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AIMS Mathematics

2020, Volume 5, Issue 3: 1985-2008. doi: 10.3934/math.2020132
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Research article

A novel approach to hesitant multi-fuzzy soft set based decision-making

  • 1.
    Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore 721 102, India
  • 2.
    School of Mathematics and Statistics, Southwest University, Beibei 400715, Chongqing, China
  • Received: 03 November 2019 Accepted: 13 February 2020 Published: 21 February 2020

  • MSC : 06D72, 90B50, 94D05

  • In this article, we present the idea of a hesitant multi-fuzzy set. We join the characteristics of a hesitant multi-fuzzy set with the parametrization of the soft set and constructs the hesitant multi-fuzzy soft set. We center around the fundamental operations for the instance of the hesitant multi-fuzzy soft subsets. Also, we look at the root mean square sum level soft set or RMSS-level soft set to deal with uncertainties. We also provide the utilization of hesitant multi-fuzzy soft set into the decision-making issues. Finally, we deliver a standard algorithm to resolve decision-making issues and test the effectiveness of it by a socialistic decision-making problem.

    Citation: Asit Dey, Tapan Senapati, Madhumangal Pal, Guiyun Chen. A novel approach to hesitant multi-fuzzy soft set based decision-making[J]. AIMS Mathematics, 2020, 5(3): 1985-2008. doi: 10.3934/math.2020132

    Related Papers:

  • In this article, we present the idea of a hesitant multi-fuzzy set. We join the characteristics of a hesitant multi-fuzzy set with the parametrization of the soft set and constructs the hesitant multi-fuzzy soft set. We center around the fundamental operations for the instance of the hesitant multi-fuzzy soft subsets. Also, we look at the root mean square sum level soft set or RMSS-level soft set to deal with uncertainties. We also provide the utilization of hesitant multi-fuzzy soft set into the decision-making issues. Finally, we deliver a standard algorithm to resolve decision-making issues and test the effectiveness of it by a socialistic decision-making problem.


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    [1] M. Akram, A. Adeel, J. C. R. Alcantud, Group decision-making methods based on hesitant N-soft sets, Expert Syst. Appl., 115 (2019), 95-105. doi: 10.1016/j.eswa.2018.07.060
    [2] J. C. R. Alcantud, A. Giarlotta, Necessary and possible hesitant fuzzy sets: A novel model for group decision making, Inform. Fusion, 46 (2019), 63-76. doi: 10.1016/j.inffus.2018.05.005
    [3] M. Ali, F. Feng, X. Liu, et al. On some new operations in soft set theory, Comput. Math. Appl., 57 (2009), 1547-1553. doi: 10.1016/j.camwa.2008.11.009
    [4] B. Bedregal, R. Reiser, H. Bustince, et al. Aggregation functions for typical hesitant fuzzy elements and the action of automorphisms, Inform. Sci., 255 (2014), 82-99. doi: 10.1016/j.ins.2013.08.024
    [5] N. Cagman, S. Enginoglu, Soft set theory and uni-int decision making, Eur. J. Oper. Res., 207 (2010), 848-855. doi: 10.1016/j.ejor.2010.05.004
    [6] N. Cagman, S. Enginoglu, Soft matrix theory and its decision making, Comput. Math. Appl., 59 (2010), 3308-3314. doi: 10.1016/j.camwa.2010.03.015
    [7] D. Chen, E. C. C. Tsang, D. S. Yeung, et al. The parameterization reduction of soft sets and its applications, Comput. Math. Appl., 49 (2005), 757-763. doi: 10.1016/j.camwa.2004.10.036
    [8] J. Chen, X. Huang, J. Tang, Distance measures for higher order dual hesitant fuzzy sets, Comput. Appl. Math., 37 (2018), 1784-1806. doi: 10.1007/s40314-017-0423-3
    [9] N. Chen, Z. S. Xu, M. M. Xia, Interval-valued hesitant preference relations and their applications to group decision making, Knowl. Based Syst., 37 (2013), 528-540. doi: 10.1016/j.knosys.2012.09.009
    [10] A. Dey, M. Pal, Genelalised multi-fuzzy soft set and its application in decision making, Pac. Sci. Rev. A, 17 (2015), 23-28.
    [11] A. Dey, M. Pal, On hesitant multi-fuzzy soft topology, Pac. Sci. Rev. B, 1 (2015), 124-130.
    [12] F. Feng, Y. B. Jun, X. Liu, et al. An adjustable approach to fuzzy soft set based decision making, J. Comput. Appl. Math., 234 (2010), 10-20. doi: 10.1016/j.cam.2009.11.055
    [13] F. Feng, Y. Li, N. Cagman, Generalized uni-int decision making schemes based on choice value soft sets, Eur. J. Oper. Res., 220 (2012), 162-170. doi: 10.1016/j.ejor.2012.01.015
    [14] X. Guan, Y. Li, F. Feng, A new order relation on fuzzy soft sets and its application, Soft Comput., 17 (2013), 63-70. doi: 10.1007/s00500-012-0903-8
    [15] J. Ignatius, S. Motlagh, M. Sepehri, et al. Hybrid models in decision making under uncertainty: The case of training provider evaluation, J. Intell. Fuzzy Syst., 21 (2010), 147-162. doi: 10.3233/IFS-2010-0443
    [16] P. Kakati, S. Borkotokey, S. Rahman, et al. Interval neutrosophic hesitant fuzzy Einstein Choquet integral operator for multicriteria decision making, Artif. Intell. Rev., (2019), 1-36.
    [17] Z. Kong, L. Gao, L. Wang, A fuzzy soft set theoretic approach to decision making problems, J. Comput. Appl. Math., 223 (2009), 540-542. doi: 10.1016/j.cam.2008.01.011
    [18] Z. Kong, L. Wang, Z. Wu, Application of fuzzy soft set in decision making problems based on grey theory, J. Comput. Appl. Math., 236 (2011), 1521-1530. doi: 10.1016/j.cam.2011.09.016
    [19] D. C. Liang, D. Liu, A novel risk decision making based on decision-theoretic rough sets under hesitant fuzzy information, IEEE Trans. Fuzzy Syst., 23 (2015), 237-247. doi: 10.1109/TFUZZ.2014.2310495
    [20] D. C. Liang, Z. S. Xu, D. Liu, Three-way decisions based on decision-theoretic rough sets with dual hesitant fuzzy information, Inform. Sci., 396 (2017), 127-143. doi: 10.1016/j.ins.2017.02.038
    [21] D. C. Liang, M. W. Wang, Z. S. Xu, et al. Risk appetite dual hesitant fuzzy three-way decisions with todim, Inform. Sci., 507 (2020), 585-605. doi: 10.1016/j.ins.2018.12.017
    [22] P. K. Maji, R. Biswas, A. R. Roy, Fuzzy soft sets, J. Fuzzy Math., 9 (2001), 589-602.
    [23] P. K. Maji, R. Biswas, A. R. Roy, An application of soft sets in a decision making problem, Comput. Math. Appl., 44 (2002), 1077-1083. doi: 10.1016/S0898-1221(02)00216-X
    [24] P. Majumdar, S. K. Samanta, Generalised fuzzy soft sets, Comput. Math. Appl., 59 (2010), 1425-1432. doi: 10.1016/j.camwa.2009.12.006
    [25] D. A. Molodtsov, Soft set theory-first results, Comput. Math. Appl., 37 (1999), 19-31.
    [26] S. Naz, M. Akram, Novel decision-making approach based on hesitant fuzzy sets and graph theory, Comput. Appl. Math., 38 (2019), 7.
    [27] B. Ozkan, E. Ozceylan, M. Kabak, et al. Evaluating the websites of academic departments through SEO criteria: A hesitant fuzzy linguistic MCDM approach, Artif. Intell. Rev., 53 (2020), 875-905. doi: 10.1007/s10462-019-09681-z
    [28] X. Qi, D. Liang, J. Zhang, Multiple attribute group decision making based on generalized power aggregation operators under interval-valued dual hesitant fuzzy linguistic environment, Int. J. Mach. Learn. Cybern., 7 (2016), 1147-1193. doi: 10.1007/s13042-015-0445-3
    [29] Z. Ren, C. Wei, A multi-attribute decision-making method with prioritization relationship and dual hesitant fuzzy decision information, Int. J. Mach. Learn. Cybern., 8 (2017), 755-763. doi: 10.1007/s13042-015-0356-3
    [30] R. M. Rodryguez, L. Martynez, V. Torra, et al. Hesitant fuzzy sets: state of the art and future directions, Int. J. Intell. Syst., 29 (2014), 495-524. doi: 10.1002/int.21654
    [31] A. R. Roy, P. K. Maji, A fuzzy soft set theoretic approach to decision making problems, J. Comput. Appl. Math., 203 (2007), 412-418. doi: 10.1016/j.cam.2006.04.008
    [32] S. Sebastian, T. V. Ramakrishnan, Multi-fuzzy sets: An extension of fuzzy sets, Fuzzy Inf. Eng., 1 (2011), 35-43.
    [33] C. Song, Y. Zhang, Z. Xu, An improved structure learning algorithm of Bayesian Network based on the hesitant fuzzy information flow, Appl. Soft Comput., 82 (2019), 105549.
    [34] V. Torra, Hesitant fuzzy sets, Int. J. Intell. Syst., 25 (2010), 529-539.
    [35] F. Wang, X. Li, X. Chen, Hesitant fuzzy soft set and its applications in multicriteria decision making, J. Appl. Math., 2014 (2014), 643785.
    [36] G. Wei, X. Zhao, R. Lin, Some hesitant intervalvalued fuzzy aggregation operators and their applications to multiple attribute decision making, Knowl. Based Syst, 46 (2013), 43-53. doi: 10.1016/j.knosys.2013.03.004
    [37] G. Wei, X. Zhao, Induced hesitant interval-valued fuzzy Einstein aggregation operators and their application to multiple attribute decision making, J. Intell. Fuzzy Syst., 24 (2013), 789-803. doi: 10.3233/IFS-2012-0598
    [38] G. Wei, Interval valued hesitant fuzzy uncertain linguistic aggregation operators in multiple attribute decision making, Int. J. Mach. Learn. Cybern., 7 (2016), 1093-1114. doi: 10.1007/s13042-015-0433-7
    [39] M. Xia, Z. S. Xu, Hesitant fuzzy information aggregation in decision making, Int. J. Approx. Reason., 52 (2011), 395-407. doi: 10.1016/j.ijar.2010.09.002
    [40] M. Xia, Z. S. Xu, Some studies on properties of hesitant fuzzy sets, Int. J. Mach. Learn. Cybern., 8 (2017), 489-495. doi: 10.1007/s13042-015-0340-y
    [41] Z. S. Xu, M. Xia, Distance and similarity measures for hesitant fuzzy sets, Inform. Sci., 181 (2011), 2128-2138. doi: 10.1016/j.ins.2011.01.028
    [42] Z. Xu, W. Zhou, Consensus building with a group of decision makers under the hesitant probabilistic fuzzy environment, Fuzzy Optim. Decis. Ma., 16 (2017), 481-503. doi: 10.1007/s10700-016-9257-5
    [43] W. Xue, Z. Xu, H. Wang, et al. Hazard assessment of landslide dams using the evidential reasoning algorithm with multi-scale hesitant fuzzy linguistic information, Appl. Soft Comput., 79 (2019), 74-86. doi: 10.1016/j.asoc.2019.03.032
    [44] Y. Yang, X. Tan, C. Meng, The multi-fuzzy soft set and its application in decision making, Appl. Math. Model., 37 (2013), 4915-4923. doi: 10.1016/j.apm.2012.10.015
    [45] Y. Yang, X. Peng, H. Chen, A decision making approach based on bipolar multi-fuzzy soft set theory, J. Intell. Fuzzy Syst., 27 (2014), 1861-1872. doi: 10.3233/IFS-141152
    [46] D. Yu, D. F. Li, J. M. Merigo, Dual hesitant fuzzy group decision making method and its application to supplier selection, Int. J. Mach. Learn. Cybern., 7 (2016), 819-831. doi: 10.1007/s13042-015-0400-3
    [47] C. Zhang, D. Li, J. Liang, Hesitant fuzzy linguistic rough set over two universes model and its applications, Int. J. Mach. Learn. Cybern., 9 (2018), 577-588. doi: 10.1007/s13042-016-0541-z
    [48] C. Zhang, D. Li, J. Liang, Multi-granularity three-way decisions with adjustable hesitant fuzzy linguistic multigranulation decision-theoretic rough sets over two universes, Inform. Sci., 507 (2020), 665-683. doi: 10.1016/j.ins.2019.01.033
    [49] C. Zhang, D. Li, J. Liang, Interval-valued hesitant fuzzy multi-granularity three-way decisions in consensus processes with applications to multi-attribute group decision making, Inform. Sci., 511 (2020), 192-211. doi: 10.1016/j.ins.2019.09.037
    [50] Z. Zhang, Hesitant fuzzy power aggregation operators and their application to multiple attribute group decision making, Inform. Sci., 234 (2013), 150-181. doi: 10.1016/j.ins.2013.01.002
    [51] Z. Zhang, C. Wang, D. Tian, et al. Induced generalized hesitant fuzzy operators and their application to multiple attribute group decision making, Comput. Ind. Eng., 67 (2014), 116-138. doi: 10.1016/j.cie.2013.10.011
    [52] Z. Zhang, H. Dong, S. Lan, Possibility multi-fuzzy soft set and its application in decision making, J. Intell. Fuzzy Syst., 27 (2013), 2115-2125.
    [53] H. Zhang, L. Xiong, W. Ma, On interval-valued hesitant fuzzy soft sets, Math. Probl. Eng., 2015 (2015), 254764.
    [54] F. Zhang, J. Ignatius, C. P. Lim, et al. A new method for ranking fuzzy numbers and its application to group decision making, Appl. Math. Model., 38 (2014), 1563-1582. doi: 10.1016/j.apm.2013.09.002
    [55] W. Zhou, Z. Xu, Hesitant fuzzy linguistic portfolio model with variable risk appetite and its application in the investment ratio calculation, Appl. Soft Comput., 84 (2019), 105719.
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