of Pythagorean fuzzy preference relations based on their partial orders in group decision making. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020086
[2]

Muhammad Qiyas, Saleem Abdullah, Shahzaib Ashraf, Saifullah Khan, Aziz Khan. Triangular picture fuzzy linguistic induced ordered weighted aggregation operators and its application on decision making problems. Mathematical Foundations of Computing, 2019, 2 (3) : 183-201. doi: 10.3934/mfc.2019013
[3]

Harish Garg, Dimple Rani. Multi-criteria decision making method based on Bonferroni mean aggregation operators of complex intuitionistic fuzzy numbers. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020069
[4]

Feyza Gürbüz, Panos M. Pardalos. A decision making process application for the slurry production in ceramics via fuzzy cluster and data mining. Journal of Industrial & Management Optimization, 2012, 8 (2) : 285-297. doi: 10.3934/jimo.2012.8.285
[5]

Harish Garg, Kamal Kumar. Group decision making approach based on possibility degree measure under linguistic interval-valued intuitionistic fuzzy set environment. Journal of Industrial & Management Optimization, 2020, 16 (1) : 445-467. doi: 10.3934/jimo.2018162
[6]

Harish Garg. Some robust improved geometric aggregation operators under interval-valued intuitionistic fuzzy environment for multi-criteria decision-making process. Journal of Industrial & Management Optimization, 2018, 14 (1) : 283-308. doi: 10.3934/jimo.2017047
[7]

G.S. Liu, J.Z. Zhang. Decision making of transportation plan, a bilevel transportation problem approach. Journal of Industrial & Management Optimization, 2005, 1 (3) : 305-314. doi: 10.3934/jimo.2005.1.305
[8]

Ana F. Carazo, Ignacio Contreras, Trinidad Gómez, Fátima Pérez. A project portfolio selection problem in a group decision-making context. Journal of Industrial & Management Optimization, 2012, 8 (1) : 243-261. doi: 10.3934/jimo.2012.8.243
[9]

Ruiyue Lin, Zhiping Chen, Zongxin Li. A new approach for allocating fixed costs among decision making units. Journal of Industrial & Management Optimization, 2016, 12 (1) : 211-228. doi: 10.3934/jimo.2016.12.211
[10]

Hamed Fazlollahtabar, Mohammad Saidi-Mehrabad. Optimizing multi-objective decision making having qualitative evaluation. Journal of Industrial & Management Optimization, 2015, 11 (3) : 747-762. doi: 10.3934/jimo.2015.11.747
[11]

Saeed Assani, Jianlin Jiang, Ahmad Assani, Feng Yang. Scale efficiency of China's regional R & D value chain: A double frontier network DEA approach. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020025
[12]

Harish Garg. Novel correlation coefficients under the intuitionistic multiplicative environment and their applications to decision-making process. Journal of Industrial & Management Optimization, 2018, 14 (4) : 1501-1519. doi: 10.3934/jimo.2018018
[13]

Jian Jin, Weijian Mi. An AIMMS-based decision-making model for optimizing the intelligent stowage of export containers in a single bay. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1101-1115. doi: 10.3934/dcdss.2019076
[14]

Xue Yan, Heap-Yih Chong, Jing Zhou, Zhaohan Sheng, Feng Xu. Fairness preference based decision-making model for concession period in PPP projects. Journal of Industrial & Management Optimization, 2020, 16 (1) : 11-23. doi: 10.3934/jimo.2018137
[15]

Gholam Hassan Shirdel, Somayeh Ramezani-Tarkhorani. A new method for ranking decision making units using common set of weights: A developed criterion. Journal of Industrial & Management Optimization, 2020, 16 (2) : 633-651. doi: 10.3934/jimo.2018171
[16]

Gleb Beliakov. Construction of aggregation operators for automated decision making via optimal interpolation and global optimization. Journal of Industrial & Management Optimization, 2007, 3 (2) : 193-208. doi: 10.3934/jimo.2007.3.193
[17]

Saber Saati, Adel Hatami-Marbini, Per J. Agrell, Madjid Tavana. A common set of weight approach using an ideal decision making unit in data envelopment analysis. Journal of Industrial & Management Optimization, 2012, 8 (3) : 623-637. doi: 10.3934/jimo.2012.8.623
[18]

Weichao Yue, Weihua Gui, Xiaofang Chen, Zhaohui Zeng, Yongfang Xie. Evaluation strategy and mass balance for making decision about the amount of aluminum fluoride addition based on superheat degree. Journal of Industrial & Management Optimization, 2020, 16 (2) : 601-622. doi: 10.3934/jimo.2018169
[19]

Bin Dan, Huali Gao, Yang Zhang, Ru Liu, Songxuan Ma. Integrated order acceptance and scheduling decision making in product service supply chain with hard time windows constraints. Journal of Industrial & Management Optimization, 2018, 14 (1) : 165-182. doi: 10.3934/jimo.2017041
[20]

Haiying Liu, Wenjie Bi, Kok Lay Teo, Naxing Liu. Dynamic optimal decision making for manufacturers with limited attention based on sparse dynamic programming. Journal of Industrial & Management Optimization, 2019, 15 (2) : 445-464. doi: 10.3934/jimo.2018050

2019 Impact Factor: 1.366

Tools

Metrics

  • PDF downloads (30)
  • HTML views (242)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences