CRM-based dynamic decision-making with hesitant fuzzy information for the evaluation of rangelands
Abstract
As one of the important components of global land ecosystem, rangeland ecosystem has important value of ecosystem services. With the degeneration of rangeland in recent years, sustainability within rangeland ecosystem has become an increasingly important issue. The aim of this paper is to develop a novel dynamic decision-making approach based on hesitant fuzzy information to evaluate rangeland sustainability that considers ecological, social and economic aspects. Firstly, a modified satisfaction degree of alternative is presented, based on which a mathematical model for determining the stage weights is constructed. Secondly, the compromise ratio method (CRM), whose basic principle is that the optimal alternative should have the nearest distance from positive ideal solution and the longest distance from negative ideal solution simultaneously, is extended to accommodate hesitant fuzzy environment, and then adopted to tackle the dynamic decision-making with hesitant fuzzy information. Compared with the existing methods, the proposed method can eliminate the impact of attribute magnitude and dimension. Lastly, a numerical example on the evaluation of rangelands is provided to illustrate the practicality and superiority of the proposed method.
Keyword : hesitant fuzzy set, dynamic decision-making, compromise ratio method, satisfaction degree, rangeland sustainability evaluation
How to Cite
Liu, X., Wang, Z., Zhang, S., & Hetzler, A. (2018). CRM-based dynamic decision-making with hesitant fuzzy information for the evaluation of rangelands. Technological and Economic Development of Economy, 24(5), 1979-2002. https://doi.org/10.3846/tede.2018.5837
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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Farhadinia, B. (2013). Information measures for hesitant fuzzy sets and interval-valued hesitant fuzzy sets. Information Sciences, 240, 129-144. https://doi.org/10.1016/j.ins.2013.03.034
Farley, K. A., Walsh, K., & Levine, A. S. (2017). Opportunities and obstacles for rangeland conservation in San Diego County, California, USA. Ecology and Society, 22(1), 38. https://doi.org/10.5751/ES-09077-220138
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Fullér, R., & Majlender, P. (2000). An analytic approach for obtaining maximal entropy OWA operator weights. Fuzzy Sets and Systems, 124(1), 53-57. https://doi.org/10.1016/S0165-0114(01)00007-0
Gross, J. E., Mcallister, R. R. J, Abel, N., Stafford Smith, D. M., & Maru, Y. (2006). Australian rangelands as complex adaptive systems: a conceptual model and preliminary results. Environmental Modelling & Software, 21(9), 1264-1272. https://doi.org/10.1016/j.envsoft.2005.04.024
Hu, J. H., Zhang, X. L., Chen, X. H., & Liu, Y. M. (2016). Hesitant fuzzy information measures and their applications in multi-criteria decision making. International Journal of System Sciences, 47(1), 62-76. https://doi.org/10.1080/00207721.2015.1036476
Jakoby, O., Quaas, M. F., Müller, B., Baumgärtner, S., & Frank, K. (2014). How do individual farmers᾽ objectives influence the evaluation of rangeland management strategies under a variable climate? Journal of Applied Ecology, 51(2), 483-493. https://doi.org/10.1111/1365-2664.12216
Laflamme, M. (2011). A framework for sustainable rangeland livelihoods. Rangeland Journal, 33(4), 339-351. https://doi.org/10.1071/RJ11023
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Li, W., Chen, G. F., & Duan, C. (2010). Research and implementation of Index weight calculation model for power grid investment return. Lecture Notes in Computer Science, 6318, 44-52. https://doi.org/10.1007/978-3-642-16515-3_7
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Liu, X. D., Wang, Z. W., & Hetzler, A. (2017). HFMADM method based on nondimensionalization and its application in the evaluation of inclusive growth. Journal of Business Economics and Management, 18(4), 726-744. https://doi.org/10.3846/16111699.2017.1341848
Liu, X. D., Zhu, J. J., Zhang, S. T., Hao, J. J., & Liu, G. D. (2015). Integrating LNMAP and TOPSIS methods for hesitant fuzzy multiple attribute decision making. Journal of Intelligent & Fuzzy Systems, 28(1), 257-269.
Meng, F. Y., & Chen X. H. (2015). Correlation coefficients of hesitant fuzzy sets and their application based on fuzzy measures. Cognitive Computation, 7(4), 445-463. https://doi.org/10.1007/s12559-014-9313-9
Nasibova, R. A., & Nasibov, E. N. (2010). Linear aggregation with weighted ranking. Automatic Control and Computer Sciences, 44(2), 96-102. https://doi.org/10.3103/S0146411610020057
Onar, S. Ç., Büyüközkan, G., Öztayşi, B., & Kahraman, C. (2016). A new hesitant fuzzy QFD approach: an application to computer workstation selection. Applied Soft Computing, 46, 1-16. https://doi.org/10.1016/j.asoc.2016.04.023
Papanastasis, V. P. (2009). Restoration of degraded grazing lands through grazing management: can it work? Restoration Ecology, 17(4), 441-445. https://doi.org/10.1111/j.1526-100X.2009.00567.x
Peano, C., Migliorini, P., & Sottile, F. (2014). A methodology for the sustainability assessments of agrifood systems: an application to the slow food president project. Ecology and Society, 19(4), 24. https://doi.org/10.5751/ES-06972-190424
Peng, D. H., & Wang, H. (2014). Dynamic hesitant fuzzy aggregation operators in multi-period decision making. Kybernetes, 43(5), 715-736. https://doi.org/10.1108/K-11-2013-0236
Peng, J. J., Wang, J. Q., & Wu, X. H. (2016). Novel multi-criteria decision-making approaches based on hesitant fuzzy sets and prospect theory. International Journal of Information Technology & Decision Making, 15(3), 621-643. https://doi.org/10.1142/S0219622016500152
Reeves, M. C., & Baggett, L. S. (2014). A remote sensing protocol for identifying rangelands with degraded productive capacity. Ecological Indicators, 43, 172-182. https://doi.org/10.1016/j.ecolind.2014.02.009
Rodríguez, R. M., Bedregal, B., Bustincec, H., Dong, Y. C., Farhadinia, B., Kahramanf, C., Martínez, L., Torra, V., Xui, Y. J., Xud, Z. S., Herreraa, F. (2016). A position and perspective analysis of hesitant fuzzy sets on information fusion in decision making: towards high quality progress. Information Fusion, 29, 89-97. https://doi.org/10.1016/j.inffus.2015.11.004
Silva, R. O., Barioni, L. G., Hall J. A. J., Carlos Moretti, A., Fonseca Veloso, R., Alexander, P., Crespolini, M., & Moran, D. (2017). Sustainable intensification of Brazilian livestock production through optimized pasture restoration. Agricultural Systems, 153, 201-211. https://doi.org/10.1016/j.agsy.2017.02.001
Sun, G. D., Guan, X., Yi, X., & Zhou, Z. (2017). Grey relational analysis between hesitant fuzzy sets with applications to pattern recognition. Expert Systems with Applications, 92, 521-532. https://doi.org/10.1016/j.eswa.2017.09.048
Torra, V. (2010). Hesitant fuzzy sets. International Journal of Intelligent Systems, 25, 529-539. https://doi.org/10.1002/int.20418
Torra, V., & Narukawa, Y. (2009). On hesitant fuzzy sets and decision. In The 18th IEEE International Conference on Fuzzy systems (pp. 1378-1382). Jeju Island, Korea.
Wang, J. Q., Wang, D. D., Zhang, H. Y., & Chen, X. H. (2014). Multi-criteria outranking approach with hesitant fuzzy sets. OR Spectrum, 36(4), 1001-1019. https://doi.org/10.1007/s00291-013-0354-3
Wei, G. W. (2012). Hesitant fuzzy prioritized operators and their application to multiple attribute decision making. Knowledge-Based Systems, 31(7), 176-182. https://doi.org/10.1016/j.knosys.2012.03.011
Wei, G. W., Alsaadi, F. E., Hayat, T., & Alsaedi, A. (2016). A linear assignment method for multiple criteria decision analysis with hesitant fuzzy sets based on fuzzy measure. International Journal of Fuzzy Systems, 19(3), 1-8. https://doi.org/10.1007/s40815-016-0177-x
World Commission on Environment and Development. (1987). Report of the world Commission on Environment and Development: our common future. Oxford: Oxford University Press.
Xia, M. M., & Xu, Z. S. (2011). Hesitant fuzzy information aggregation in decision making. International Journal of Approximate Reasoning, 52(3), 395-407. https://doi.org/10.1016/j.ijar.2010.09.002
Xu, Z. S., & Xia, M. M. (2011). Distance and similarity measures for hesitant fuzzy sets. Information Sciences, 181(11), 2128-2138. https://doi.org/10.1016/j.ins.2011.01.028
Xu, Z. S., & Zhang, X. L. (2013). Hesitant fuzzy multi-attribute decision making based on TOPSIS with incomplete weight information. Knowledge-Based Systems, 52, 53-64. https://doi.org/10.1016/j.knosys.2013.05.011
Yager, R. R. (2008). Time series smoothing and OWA aggregation. IEEE Transactions on Fuzzy Systems, 16(4), 994-1007. https://doi.org/10.1109/TFUZZ.2008.917299
Yu, D. J. (2014). Group decision making under multiplicative hesitant fuzzy environment. International Journal of Fuzzy Systems, 16(2), 233-241.
Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
Zendehedl, K., Rademaker, M., Baets, B. D., & Huylenbroeck, G. V. (2008). Qualitative valuation of environmental criteria through a group consensus based on stochastic dominance. Ecological Economics, 67(2), 253-264. https://doi.org/10.1016/j.ecolecon.2008.05.013
Zendehedl, K., Rademaker, M., Baets, B. D., & Huylenbroeck, G. V. (2009). Improving tractability of group decision making on environmental problems through the use of social intensities of preferences. Environmental Modelling & Software, 24(12), 1457-1466. https://doi.org/10.1016/j.envsoft.2009.05.017
Zendehdel, K., Rademaker, M., Baets, B. D., & Huylenbroeck, G. V. (2010). Environmental decision making with conflicting social groups: a case study of the lar rangeland in Iran. Journal of Arid Environments, 74(3), 394-402. https://doi.org/10.1016/j.jaridenv.2009.09.011
Zhang, Z. M. (2013). Hesitant fuzzy power aggregation operators and their application to multiple attribute group decision making. Information Sciences, 234(10), 150-181. https://doi.org/10.1016/j.ins.2013.01.002
Zhu, B. (2014). Decision method for research and application based on preference relation (PhD thesis). Southeast University, Nanjing, China.
Alcantud, J. C. R., de Andrés Calle, R., & Torrecillas, M. J. M. (2016). Hesitant fuzzy worth: an innovative ranking methodology for hesitant fuzzy sets. Applied Soft Computing, 38: 232–243. https://doi.org/10.1016/j.asoc.2015.09.035
Azadi, H., Shahvali, M., Berg, J. V. D., & Faghih, N. (2007). Sustainable rangeland management using a multi-fuzzy model: how to deal with heterogeneous experts’ knowledge. Journal of Environmental Management, 83(2), 236-249. https://doi.org/10.1016/j.jenvman.2006.03.012
Campbell, W. B., Rodríguze, J. J., Ortiz, S. L., & Gallegos, E. C. (2013). Does stocking rate manipulation promote pasture sustainability in the humid tropics? Rangeland Ecology & Management, 66(3), 348-355. https://doi.org/10.2111/REM-D-11-00110.1
Chen, N., Xu, Z. S., & Xia, M. M. (2013). Correlation coefficients of hesitant fuzzy sets and their applications to clustering analysis. Applied Mathematical Modelling, 37(4), 2197-2211. https://doi.org/10.1016/j.apm.2012.04.031
Farhadinia, B. (2013). Information measures for hesitant fuzzy sets and interval-valued hesitant fuzzy sets. Information Sciences, 240, 129-144. https://doi.org/10.1016/j.ins.2013.03.034
Farley, K. A., Walsh, K., & Levine, A. S. (2017). Opportunities and obstacles for rangeland conservation in San Diego County, California, USA. Ecology and Society, 22(1), 38. https://doi.org/10.5751/ES-09077-220138
Filev, D., & Yager, R. R. (1995). Analytic properties of maximum entropy OWA operators. Information Sciences, 85(1-3), 11-27. https://doi.org/10.1016/0020-0255(94)00109-O
Fullér, R., & Majlender, P. (2000). An analytic approach for obtaining maximal entropy OWA operator weights. Fuzzy Sets and Systems, 124(1), 53-57. https://doi.org/10.1016/S0165-0114(01)00007-0
Gross, J. E., Mcallister, R. R. J, Abel, N., Stafford Smith, D. M., & Maru, Y. (2006). Australian rangelands as complex adaptive systems: a conceptual model and preliminary results. Environmental Modelling & Software, 21(9), 1264-1272. https://doi.org/10.1016/j.envsoft.2005.04.024
Hu, J. H., Zhang, X. L., Chen, X. H., & Liu, Y. M. (2016). Hesitant fuzzy information measures and their applications in multi-criteria decision making. International Journal of System Sciences, 47(1), 62-76. https://doi.org/10.1080/00207721.2015.1036476
Jakoby, O., Quaas, M. F., Müller, B., Baumgärtner, S., & Frank, K. (2014). How do individual farmers᾽ objectives influence the evaluation of rangeland management strategies under a variable climate? Journal of Applied Ecology, 51(2), 483-493. https://doi.org/10.1111/1365-2664.12216
Laflamme, M. (2011). A framework for sustainable rangeland livelihoods. Rangeland Journal, 33(4), 339-351. https://doi.org/10.1071/RJ11023
Li, D. F. (2007). Compromise ratio method for fuzzy multi-attribute group decision making. Applied Soft Computing, 7, 807-817. https://doi.org/10.1016/j.asoc.2006.02.003
Li, W., Chen, G. F., & Duan, C. (2010). Research and implementation of Index weight calculation model for power grid investment return. Lecture Notes in Computer Science, 6318, 44-52. https://doi.org/10.1007/978-3-642-16515-3_7
Liao, H. C., & Xu, Z. S. (2014). Satisfaction degree based interactive decision making under hesitant fuzzy environment with incomplete weights. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 22(4): 553-572. https://doi.org/10.1142/S0218488514500275
Liao, H. C., Xu, Z. S., & Xu, J. P. (2014). An approach to hesitant fuzzy multi-stage multi-criterion decision making. Kybernets, 43(9/10), 1447-1468. https://doi.org/10.1108/K-11-2013-0246
Liao, H. C., Xu, Z. S., & Zeng, X. J. (2015). Novel correlation coefficients between hesitant fuzzy sets and their application in decision making. Knowledge-Based Systems, 82(C), 115-127. https://doi.org/10.1016/j.knosys.2015.02.020
Liu, S. T. (2016). A mathematical programming approach to sample coefficient of variation with interval-valued observations. TOP, 24, 1-18. https://doi.org/10.1007/s11750-015-0391-y
Liu, X. D., Wang, Z. W., & Hetzler, A. (2017). HFMADM method based on nondimensionalization and its application in the evaluation of inclusive growth. Journal of Business Economics and Management, 18(4), 726-744. https://doi.org/10.3846/16111699.2017.1341848
Liu, X. D., Zhu, J. J., Zhang, S. T., Hao, J. J., & Liu, G. D. (2015). Integrating LNMAP and TOPSIS methods for hesitant fuzzy multiple attribute decision making. Journal of Intelligent & Fuzzy Systems, 28(1), 257-269.
Meng, F. Y., & Chen X. H. (2015). Correlation coefficients of hesitant fuzzy sets and their application based on fuzzy measures. Cognitive Computation, 7(4), 445-463. https://doi.org/10.1007/s12559-014-9313-9
Nasibova, R. A., & Nasibov, E. N. (2010). Linear aggregation with weighted ranking. Automatic Control and Computer Sciences, 44(2), 96-102. https://doi.org/10.3103/S0146411610020057
Onar, S. Ç., Büyüközkan, G., Öztayşi, B., & Kahraman, C. (2016). A new hesitant fuzzy QFD approach: an application to computer workstation selection. Applied Soft Computing, 46, 1-16. https://doi.org/10.1016/j.asoc.2016.04.023
Papanastasis, V. P. (2009). Restoration of degraded grazing lands through grazing management: can it work? Restoration Ecology, 17(4), 441-445. https://doi.org/10.1111/j.1526-100X.2009.00567.x
Peano, C., Migliorini, P., & Sottile, F. (2014). A methodology for the sustainability assessments of agrifood systems: an application to the slow food president project. Ecology and Society, 19(4), 24. https://doi.org/10.5751/ES-06972-190424
Peng, D. H., & Wang, H. (2014). Dynamic hesitant fuzzy aggregation operators in multi-period decision making. Kybernetes, 43(5), 715-736. https://doi.org/10.1108/K-11-2013-0236
Peng, J. J., Wang, J. Q., & Wu, X. H. (2016). Novel multi-criteria decision-making approaches based on hesitant fuzzy sets and prospect theory. International Journal of Information Technology & Decision Making, 15(3), 621-643. https://doi.org/10.1142/S0219622016500152
Reeves, M. C., & Baggett, L. S. (2014). A remote sensing protocol for identifying rangelands with degraded productive capacity. Ecological Indicators, 43, 172-182. https://doi.org/10.1016/j.ecolind.2014.02.009
Rodríguez, R. M., Bedregal, B., Bustincec, H., Dong, Y. C., Farhadinia, B., Kahramanf, C., Martínez, L., Torra, V., Xui, Y. J., Xud, Z. S., Herreraa, F. (2016). A position and perspective analysis of hesitant fuzzy sets on information fusion in decision making: towards high quality progress. Information Fusion, 29, 89-97. https://doi.org/10.1016/j.inffus.2015.11.004
Silva, R. O., Barioni, L. G., Hall J. A. J., Carlos Moretti, A., Fonseca Veloso, R., Alexander, P., Crespolini, M., & Moran, D. (2017). Sustainable intensification of Brazilian livestock production through optimized pasture restoration. Agricultural Systems, 153, 201-211. https://doi.org/10.1016/j.agsy.2017.02.001
Sun, G. D., Guan, X., Yi, X., & Zhou, Z. (2017). Grey relational analysis between hesitant fuzzy sets with applications to pattern recognition. Expert Systems with Applications, 92, 521-532. https://doi.org/10.1016/j.eswa.2017.09.048
Torra, V. (2010). Hesitant fuzzy sets. International Journal of Intelligent Systems, 25, 529-539. https://doi.org/10.1002/int.20418
Torra, V., & Narukawa, Y. (2009). On hesitant fuzzy sets and decision. In The 18th IEEE International Conference on Fuzzy systems (pp. 1378-1382). Jeju Island, Korea.
Wang, J. Q., Wang, D. D., Zhang, H. Y., & Chen, X. H. (2014). Multi-criteria outranking approach with hesitant fuzzy sets. OR Spectrum, 36(4), 1001-1019. https://doi.org/10.1007/s00291-013-0354-3
Wei, G. W. (2012). Hesitant fuzzy prioritized operators and their application to multiple attribute decision making. Knowledge-Based Systems, 31(7), 176-182. https://doi.org/10.1016/j.knosys.2012.03.011
Wei, G. W., Alsaadi, F. E., Hayat, T., & Alsaedi, A. (2016). A linear assignment method for multiple criteria decision analysis with hesitant fuzzy sets based on fuzzy measure. International Journal of Fuzzy Systems, 19(3), 1-8. https://doi.org/10.1007/s40815-016-0177-x
World Commission on Environment and Development. (1987). Report of the world Commission on Environment and Development: our common future. Oxford: Oxford University Press.
Xia, M. M., & Xu, Z. S. (2011). Hesitant fuzzy information aggregation in decision making. International Journal of Approximate Reasoning, 52(3), 395-407. https://doi.org/10.1016/j.ijar.2010.09.002
Xu, Z. S., & Xia, M. M. (2011). Distance and similarity measures for hesitant fuzzy sets. Information Sciences, 181(11), 2128-2138. https://doi.org/10.1016/j.ins.2011.01.028
Xu, Z. S., & Zhang, X. L. (2013). Hesitant fuzzy multi-attribute decision making based on TOPSIS with incomplete weight information. Knowledge-Based Systems, 52, 53-64. https://doi.org/10.1016/j.knosys.2013.05.011
Yager, R. R. (2008). Time series smoothing and OWA aggregation. IEEE Transactions on Fuzzy Systems, 16(4), 994-1007. https://doi.org/10.1109/TFUZZ.2008.917299
Yu, D. J. (2014). Group decision making under multiplicative hesitant fuzzy environment. International Journal of Fuzzy Systems, 16(2), 233-241.
Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
Zendehedl, K., Rademaker, M., Baets, B. D., & Huylenbroeck, G. V. (2008). Qualitative valuation of environmental criteria through a group consensus based on stochastic dominance. Ecological Economics, 67(2), 253-264. https://doi.org/10.1016/j.ecolecon.2008.05.013
Zendehedl, K., Rademaker, M., Baets, B. D., & Huylenbroeck, G. V. (2009). Improving tractability of group decision making on environmental problems through the use of social intensities of preferences. Environmental Modelling & Software, 24(12), 1457-1466. https://doi.org/10.1016/j.envsoft.2009.05.017
Zendehdel, K., Rademaker, M., Baets, B. D., & Huylenbroeck, G. V. (2010). Environmental decision making with conflicting social groups: a case study of the lar rangeland in Iran. Journal of Arid Environments, 74(3), 394-402. https://doi.org/10.1016/j.jaridenv.2009.09.011
Zhang, Z. M. (2013). Hesitant fuzzy power aggregation operators and their application to multiple attribute group decision making. Information Sciences, 234(10), 150-181. https://doi.org/10.1016/j.ins.2013.01.002
Zhu, B. (2014). Decision method for research and application based on preference relation (PhD thesis). Southeast University, Nanjing, China.