Published May 9, 2017
Ningkui WANG Daijun WEI


Environmental impact assessment (EIA) is usually evaluated by many factors influenced by various kinds of uncertainty or fuzziness. As a result, the key issues of EIA problem are to rep­resent and deal with the uncertain or fuzzy information. D numbers theory, as the extension of Dempster-Shafer theory of evidence, is a desirable tool that can express uncertainty and fuzziness, both complete and incomplete, quantitative or qualitative. However, some shortcomings do exist in D numbers combination process, the commutative property is not well considered when multiple D numbers are combined. Though some attempts have made to solve this problem, the previous method is not appropriate and convenience as more information about the given evaluations rep­resented by D numbers are needed. In this paper, a data-driven D numbers combination rule is proposed, commutative property is well considered in the proposed method. In the combination process, there does not require any new information except the original D numbers. An illustrative example is provided to demonstrate the effectiveness of the method.



D numbers theory, EIA, decision making, uncertainty, incompleteness, fuzziness

Ahmadi, A.; Moridi, A.; Han, D. 2015. Uncertainty assessment in environmental risk through Bayesian networks, Journal of Environmental Informatics 25(1): 46–59. https://doi.org/10.3808/jei.201500294

Akhavan, P.; Barak, S.; Maghsoudlou, H.; Antuchevičienė, J. 2015. FQSPM-SWOT for strategic alliance planning and partner selection; case study in a holding car manufacturer company, Technological and Economic Development of Economy 21(2): 165–185. https://doi.org/10.3846/20294913.2014.965240

Baležentis, T.; Baležentis, A. 2014. A survey on development and applications of the multi-criteria decision making method MULTIMOORA, Journal of Multi-Criteria Decision Analysis 21(3–4): 209–222. https://doi.org/10.1002/mcda.1501

Beynon, M.; Cosker, D.; Marshall, D. 2001. An expert system for multi-criteria decision making using Dempster-Shafer theory, Expert Systems with Applications 20(4): 357–367. https://doi.org/10.1016/S0957-4174(01)00020-3

Bigum, M.; Brogaard, L.; Christensen, T. H. 2012. Metal recovery from high-grade WEEE: a life cycle assessment, Journal of Hazardous Materials 207–208: 8–14. https://doi.org/10.1016/j.jhazmat.2011.10.001

Canter, L. W. 1996. Environmental impact assessment. McGraw-Hill New York.

De Boer, I. J. M. 2003. Environmental impact assessment of conventional and organic milk production, Livestock Production Science 80(1): 69–77. https://doi.org/10.1016/S0301-6226(02)00322-6

Dempster, A. P. 1967. Upper and lower probabilities induced by a multivalued mapping, The Annals of Mathematical Statistics 38(2): 325–339. https://doi.org/10.1214/aoms/1177698950

Deng, X. Y.; Hu, Y.; Deng, Y. 2014a. Bridge condition assessment using D numbers, The Scientific World Journal 2014(5): 1–10.

Deng, X. Y.; Hu, Y.; Deng, Y.; Mahadevan, S. 2014b. Environmental impact assessment based on D numbers, Expert Systems with Applications 41(2): 635–643. https://doi.org/10.1016/j.eswa.2013.07.088

Deng, X. Y.; Hu, Y.; Deng, Y.; Mahadevan, S. 2014c. Supplier selection using AHP methodology extended by D numbers, Expert Systems with Applications 41(1): 156–167. https://doi.org/10.1016/j.eswa.2013.07.018

Deng, X. Y.; Lu, X.; Chan, F. T. S.; Sadiq, R.; Mahadevan, S.; Deng, Y. 2014d. D-CFPR: D numbers extended consistent fuzzy preference relations, Knowledge-Based Systems 73: 61–68. https://doi.org/10.1016/j.knosys.2014.09.007

Deng, Y. 2012. D numbers: theory and applications, Journal of Information and Computational Science 9(9): 2421–2428.

Deng, Y. 2015a. Generalized evidence theory, Applied Intelligence 43(3): 530–543. https://doi.org/10.1007/s10489-015-0661-2

Deng, Y. 2015b. A threat assessment model under uncertain environment, Mathematical Problems in Engineering 2015, Article ID 878024. https://doi.org/10.1155/2015/878024

Deng, Y.; Jiang, W.; Sadiq, R. 2011a. Modeling contaminant intrusion in water distribution networks: A new similarity-based DST method, Expert Systems with Applications 38(1): 571–578. https://doi.org/10.1016/j.eswa.2010.07.004

Deng, Y.; Liu, Y.; Zhou, D. Y. 2015a. An improved genetic algorithm with initial population strategy for symmetric TSP, Mathematical Problems in Engineering 2015, Article ID 212794. https://doi.org/10.1155/2015/212794

Deng, Y.; Mahadevan, S.; Zhou, D. Y. 2015b. Vulnerability assessment of physical protection systems: a bio-inspired approach, International Journal of Unconventional Computing 11(3–4): 227–243.

Deng, Y.; Sadiq, R.; Jiang, W.; Tesfamariam, S. 2011b. Risk analysis in a linguistic environment: a fuzzy evidential reasoning-based approach, Expert Systems with Applications 38(12): 15438–15446. https://doi.org/10.1016/j.eswa.2011.06.018

Dreyer, L.; Hauschild, M.; Schierbeck, J. 2006. A framework for social life cycle impact assessment, The International Journal of Life Cycle Assessment 11(2): 88–97. https://doi.org/10.1065/lca2005.08.223

Fan, G. C.; Zhong, D. H.; Yan, F. G.; Yue, P. 2016. A hybrid fuzzy evaluation method for curtain grouting efficiency assessment based on an AHP method extended by D numbers, Expert Systems with Applications 44: 289–303. https://doi.org/10.1016/j.eswa.2015.09.006

Fu, C.; Chin, K. S. 2014. Robust evidential reasoning approach with unknown attribute weights, Knowledge-Based Systems 59: 9–20. https://doi.org/10.1016/j.knosys.2014.01.024

Fu, C.; Yang, S. L. 2012. An evidential reasoning based consensus model for multiple attribute group decision analysis problems with interval-valued group consensus requirements, European Journal of Operational Research 223(1): 167–176. https://doi.org/10.1016/j.ejor.2012.05.048

Hashemkhani Zolfani, S.; Aghdaie, M. H.; Derakhti, A.; Zavadskas, E. K.; Varzandeh, M. H. M. 2013. Decision making on business issues with foresight perspective; an application of new hybrid MCDM model in shopping mall locating, Expert Systems with Applications 40(17): 7111–7121. https://doi.org/10.1016/j.eswa.2013.06.040

Hu, Q. Z.; Lu, H. P. 2009. Rough set comprehensive evaluation model for environmental security effect of highway construction projects, in Energy and Environment Technology 2009 (ICEET’09), 16–18 October 2009, Guilin, China, 301–304.

Jiang, W.; Luo, Y.; Qin, X. Y.; Zhan, J. 2015a. An improved method to rank generalized fuzzy numbers with different left heights and right heights, Journal of Intelligent and Fuzzy Systems 28(5): 2343–2355. https://doi.org/10.3233/IFS-151639

Jiang, W.; Yang, Y.; Luo, Y.; Qin, X. Y. 2015b. Determining basic probability assignment based on the improved similarity measures of generalized fuzzy numbers, International Journal of Computers Communications and Control 10(3): 333–347. https://doi.org/10.15837/ijccc.2015.3.1656

Jordan, Y. C.; Ghulam, A.; Chu, M. L. 2014. Assessing the impacts of future urban development patterns and climate changes on total suspended sediment loading in surface waters using geoinformatics, Journal of Environmental Informatics 24(2): 65–79. https://doi.org/10.3808/jei.201400283

Ju, H. C.; Yoo, S. H. 2014. Using the fuzzy set theory to developing an environmental impact assessment index for a thermal power plant, Quality and Quantity 48(2): 673–680. https://doi.org/10.1007/s11135-012-9794-0

Kaplinski, O.; Peldschus, F.; Tupenaite, L. 2014. Development of MCDM methods-in honour of Professor Edmundas Kazimieras Zavadskas on the occasion of his 70th birthday, International Journal of Computers Communications and Control 9(3): 305–312. https://doi.org/10.15837/ijccc.2014.3.1084

Khan, M.; Fitzcharles, K. 1998. Environmental management field handbook for rural road improvement projects. CARE International Bangladesh, Dhaka.

Kiliç, E.; Puig, R.; Baquero, G.; Font, J.; Çolak, S.; Gürler, D. 2011. Environmental optimization of chromium recovery from tannery sludge using a life cycle assessment approach, Journal of Hazardous Materials 192(1): 393–401.

Lenzen, M.; Murray, S. A.; Korte, B.; Dey, C. J. 2003. Environmental impact assessment including indirect effects – a case study using input-output analysis, Environmental Impact Assessment Review 23(3): 263–282. https://doi.org/10.1016/S0195-9255(02)00104-X

Liu, B. D. 2014. Uncertainty theory. Springer.

Liu, H. C.; You, J. X.; Fan, X. J.; Lin, Q. L. 2014a. Failure mode and effects analysis using D numbers and grey relational projection method, Expert Systems with Applications 41(10): 4670–4679. https://doi.org/10.1016/j.eswa.2014.01.031

Liu, Z. G.; Pan, Q.; Dezert, J. 2014b. Classification of uncertain and imprecise data based on evidence theory, Neurocomputing 133: 459–470. https://doi.org/10.1016/j.neucom.2013.12.009

Ma, Z. Z.; Wang, Z. J.; Xia, T.; Gippel, C. J.; Speed, R. 2014. Hydrograph-based hydrologic alteration assessment and its application to the yellow river, Journal of Environmental Informatics 23(1): 1–13. https://doi.org/10.3808/jei.201400252

Mardani, A.; Jusoh, A.; Zavadskas, E. K. 2015. Fuzzy multiple criteria decision-making techniques and applications-two decades review from 1994 to 2014, Expert Systems with Applications 42(8): 4126–4148. https://doi.org/10.1016/j.eswa.2015.01.003

Miao, D. Y.; Huang, W. W.; Li, Y. P.; Yang, Z. F. 2014. Planning water resources systems under uncertainty using an interval-fuzzy de novo programming method, Journal of Environmental Informatics 24(1): 11–23. https://doi.org/10.3808/jei.201400277

Morón, A. B.; Calvo-Flores, M. D.; Ramos, J. M.; Almohano, M. P. 2009. AIEIA: Software for fuzzy environmental impact assessment, Expert Systems with Applications 36(5): 9135–9149. https://doi.org/10.1016/j.eswa.2008.12.055

Ni, J. R.; Wu, A.; Li, T. H.; Yue, Y.; Borthwick, A. G. L. 2014. Efficient soil loss assessment for large basins using smart coded polygons, Journal of Environmental Informatics 23(2): 47–57. https://doi.org/10.3808/jei.201400264

Pastakia, C. M.; Jensen, A. 1998. The rapid impact assessment matrix (RIAM) for EIA, Environmental Impact Assessment Review 18(5): 461–482. https://doi.org/10.1016/S0195-9255(98)00018-3

Pawlak, Z.; Skowron, A. 2007. Rudiments of rough sets, Information Sciences 177(1): 3–27. https://doi.org/10.1016/j.ins.2006.06.003

Pun, K. F.; Hui, I. K.; Lewis, W. G.; Lau, H. C. 2003. A multiple-criteria environmental impact assessment for the plastic injection molding process: a methodology, Journal of Cleaner Production 11(1): 41–49. https://doi.org/10.1016/S0959-6526(02)00019-7

Rabbani, A.; Zamani, M.; Yazdani-Chamzini, A.; Zavadskas, E. K. 2014. Proposing a new integrated model based on sustainability balanced scorecard (SBSC) and MCDM approaches by using linguistic variables for the performance evaluation of oil producing companies, Expert Systems with Applications 41(16): 7316–7327. https://doi.org/10.1016/j.eswa.2014.05.023

Riga, M.; Stocker, M.; Rönkkö, M.; Karatzas, K.; Kolehmainen, M. 2015. Atmospheric environment and quality of life information extraction from twitter with the use of self-organizing maps, Journal of Environmental Informatics 26(1): 27–40.

Rikhtegar, N.; Mansouri, N.; Oroumieh, A. A.; Yazdani-Ccamzini, A.; Zavadskas, E. K.; Kildienė, S.; 2014. Environmental impact assessment based on group decision-making methods in mining projects, Economic Research-Ekonomska Istraživanja 27(1): 378–392. https://doi.org/10.1080/1331677X.2014.966971

Sadiq, R.; Kleiner, Y.; Rajani, B. 2006. Estimating risk of contaminant intrusion in water distribution networks using Dempster-Shafer theory of evidence, Civil Engineering and Environmental Systems 23(3): 129–141. https://doi.org/10.1080/10286600600789276

Shafer, G. 1976. A mathematical theory of evidence. Princeton University Press.

Su, X. Y.; Mahadevan, S.; Xu, P. D.; Deng, Y. 2015. Dependence assessment in human reliability analysis using evidence theory and AHP, Risk Analysis 35(7): 1296–1316. https://doi.org/10.1111/risa.12347

Sueyoshi, T.; Goto, M. 2012. Data envelopment analysis for environmental assessment: comparison between public and private ownership in petroleum industry, European Journal of Operational Research 216(3): 668–678. https://doi.org/10.1016/j.ejor.2011.07.046

Taroun, A.; Yang, J. B. 2011. Dempster-shafer theory of evidence: potential usage for decision making and risk analysis in construction project management, The Built and Human Environment Review 4(1): 155–166.

Tian, J. F.; Zhao, W. D.; Du, R. Z.; Zhang, Z. 2005. D-S evidence theory and its data fusion application in intrusion detection, in Parallel and Distributed Computing, Applications and Technologies 2005(PDCAT 2005), 5–8 December 2005, Dalian, China, 115–119.

Tukker, A. 2000. Life cycle assessment as a tool in environmental impact assessment, Environmental Impact Assessment Review 20(4): 435–456. https://doi.org/10.1016/S0195-9255(99)00045-1

Wang, Y. M.; Yang, J. B.; Xu, D. L. 2006. Environmental impact assessment using the evidential reasoning approach, European Journal of Operational Research 174(3): 1885–1913. https://doi.org/10.1016/j.ejor.2004.09.059

Wei, D. J.; Deng, X. Y.; Zhang, X. G.; Deng, Y.; Mahadevan, S. 2013. Identifying influential nodes in weighted networks based on evidence theory, Physica A: Statistical Mechanics and its Applications 392(10): 2564–2575.

Wood, G.; Rodriguez-Bachiller, A.; Becker, J. 2007. Fuzzy sets and simulated environmental change: evaluating and communicating impact significance in environmental impact assessment, Environment and Planning A 39(4): 810–829. https://doi.org/10.1068/a3878

Xu, Y.; Huang, G. H.; Cheng, G. H.; Liu, Y.; Li, Y. F. 2014. A two-stage fuzzy chance-constrained model for solid waste allocation planning, Journal of Environmental Informatics 24(2): 101–110. https://doi.org/10.3808/jei.201400261

Yager, R. R.; Alajlan, N. 2015. Dempster-Shafer belief structures for decision making under uncertainty, Knowledge-Based Systems 80: 58–66. https://doi.org/10.1016/j.knosys.2014.12.031

Yang, J. B.; Xu, D. L. 2002. On the evidential reasoning algorithm for multiple attribute decision analysis under uncertainty, IEEE Transactions on Systems, Man, and Cybernetics – Part A: Systems and Humans 32(3): 289–304. https://doi.org/10.1109/TSMCA.2002.802746

Zadeh, L. A. 1965. Fuzzy sets, Information and Control 8(3): 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X

Zapp, P.; Schreiber, A.; Marx, J.; Haines, M.; Hake, J. F.; Gale, J. 2012. Overall environmental impacts of CCS technologies – a life cycle approach, International Journal of Greenhouse Gas Control 8: 12–21. https://doi.org/10.1016/j.ijggc.2012.01.014

Zavadskas, E. K.; Antucheviciene, J.; Hajiagha, S. H. R.; Hashemi, S. S. 2014. Extension of weighted aggregated sum product assessment with interval-valued intuitionistic fuzzy numbers (WASPAS-IVIF), Applied Soft Computing 24: 1013–1021. https://doi.org/10.1016/j.asoc.2014.08.031

Zavadskas, E. K.; Turskis, Z.; Bagočius, V. 2015. Multi-criteria selection of a deep-water port in the eastern baltic sea, Applied Soft Computing 26: 180–192. https://doi.org/10.1016/j.asoc.2014.09.019