An overview on the applications of the hesitant fuzzy sets in group decision-making: theory, support and methods

Abstract

Due to the characteristics of hesitant fuzzy sets (HFSs), one hesitant fuzzy element (HFE), which is the basic component of HFSs, can express the evaluation values of multiple decision makers (DMs) on the same alternative under a certain attribute. Thus, the HFS has its unique advantages in group decision making (GDM). Based on which, many scholars have conducted in-depth research on the applications of HFSs in GDM. We have viewed lots of relevant literature and divided the existing studies into three categories: theory, support and methods. In this paper, we elaborate on hesitant fuzzy GDM from these three aspects. The first aspect is mainly about the introduction of HFSs, HFPRs and some hesitant fuzzy aggregation operators. The second aspect describes the consensus process under hesitant fuzzy environment, which is an important support for a complete decision-making process. In the third aspect, we introduce seven hesitant fuzzy GDM approaches, which can be applied in GDM under different decision-making conditions. Finally, we summarize the research status of hesitant fuzzy GDM and put forward some directions of future research.

Keywords

hesitant fuzzy set / hesitant fuzzy preference relation / group decision-making

References

[1] Acar C, Beskese A, Temur G T (2018). Sustainability analysis of different hydrogen production options using hesitant fuzzy AHP. International Journal of Hydrogen Energy, 43(39): 18059–18076

[2] Alcantud J C R, Giarlotta A (2019). Necessary and possible hesitant fuzzy sets: A novel model for group decision making. Information Fusion, 46: 63–76

[3] Asan U, Kadaifci C, Bozdag E, Soyer A, Serdarasan S (2018). A new approach to DEMATEL based on interval-valued hesitant fuzzy sets. Applied Soft Computing, 66: 34–49

[4] Ashtiani M, Azgomi M A (2016). A hesitant fuzzy model of computational trust considering hesitancy, vagueness and uncertainty. Applied Soft Computing, 42: 18–37

[5] Camerer C (1998). Bounded rationality in individual decision making. Experimental Economics, 1(2): 163–183

[6] 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

[7] Chen N, Xu Z S, Xia M M (2013a). Correlation coefficients of hesitant fuzzy sets and their applications to clustering analysis. Applied Mathematical Modelling, 37(4): 2197–2211

[8] Chen N, Xu Z S, Xia M M (2013b). Interval-valued hesitant preference relations and their applications to group decision making. Knowledge-Based Systems, 37: 528–540

[9] Chen N, Xu Z S, Xia M M (2015). The ELECTRE I multi-criteria decision making method based on hesitant fuzzy sets. International Journal of Information Technology & Decision Making, 14(03): 621–657

[10] Cheng S H (2018). Autocratic decision making using group recommendations based on hesitant fuzzy sets for green hotels selection and bidders selection. Information Sciences, 467: 604–617

[11] De S K, Sana S S (2017). Multi-criterion multi-attribute decision-making for an EOQ model in a hesitant fuzzy environment. Pacific Science Review A. Natural Science and Engineering, 17: 61–68

[12] Dincer H, Yuksel S, Martinez L (2019). Balanced scorecard-based analysis about European energy investment policies: A hybrid hesitant fuzzy decision-making approach with Quality Function Deployment. Expert Systems with Applications, 115: 152–171

[13] Ding J, Xu Z S, Zhao N (2017). An interactive approach to probabilistic hesitant fuzzy multi-attribute group decision-making with incomplete weight information. Journal of Intelligent & Fuzzy Systems, 32(3): 2523–2536

[14] Farhadinia B (2014). Distance and similarity measures for higher order hesitant fuzzy sets. Knowledge-Based Systems, 55: 43–48

[15] Farhadinia B (2016a). Hesitant fuzzy set lexicographical ordering and its application to multi-attribute decision making. Information Sciences, 327: 233–245

[16] Farhadinia B (2016b). Utility of correlation measures for weighted hesitant fuzzy sets in medical diagnosis problems. Mathematical Modelling and Applications, 1(2): 36–45

[17] Galo N R, Calache L D D R, Carpinetti L C R (2018). A group decision approach for supplier categorization based on hesitant fuzzy and ELECTRI TRI. International Journal of Production Economics, 202: 182–196

[18] He Y D, He Z, Shi L X, Meng S S (2016). Multiple attribute group decision making based on IVHFPBMs and a new ranking method for interval-valued hesitant fuzzy information. Computers & Industrial Engineering, 99: 63–77

[19] He Y, Xu Z S (2017). A consensus reaching model for hesitant information with different preference structures. Knowledge-Based Systems, 135: 99–112

[20] He Y, Xu Z S, Gu J (2016). An approach to group decision making with hesitant information and its application in credit risk evaluation of enterprises. Applied Soft Computing, 43: 159–169

[21] Hwang C L, Yoon K (1981). Multiple Attribute Decision Making Methods and Applications. Berlin: Springer

[22] Jiang H M, Kwong C K, Park W Y (2017). Probabilistic fuzzy regression approach for preference modeling. Engineering Applications of Artificial Intelligence, 64: 286–294

[23] Jin F F, Ni Z W, Chen H Y, Li Y P, Zhou L G (2016). Multiple attribute group decision making based on interval-valued hesitant fuzzy information measures. Computers & Industrial Engineering, 101: 103–115

[24] Lan J B, Jin R F, Zheng A Y, Hu M M (2017). Priority degrees for hesitant fuzzy sets: Applications to multiple attribute decision making. Operations Research Perspectives, 4: 67–73

[25] Li D Q, Zeng W Y, Li J H (2015). New distance and similarity measures on hesitant fuzzy sets and their applications in multiple criteria decision making. Engineering Applications of Artificial Intelligence, 40: 11–16

[26] Liang D C, Xu Z S (2017). The new extension of TOPSIS method for multiple criteria decision making with hesitant Pythagorean fuzzy sets. Applied Soft Computing, 60: 167–179

[27] Liao H C, Xu Z S (2013). A VIKOR-based method for hesitant fuzzy multi-criteria decision making. Fuzzy Optimization and Decision Making, 12(4): 373–392

[28] Liao H C, Xu Z S (2014a). Some new hybrid weighted aggregation operators under hesitant fuzzy multi-criteria decision making environment. Journal of Intelligent & Fuzzy Systems, 26(4): 1601–1617

[29] Liao H C, Xu Z S (2014b). Subtraction and division operations over hesitant fuzzy sets. Journal of Intelligent & Fuzzy Systems, 27(1): 65–72

[30] Liao H C, Xu Z S, Xia M M (2014). Multiplicative consistency of hesitant fuzzy preference relation and its application in group decision making. International Journal of Information Technology & Decision Making, 13(1): 47–76

[31] Mahmoudi A, Sadi-Nezhad S, Makui A, Vakili M R (2016). An extension on PROMETHEE based on the typical hesitant fuzzy sets to solve multi-attribute decision-making problem. Kybernetes, 45(8): 1213–1231

[32] Meng F Y, An Q X (2017). A new approach for group decision making method with hesitant fuzzy preference relations. Knowledge-Based Systems, 127: 1–15

[33] Meng F Y, Chen X H, Zhang Q (2015). Induced generalized hesitant fuzzy Shapley hybrid operators and their application in multi-attribute decision making. Applied Soft Computing, 28: 599–607

[34] Osiro L, Lima-Junior F R, Carpinetti L C R (2018). A group decision model based on quality function deployment and hesitant fuzzy for selecting supply chain sustainability metrics. Journal of Cleaner Production, 183: 964–978

[35] 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

[36] Peng J J, Wang J Q, Wang J, Yang L J, Chen X H (2015). An extension of ELECTRE to multi-criteria decision-making problems with multi-hesitant fuzzy sets. Information Sciences, 307: 113–126

[37] Perez-Fernandez R, Alonso P, Bustince H, Diaz I, Montes S (2016). Applications of finite interval-valued hesitant fuzzy preference relations in group decision making. Information Sciences, 326: 89–101

[38] Qian G, Wang H, Feng X Q (2013). Generalized hesitant fuzzy sets and their application in decision support system. Knowledge-Based Systems, 37: 357–365

[39] Qin J D, Liu X W, Pedrycy W (2016). Frank aggregation operators and their application to hesitant fuzzy multiple attribute decision making. Applied Soft Computing, 41: 428–452

[40] Sevastjanov P, Dymova L (2015). Generalized operations on hesitant fuzzy values in the framework of Dempster-Shafer theory. Information Sciences, 311: 39–58

[41] Sun G D, Guan X, Yi X, Zhou Z (2018). An innovative TOPSIS approach based on hesitant fuzzy correlation coefficient and its applications. Applied Soft Computing, 68: 249–267

[42] 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

[43] Tian X L, Xu Z S, Fujita H (2018). Sequential funding the venture project or not? A prospect consensus process with probabilistic hesitant fuzzy preference information. Knowledge-Based Systems, 161: 172–184

[44] Torra V (2010). Hesitant fuzzy sets. International Journal of Intelligent Systems, 25: 529–539

[45] Wan S P, Qin Y L, Dong J Y (2017). A hesitant fuzzy mathematical programming method for hybrid multi-criteria group decision making with hesitant fuzzy truth degrees. Knowledge-Based Systems, 138: 232–248

[46] Wei G W (2012). Hesitant fuzzy prioritized operators and their application to multiple attribute decision making. Knowledge-Based Systems, 31: 176–182

[47] Wu Z B, Jin B M, Xu J P (2018). Local feedback strategy for consensus building with probability-hesitant fuzzy preference relations. Applied Soft Computing, 67: 691–705

[48] Wu Z B, Xu J P (2018). A consensus model for large-scale group decision making with hesitant fuzzy information and changeable clusters. Information Fusion, 41: 217–231

[49] Xia M M, Xu Z S (2013). Managing hesitant information GDM problems under fuzzy and multiplicative preference relations. International Journal of Uncertainty, Fuzziness and Knowledge-based Systems, 21(06): 865–897

[50] Xia M M, Xu Z S (2011a). Some techniques for aggregating hesitant and intuitionistic information based on Sasty’s 1-9 scale. Technical report

[51] Xia M M, Xu Z S (2011b). Hesitant fuzzy information aggregation in decision making. International Journal of Approximate Reasoning, 52(3): 395–407

[52] Xia M M, Xu Z S, Chen N (2013). Some hesitant fuzzy aggregation operators with their application in group decision making. Group Decision and Negotiation, 22(2): 259–279

[53] Xu Y J, Li C Y, Wen X W (2018). Missing values estimation and consensus building for incomplete hesitant fuzzy preference relations with multiplicative consistency. International Journal of Computational Intelligence Systems, 11(1): 101–119

[54] Xu Y J, Rui D, Wang H M (2017). A dynamically weight adjustment in the consensus reaching process for group decision-making with hesitant fuzzy preference relations. International Journal of Systems Science, 48(6): 1311–1321

[55] Xu Y J, Cabrerizo F J, Herrera-Viedma N (2017). A consensus model for hesitant fuzzy preference relations and its application in water allocation management. Applied Soft Computing, 58: 265–284

[56] Xu Y J, Chen L, Rodriguez R M, Herrera F, Wang H M (2016). Deriving the priority weights from incomplete hesitant fuzzy preference relations in group decision making. Knowledge-Based Systems, 99: 71–78

[57] Xu Z S, Xia M M (2011). On distance and correlation measures of hesitant fuzzy information. International Journal of Intelligent Systems, 26(5): 410–425

[58] Xu Z S, Zhou W (2017). Consensus building with a group of decision makers under the hesitant probabilistic fuzzy environment. Fuzzy Optimization and Decision Making, 16(4): 481–503

[59] 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

[60] 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

[61] Zhang S, Xu Z S, Wu H Y (2018). Fusions and preference relations based on probabilistic interval-valued hesitant fuzzy information in group decision making. Soft Computing, DOI: http://doi.org/10.1007/s00500-018-3465-6

[62] Zhang S, Xu Z S, He Y (2017). Operations and integrations of probabilistic hesitant fuzzy information in decision making. Information Fusion, 38: 1–11

[63] Zhang X L, Xu Z S (2014a). Interval programming method for hesitant fuzzy multi-attribute group decision making with incomplete preference over alternatives. Computers & Industrial Engineering, 75: 217–229

[64] Zhang X L, Xu Z S (2014b). The TODIM analysis approach based on novel measured functions under hesitant fuzzy environment. Knowledge-Based Systems, 61: 48–58

[65] Zhang X L, Xu Z S (2015). Hesitant fuzzy QUALIFLEX approach with a signed distance-based comparison method for multiple criteria decision analysis. Expert Systems with Applications, 42(2): 873–884

[66] Zhang Z M (2013). Hesitant fuzzy power aggregation operators and their application to multiple attribute group decision making. Information Sciences, 234: 150–181

[67] Zhang Z M (2016). Deriving the priority weights from incomplete hesitant fuzzy preference relations based on multiplicative consistency. Applied Soft Computing, 46: 37–59

[68] 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

[69] Zhang Z M, Wang C, Tian X D (2015a). A decision support model for group decision making with hesitant fuzzy preference relations. Knowledge-Based Systems, 86: 77–101

[70] Zhang Z M, Wang C, Tian X D (2015b). Multi-criteria group decision making with incomplete hesitant fuzzy preference relations. Applied Soft Computing, 36: 1–23

[71] Zhang Z M, Wu C (2014a). Deriving the priority weights from hesitant multiplicative preference relations in group decision making. Applied Soft Computing, 25: 107–117

[72] Zhang Z M, Wu C (2014b). Weighted hesitant fuzzy sets and their application to multi-criteria decision making. British Journal of Mathematics and Computer Science, 4(8): 1091–1123

[73] Zhang Z, Kou X Y, Dong Q X (2018). Additive consistency analysis and improvement for hesitant fuzzy preference relations. Expert Systems with Applications, 98: 118–128

[74] Zhang Z, Kou X Y, Yu W Y, Guo C H (2018). On priority weights and consistency for incomplete hesitant fuzzy preference relations. Knowledge-Based Systems, 143: 115–126

[75] Zhao N, Xu Z S, Ren Z L (2015). On typical hesitant fuzzy prioritized “or” operator in multi-attribute decision making. International Journal of Intelligent Systems, 31(1): 73–100

[76] Zhao X F, Lin R, Wei G W (2014). Hesitant triangular fuzzy information aggregation based on Einstein operations and their application to multiple attribute decision making. Expert Systems with Applications, 41(4): 1086–1094

[77] Zhou W, Xu Z S (2017a). Expected hesitant VaR for tail decision making under probabilistic hesitant fuzzy environment. Applied Soft Computing, 60: 297–311

[78] Zhou W, Xu Z S (2017b). Group consistency and group decision making under uncertain probabilistic hesitant fuzzy preference environment. Information Sciences, 414: 276–288

[79] Zhou W, Xu Z S (2018). Probability calculation and element optimization of probabilistic hesitant fuzzy preference relations based on expected consistency. IEEE Transactions on Fuzzy Systems, 26(3): 1367–1378

[80] Zhou W, Xu Z S, Chen M H (2015). Preference relations based on hesitant-intuitionistic fuzzy information and their application in group decision making. Computers & Industrial Engineering, 87: 163–175

[81] Zhu B (2014). Decision method for research and application based on preference relations. Nanjing: Southeast University

[82] Zhu B, Xu Z S (2014). Analytic hierarchy process-hesitant group decision making. European Journal of Operational Research, 239(3): 794–801

[83] Zhu B, Xu Z S (2018). Probability-hesitant fuzzy sets and the representation of preference relations. Technological and Economic Development of Economy, 24(3): 1029–1040

[84] Zhu B, Xu Z S, Xu J P (2014). Deriving a ranking from hesitant fuzzy preference relations under group decision making. IEEE Transactions on Cybernetics, 44(8): 1328–1337

[85] Zhu B, Xu Z S, Xia M M (2012). Hesitant fuzzy geometric Bonferroni means. Information Sciences, 2015: 72–85

[86] Zhu B, Xu Z S, Xia M M (2013). Hesitant fuzzy Bonferroni means for multi-criteria decision making. Journal of the Operational Research Society, 64(12): 1831–1840

[87] Zhu B, Xu Z S, Zhang R, Hong M (2015). Generalized analytic network process. European Journal of Operational Research, 244(1): 277–288

[88] Zhu B, Xu Z S, Zhang R, Hong M (2016). Hesitant analytic hierarchy process. European Journal of Operational Research, 250(2): 602–614

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