A method based on TOPSIS and distance measures for hesitant fuzzy multiple attribute decision making
Abstract
The aim of this paper is to provide a methodology to hesitant fuzzy multiple attribute decision making using technique for order preference by similarity to ideal solution (TOPSIS) and distance measures. Firstly, the inadequacies of the existing hesitant fuzzy TOPSIS method are analyzed in detail. Then, based on the developed hesitant fuzzy ordered weighted averaging weighted aver-aging distance (HFOWAWAD) measure, a modified hesitant fuzzy TOPSIS, called HFOWAWAD-TOPSIS is introduced for hesitant fuzzy multiple attribute decision making problems. Moreover, the advantages and some special cases of the HFOWAWAD-TOPSIS are presented. Finally, a numerical example about energy policy selection is provided to illustrate the practicality and feasibility of the developed approach.
Keyword : hesitant fuzzy information, TOPSIS, distance measures, multiple attribute decision making
How to Cite
Zeng, S., & Xiao, Y. (2018). A method based on TOPSIS and distance measures for hesitant fuzzy multiple attribute decision making. Technological and Economic Development of Economy, 24(3), 969-983. https://doi.org/10.3846/20294913.2016.1216472
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
Atanassov, K. T. 1986. Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20(1): 87–96. https://doi.org/10.1016/S0165-0114(86)80034-3
Cables, E.; Socorro, M.; Teresa, M. 2012. The LTOPSIS: an alternative to TOPSIS decision-making approach for linguistic variables, Expert Systems with Applications 39(2): 2119–2126. https://doi.org/10.1016/j.eswa.2011.07.119
Casanovas, M.; Merigó, J. M. 2012. Fuzzy aggregation operators in decision making with Dempster-Shafer belief structure, Expert Systems with Applications 39(8): 7138–7149. https://doi.org/10.1016/j.eswa.2012.01.030
Chen, N.; Xu, Z. S. 2015. Hesitant fuzzy ELECTRE II approach: a new way to handle multi-criteria decision making problems, Information Sciences 292: 175–197. https://doi.org/10.1016/j.ins.2014.08.054
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
Chen, T. Y. 2000. Extensions of the TOPSIS for group decision-making under fuzzy environment, Fuzzy Sets and Systems 144(1): 1–9. https://doi.org/10.1016/S0165-0114(97)00377-1
Chen, T. Y. 2015. The inclusion-based TOPSIS method with interval-valued intuitionistic fuzzy sets for multiple criteria group decision making, Applied Soft Computing 26: 57–73. https://doi.org/10.1016/j.asoc.2014.09.015
Chen, T. Y.; Tsao, C. Y. 2008. The interval-valued fuzzy TOPSIS method and experimental analysis, Fuzzy Sets and Systems 159(11): 1410–1428. https://doi.org/10.1016/j.fss.2007.11.004
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
Hwang, C. L.; Yoon, K. S. 1981. Multiple attributes decision methods and applications. Springer, Berlin.
Jin, F.; Liu, P. D.; Zhang, X. 2013. The multi-attribute group decision making method based on the interval grey linguistic variables weighted harmonic aggregation operators, Technological and Economic Development of Economy 19(3): 409–430. https://doi.org/10.3846/20294913.2013.821685
Kim, G; Park, C. S.; Yoon, K. P. 1997. Identifying investment opportunities for advanced manufacturing systems with comparative-integrated performance measurement, International Journal of Production Economics 50(1): 23–33. https://doi.org/10.1016/S0925-5273(97)00014-5
Liao, H. C.; Xu, Z. S. 2014. Satisfaction degree based interactive decision making method 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.; Zeng, X. J.; Merigó, J. M. 2015. Qualitative decision making with correlation coefficients of hesitant fuzzy linguistic term sets, Knowledge-Based Systems 76: 127–138. https://doi.org/10.1016/j.knosys.2014.12.009
Liu, P. D.; Jin, F. 2012. Methods for aggregating intuitionistic uncertain linguistic variables and their application to group decision making, Information Sciences 205(1): 58–71. https://doi.org/10.1016/j.ins.2012.04.014
Merigó, J. M. 2011. A unified model between the weighted average and the induced OWA operator, Expert Systems with Applications 38(9): 11560–11572. https://doi.org/10.1016/j.eswa.2011.03.034
Merigó, J. M.; Casanovas, M. 2010. The fuzzy generalized OWA operator and its application in strategic decision making, Cybernetics and Systems 41(5): 359–370. http://dx.doi.org/10.1080/01969722.2010.486223
Merigó, J. M.; Engemann, K. J.; Palacios-Marqués, D. 2013b. Decision making with Dempster-Shafer theory and the OWAWA operator, Technological and Economic Development of Economy 19(S1): S194–S212. https://doi.org/10.3846/20294913.2013.869517
Merigó, J. M.; Guillén, M; Sarabia, J. M. 2015. The ordered weighted average in the variance and the covariance, International Journal of Intelligent Systems 30(9): 985–1005. http://dx.doi.org/10.1002/int.21716
Merigó, J. M.; Palacios-Marqués, D.; Soto-Acosta, P. 2016b. Distance measures, weighted averages, OWA operators and Bonferroni means, Applied Soft Computing 50: 356–366. https://doi.org/10.1016/j.asoc.2016.11.024
Merigó, J. M.; Palacios-Marqués, D; Zeng, S. Z. 2016a. Subjective and objective information in linguistic multi-criteria group decision making, European Journal of Operational Research 248(2): 522–531. https://doi.org/10.1016/j.ejor.2015.06.063
Merigó, J. M.; Peris-Ortiz, M.; Palacios-Marqués, D. 2014. Entrepreneurial fuzzy group decision-making under complex environments, Journal of Intelligent & Fuzzy Systems 27: 901–912. https://doi.org/10.3233/IFS-131048
Merigó, J. M.; Xu, Y. J.; Zeng, S. Z. 2013a. Group decision making with distance measures and probabilistic information, Knowledge-Based Systems 40: 81–87. http://doi.org/10.1016/j.knosys.2012.11.014
Merigó, J. M.; Yager, R. R. 2013. Generalized moving averages, distance measures and OWA operators, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 21(4): 533–559. https://doi.org/10.1142/S0218488513500268
Merigó, J. M.; Gil-Lafuente, A. M. 2010. New decision-making techniques and their application in the selection of financial products, Information Sciences 180(11): 2085–2094. https://doi.org/10.1016/j.ins.2010.01.028
Mu, Z. M.; Zeng, S. Z.; Baležentis, T. 2015. A novel aggregation principle for hesitant fuzzy elements, Knowledge-Based Systems 84: 134–143. https://doi.org/10.1016/j.knosys.2015.04.008
Peng, D. H.; Gao, C. Y.; Gao, Z. F. 2013. Generalized hesitant fuzzy synergetic weighted distance measures and their application to multiple criteria decision-making, Applied Mathematical Modelling 37(8): 5837–5850. https://doi.org/10.1016/j.apm.2012.11.016
Rodríguez, R. M.; Martínez, L.; Torra, V.; Xu, Z. S.; Herrera, F. 2014. Hesitant fuzzy sets: state of the art and future directions, International Journal of Intelligent Systems 29(6): 495–524. https://doi.org/10.1002/int.21654
Sevastjanov, P.; Dymova, L. 2015. Generalised operations on hesitant fuzzy values in the framework of Dempster-Shafer theory, Information Sciences 311: 39–58. https://doi.org/10.1016/j.ins.2015.03.041
Tan, C. Q.; Yi, W. T.; Chen, X. H. 2015. Hesitant fuzzy Hamacher aggregation operators for multicriteria decision making, Applied Soft Computing 26: 325–349. https://doi.org/10.1016/j.asoc.2014.10.007
Torra, V. 2010. Hesitant fuzzy sets, International Journal of Intelligent Systems 25(6): 529–539. https://doi.org/10.1002/int.20418
Vizuete, E.; Merigó, J. M.; Gil, A. M.; Boria, S. 2015. Decision making in the assignment process by using the Hungarian algorithm with the OWA operator, Technological and Economic Development of Economy 21(5): 684–704. https://doi.org/10.3846/20294913.2015.1056275
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, Y. J.; Wang, H. M. 2012. The induced generalized aggregation operators for intuitionistic fuzzy sets and their application in group decision making, Applied Soft Computing 12(3): 1168–1179. https://doi.org/10.1016/j.asoc.2011.11.003
Xu, Y.; Zhang, W.; Xu, W.; Wang, H. 2014. A conflict resolution approach for emergency decision of unconventional incidents, in IEEE International Conference on Systems, Man and Cybernetics, 5–8 October 2014, San Diego, CA, USA, 1922–1927. https://doi.org/10.1109/smc.2014.6974202
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. 1988. On ordered weighted averaging aggregation operators in multi-criteria decision making, IEEE Transactions on Systems, Man and Cybernetics B 18(1): 183–190. https://doi.org/10.1109/21.87068
Yager, R. R. 2014. Pythagorean membership grades in multi-criteria decision making, IEEE Transactions on Fuzzy Systems 22(4): 958–965. https://doi.org/10.1109/TFUZZ.2013.2278989
Yager, R. R.; Kacprzyk, J.; Beliakov, G. 2011. Recent developments on the ordered weighted averaging operators: theory and practice. Springer-Verlag, Berlin.
Ye, J. 2014. Correlation coefficient of dual hesitant fuzzy sets and its application to multiple attribute decision making, Applied Mathematical Modelling 38(2): 659–666. https://doi.org/10.1016/j.apm.2013.07.010
Yu, D. J.; Zhang, W. Y.; Xu, Y. J. 2013. Group decision making under hesitant fuzzy environment with application to personnel evaluation, Knowledge-Based Systems 52: 1–10. https://doi.org/10.1016/j.knosys.2013.04.010
Yue, Z. L. 2014. TOPSIS-based group decision-making methodology in intuitionistic fuzzy setting, Information Sciences 277: 141–153. https://doi.org/10.1016/j.ins.2014.02.013
Zeng, S. Z.; Baležentis, T.; Su, W. H. 2013a. The multi-criteria hesitant fuzzy group decision making with multimoora method, Economic Computer and Economic Cybernetics Studies and Research 47(3): 171–184.
Zeng, S. Z.; Chen, J. P.; Li, X. S. 2016b. A hybrid method for pythagorean fuzzy multiple-criteria decision making, International Journal of Information Technology & Decision Making 15(2): 403–422. https://doi.org/10.1142/S0219622016500012
Zeng, S. Z.; Chen, S. 2015. Extended VIKOR method based on induced aggregation operators for intuitionistic fuzzy financial decision making, Economic Computation and Economic Cybernetics Studies and Research Issue 49(4): 289–303.
Zeng, S. Z.; Merigó, J. M; Su, W. H. 2013b. The uncertain probabilistic OWA distance operator and its application in group decision making, Applied Mathematical Modelling 37(9): 6266–6275. https://doi.org/10.1016/j.apm.2013.01.022
Zeng, S. Z.; Su, W. H.; Merigó, J. M. 2013c. Extended induced ordered weighted averaging distance operators and their applicator group decision-making, International Journal of Information Technology and Decision Making 12(4): 789–811. https://doi.org/10.1142/S0219622013500296
Zeng, S. Z.; Su, W. H.; Zhang, C. H. 2016a. Intuitionistic fuzzy generalized probabilistic ordered weighted averaging operator and its application to group decision making, Technological and Economic Development of Economy 22(2): 177–193. https://doi.org/10.3846/20294913.2014.984253
Zeng, S. Z.; Wang, Q. F.; Merigó, J. M.; Pan, T. J. 2014. Induced intuitionistic fuzzy ordered weighted averaging – weighted average operator and its application to business decision-making, Computer Science and Information Systems 11(2): 839–857.
Zeng, S. Z.; Xiao, Y. 2016. TOPSIS method for intuitionistic fuzzy multiple-criteria decision making and its application to investment selection, Kybernetes 45(2): 282–296. https://doi.org/10.1108/K-03-2013-0059
Zhang, N.; Wei, G. W. 2013. Extension of VIKOR method for decision making problem based on hesitant fuzzy set, Applied Mathematical Modelling 37(7): 4938–4947. https://doi.org/10.1016/j.apm.2012.10.002
Zhang, X. L.; Xu, Z. S. 2014. Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets, International Journal of Intelligent Systems 29(12): 1061–1078. https://doi.org/10.1002/int.21676
Zhang, Z. M.; Wang. C.; Tian, D. Z.; Li, K. 2014. Induced generalized hesitant fuzzy operators and their application to multiple attribute group decision making, Computers & Industrial Engineering 67: 116–138. https://doi.org/10.1016/j.cie.2013.10.011
Zhang, Z. Z. 2013. Hesitant fuzzy power aggregation operators and their application to multiple attribute group decision making, Information Sciences 234: 150–181. https://doi.org/10.1016/j.ins.2013.01.002
Zhou, L. G.; Chen, H. Y.; Liu, J. B. 2012. Generalized power aggregation operators and their applications in group decision making, Computers & Industrial Engineering 62(4): 989–999. https://doi.org/10.1016/j.cie.2011.12.025
Cables, E.; Socorro, M.; Teresa, M. 2012. The LTOPSIS: an alternative to TOPSIS decision-making approach for linguistic variables, Expert Systems with Applications 39(2): 2119–2126. https://doi.org/10.1016/j.eswa.2011.07.119
Casanovas, M.; Merigó, J. M. 2012. Fuzzy aggregation operators in decision making with Dempster-Shafer belief structure, Expert Systems with Applications 39(8): 7138–7149. https://doi.org/10.1016/j.eswa.2012.01.030
Chen, N.; Xu, Z. S. 2015. Hesitant fuzzy ELECTRE II approach: a new way to handle multi-criteria decision making problems, Information Sciences 292: 175–197. https://doi.org/10.1016/j.ins.2014.08.054
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
Chen, T. Y. 2000. Extensions of the TOPSIS for group decision-making under fuzzy environment, Fuzzy Sets and Systems 144(1): 1–9. https://doi.org/10.1016/S0165-0114(97)00377-1
Chen, T. Y. 2015. The inclusion-based TOPSIS method with interval-valued intuitionistic fuzzy sets for multiple criteria group decision making, Applied Soft Computing 26: 57–73. https://doi.org/10.1016/j.asoc.2014.09.015
Chen, T. Y.; Tsao, C. Y. 2008. The interval-valued fuzzy TOPSIS method and experimental analysis, Fuzzy Sets and Systems 159(11): 1410–1428. https://doi.org/10.1016/j.fss.2007.11.004
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
Hwang, C. L.; Yoon, K. S. 1981. Multiple attributes decision methods and applications. Springer, Berlin.
Jin, F.; Liu, P. D.; Zhang, X. 2013. The multi-attribute group decision making method based on the interval grey linguistic variables weighted harmonic aggregation operators, Technological and Economic Development of Economy 19(3): 409–430. https://doi.org/10.3846/20294913.2013.821685
Kim, G; Park, C. S.; Yoon, K. P. 1997. Identifying investment opportunities for advanced manufacturing systems with comparative-integrated performance measurement, International Journal of Production Economics 50(1): 23–33. https://doi.org/10.1016/S0925-5273(97)00014-5
Liao, H. C.; Xu, Z. S. 2014. Satisfaction degree based interactive decision making method 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.; Zeng, X. J.; Merigó, J. M. 2015. Qualitative decision making with correlation coefficients of hesitant fuzzy linguistic term sets, Knowledge-Based Systems 76: 127–138. https://doi.org/10.1016/j.knosys.2014.12.009
Liu, P. D.; Jin, F. 2012. Methods for aggregating intuitionistic uncertain linguistic variables and their application to group decision making, Information Sciences 205(1): 58–71. https://doi.org/10.1016/j.ins.2012.04.014
Merigó, J. M. 2011. A unified model between the weighted average and the induced OWA operator, Expert Systems with Applications 38(9): 11560–11572. https://doi.org/10.1016/j.eswa.2011.03.034
Merigó, J. M.; Casanovas, M. 2010. The fuzzy generalized OWA operator and its application in strategic decision making, Cybernetics and Systems 41(5): 359–370. http://dx.doi.org/10.1080/01969722.2010.486223
Merigó, J. M.; Engemann, K. J.; Palacios-Marqués, D. 2013b. Decision making with Dempster-Shafer theory and the OWAWA operator, Technological and Economic Development of Economy 19(S1): S194–S212. https://doi.org/10.3846/20294913.2013.869517
Merigó, J. M.; Guillén, M; Sarabia, J. M. 2015. The ordered weighted average in the variance and the covariance, International Journal of Intelligent Systems 30(9): 985–1005. http://dx.doi.org/10.1002/int.21716
Merigó, J. M.; Palacios-Marqués, D.; Soto-Acosta, P. 2016b. Distance measures, weighted averages, OWA operators and Bonferroni means, Applied Soft Computing 50: 356–366. https://doi.org/10.1016/j.asoc.2016.11.024
Merigó, J. M.; Palacios-Marqués, D; Zeng, S. Z. 2016a. Subjective and objective information in linguistic multi-criteria group decision making, European Journal of Operational Research 248(2): 522–531. https://doi.org/10.1016/j.ejor.2015.06.063
Merigó, J. M.; Peris-Ortiz, M.; Palacios-Marqués, D. 2014. Entrepreneurial fuzzy group decision-making under complex environments, Journal of Intelligent & Fuzzy Systems 27: 901–912. https://doi.org/10.3233/IFS-131048
Merigó, J. M.; Xu, Y. J.; Zeng, S. Z. 2013a. Group decision making with distance measures and probabilistic information, Knowledge-Based Systems 40: 81–87. http://doi.org/10.1016/j.knosys.2012.11.014
Merigó, J. M.; Yager, R. R. 2013. Generalized moving averages, distance measures and OWA operators, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 21(4): 533–559. https://doi.org/10.1142/S0218488513500268
Merigó, J. M.; Gil-Lafuente, A. M. 2010. New decision-making techniques and their application in the selection of financial products, Information Sciences 180(11): 2085–2094. https://doi.org/10.1016/j.ins.2010.01.028
Mu, Z. M.; Zeng, S. Z.; Baležentis, T. 2015. A novel aggregation principle for hesitant fuzzy elements, Knowledge-Based Systems 84: 134–143. https://doi.org/10.1016/j.knosys.2015.04.008
Peng, D. H.; Gao, C. Y.; Gao, Z. F. 2013. Generalized hesitant fuzzy synergetic weighted distance measures and their application to multiple criteria decision-making, Applied Mathematical Modelling 37(8): 5837–5850. https://doi.org/10.1016/j.apm.2012.11.016
Rodríguez, R. M.; Martínez, L.; Torra, V.; Xu, Z. S.; Herrera, F. 2014. Hesitant fuzzy sets: state of the art and future directions, International Journal of Intelligent Systems 29(6): 495–524. https://doi.org/10.1002/int.21654
Sevastjanov, P.; Dymova, L. 2015. Generalised operations on hesitant fuzzy values in the framework of Dempster-Shafer theory, Information Sciences 311: 39–58. https://doi.org/10.1016/j.ins.2015.03.041
Tan, C. Q.; Yi, W. T.; Chen, X. H. 2015. Hesitant fuzzy Hamacher aggregation operators for multicriteria decision making, Applied Soft Computing 26: 325–349. https://doi.org/10.1016/j.asoc.2014.10.007
Torra, V. 2010. Hesitant fuzzy sets, International Journal of Intelligent Systems 25(6): 529–539. https://doi.org/10.1002/int.20418
Vizuete, E.; Merigó, J. M.; Gil, A. M.; Boria, S. 2015. Decision making in the assignment process by using the Hungarian algorithm with the OWA operator, Technological and Economic Development of Economy 21(5): 684–704. https://doi.org/10.3846/20294913.2015.1056275
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, Y. J.; Wang, H. M. 2012. The induced generalized aggregation operators for intuitionistic fuzzy sets and their application in group decision making, Applied Soft Computing 12(3): 1168–1179. https://doi.org/10.1016/j.asoc.2011.11.003
Xu, Y.; Zhang, W.; Xu, W.; Wang, H. 2014. A conflict resolution approach for emergency decision of unconventional incidents, in IEEE International Conference on Systems, Man and Cybernetics, 5–8 October 2014, San Diego, CA, USA, 1922–1927. https://doi.org/10.1109/smc.2014.6974202
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. 1988. On ordered weighted averaging aggregation operators in multi-criteria decision making, IEEE Transactions on Systems, Man and Cybernetics B 18(1): 183–190. https://doi.org/10.1109/21.87068
Yager, R. R. 2014. Pythagorean membership grades in multi-criteria decision making, IEEE Transactions on Fuzzy Systems 22(4): 958–965. https://doi.org/10.1109/TFUZZ.2013.2278989
Yager, R. R.; Kacprzyk, J.; Beliakov, G. 2011. Recent developments on the ordered weighted averaging operators: theory and practice. Springer-Verlag, Berlin.
Ye, J. 2014. Correlation coefficient of dual hesitant fuzzy sets and its application to multiple attribute decision making, Applied Mathematical Modelling 38(2): 659–666. https://doi.org/10.1016/j.apm.2013.07.010
Yu, D. J.; Zhang, W. Y.; Xu, Y. J. 2013. Group decision making under hesitant fuzzy environment with application to personnel evaluation, Knowledge-Based Systems 52: 1–10. https://doi.org/10.1016/j.knosys.2013.04.010
Yue, Z. L. 2014. TOPSIS-based group decision-making methodology in intuitionistic fuzzy setting, Information Sciences 277: 141–153. https://doi.org/10.1016/j.ins.2014.02.013
Zeng, S. Z.; Baležentis, T.; Su, W. H. 2013a. The multi-criteria hesitant fuzzy group decision making with multimoora method, Economic Computer and Economic Cybernetics Studies and Research 47(3): 171–184.
Zeng, S. Z.; Chen, J. P.; Li, X. S. 2016b. A hybrid method for pythagorean fuzzy multiple-criteria decision making, International Journal of Information Technology & Decision Making 15(2): 403–422. https://doi.org/10.1142/S0219622016500012
Zeng, S. Z.; Chen, S. 2015. Extended VIKOR method based on induced aggregation operators for intuitionistic fuzzy financial decision making, Economic Computation and Economic Cybernetics Studies and Research Issue 49(4): 289–303.
Zeng, S. Z.; Merigó, J. M; Su, W. H. 2013b. The uncertain probabilistic OWA distance operator and its application in group decision making, Applied Mathematical Modelling 37(9): 6266–6275. https://doi.org/10.1016/j.apm.2013.01.022
Zeng, S. Z.; Su, W. H.; Merigó, J. M. 2013c. Extended induced ordered weighted averaging distance operators and their applicator group decision-making, International Journal of Information Technology and Decision Making 12(4): 789–811. https://doi.org/10.1142/S0219622013500296
Zeng, S. Z.; Su, W. H.; Zhang, C. H. 2016a. Intuitionistic fuzzy generalized probabilistic ordered weighted averaging operator and its application to group decision making, Technological and Economic Development of Economy 22(2): 177–193. https://doi.org/10.3846/20294913.2014.984253
Zeng, S. Z.; Wang, Q. F.; Merigó, J. M.; Pan, T. J. 2014. Induced intuitionistic fuzzy ordered weighted averaging – weighted average operator and its application to business decision-making, Computer Science and Information Systems 11(2): 839–857.
Zeng, S. Z.; Xiao, Y. 2016. TOPSIS method for intuitionistic fuzzy multiple-criteria decision making and its application to investment selection, Kybernetes 45(2): 282–296. https://doi.org/10.1108/K-03-2013-0059
Zhang, N.; Wei, G. W. 2013. Extension of VIKOR method for decision making problem based on hesitant fuzzy set, Applied Mathematical Modelling 37(7): 4938–4947. https://doi.org/10.1016/j.apm.2012.10.002
Zhang, X. L.; Xu, Z. S. 2014. Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets, International Journal of Intelligent Systems 29(12): 1061–1078. https://doi.org/10.1002/int.21676
Zhang, Z. M.; Wang. C.; Tian, D. Z.; Li, K. 2014. Induced generalized hesitant fuzzy operators and their application to multiple attribute group decision making, Computers & Industrial Engineering 67: 116–138. https://doi.org/10.1016/j.cie.2013.10.011
Zhang, Z. Z. 2013. Hesitant fuzzy power aggregation operators and their application to multiple attribute group decision making, Information Sciences 234: 150–181. https://doi.org/10.1016/j.ins.2013.01.002
Zhou, L. G.; Chen, H. Y.; Liu, J. B. 2012. Generalized power aggregation operators and their applications in group decision making, Computers & Industrial Engineering 62(4): 989–999. https://doi.org/10.1016/j.cie.2011.12.025