×
Zhou, Huan; Wang, Jian-Qiang; Zhang, Hong-Yu; Chen, Xiao-Hong

Linguistic hesitant fuzzy multi-criteria decision-making method based on evidential reasoning. (English) Zbl 1333.94081

Int. J. Syst. Sci., Princ. Appl. Syst. Integr. 47, No. 2, 314-327 (2016).
Summary: Linguistic hesitant fuzzy sets (LHFSs), which can be used to represent decision-makers’ qualitative preferences as well as reflect their hesitancy and inconsistency, have attracted a great deal of attention due to their flexibility and efficiency. This paper focuses on a multi-criteria decision-making approach that combines LHFSs with the evidential reasoning (ER) method. After reviewing existing studies of LHFSs, a new order relationship and Hamming distance between LHFSs are introduced and some linguistic scale functions are applied. Then, the ER algorithm is used to aggregate the distributed assessment of each alternative. Subsequently, the set of aggregated alternatives on criteria are further aggregated to get the overall value of each alternative. Furthermore, a nonlinear programming model is developed and genetic algorithms are used to obtain the optimal weights of the criteria. Finally, two illustrative examples are provided to show the feasibility and usability of the method, and comparison analysis with the existing method is made.

Cited in 9 Documents

MSC:

94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory)

Keywords:

multi-criteria decision-making; linguistic hesitant fuzzy sets; evidential reasoning; genetic algorithms
Cite Review PDF
Full Text: DOI

References:

[1] Bao G.Y., Control and Decision 5 pp 780– (2010)
[2] DOI: 10.1109/3468.553232 · doi:10.1109/3468.553232
[3] DOI: 10.1016/j.apm.2012.04.031 · Zbl 1349.62293 · doi:10.1016/j.apm.2012.04.031
[4] DOI: 10.1002/int.4550070507 · Zbl 0756.90001 · doi:10.1002/int.4550070507
[5] DOI: 10.1214/aoms/1177698950 · Zbl 0168.17501 · doi:10.1214/aoms/1177698950
[6] DOI: 10.1016/j.ins.2013.03.034 · Zbl 1320.68187 · doi:10.1016/j.ins.2013.03.034
[7] DOI: 10.1016/j.ins.2007.09.007 · Zbl 1132.91373 · doi:10.1016/j.ins.2007.09.007
[8] DOI: 10.2307/1914185 · Zbl 0411.90012 · doi:10.2307/1914185
[9] DOI: 10.1016/j.dss.2013.01.030 · doi:10.1016/j.dss.2013.01.030
[10] Lin R., Journal of Intelligent & Fuzzy Systems 26 (5) pp 2155– (2014)
[11] DOI: 10.1016/j.ins.2014.02.012 · Zbl 1339.91044 · doi:10.1016/j.ins.2014.02.012
[12] DOI: 10.1016/j.ins.2015.02.030 · Zbl 1390.91115 · doi:10.1016/j.ins.2015.02.030
[13] Peng J.J., Applied Mathematics & Information Sciences 9 (4) pp 2087– (2015)
[14] DOI: 10.1109/TFUZZ.2011.2170076 · doi:10.1109/TFUZZ.2011.2170076
[15] Said B., Mathematics and Statistics 2 (2) pp 62– (2014)
[16] Shafer G., A mathematical theory of evidence (1976) · Zbl 0359.62002
[17] DOI: 10.1016/j.eswa.2011.04.036 · doi:10.1016/j.eswa.2011.04.036
[18] Torra V., International Journal of Intelligent Systems 25 pp 529– (2010)
[19] DOI: 10.1080/18756891.2013.804144 · doi:10.1080/18756891.2013.804144
[20] DOI: 10.1016/j.knosys.2013.02.002 · doi:10.1016/j.knosys.2013.02.002
[21] DOI: 10.1016/j.asoc.2012.12.019 · doi:10.1016/j.asoc.2012.12.019
[22] DOI: 10.1016/j.ins.2014.02.130 · Zbl 1341.91047 · doi:10.1016/j.ins.2014.02.130
[23] DOI: 10.1007/s10726-014-9385-7 · doi:10.1007/s10726-014-9385-7
[24] DOI: 10.1109/TFUZZ.2014.2317500 · doi:10.1109/TFUZZ.2014.2317500
[25] DOI: 10.1007/s00291-013-0354-3 · Zbl 1305.90239 · doi:10.1007/s00291-013-0354-3
[26] DOI: 10.1007/s00500-014-1259-z · Zbl 1349.91098 · doi:10.1007/s00500-014-1259-z
[27] DOI: 10.1016/j.ins.2014.07.034 · Zbl 1355.91037 · doi:10.1016/j.ins.2014.07.034
[28] DOI: 10.1007/s00500-015-1609-5 · doi:10.1007/s00500-015-1609-5
[29] DOI: 10.1142/S0218539301000335 · doi:10.1142/S0218539301000335
[30] DOI: 10.1109/TFUZZ.2012.2210427 · doi:10.1109/TFUZZ.2012.2210427
[31] Wei G.W., Systems Engineering and Electronics 30 (2) pp 273– (2008)
[32] DOI: 10.1016/j.knosys.2012.03.011 · doi:10.1016/j.knosys.2012.03.011
[33] DOI: 10.1016/j.ijar.2010.09.002 · Zbl 1217.68216 · doi:10.1016/j.ijar.2010.09.002
[34] DOI: 10.1007/s10726-011-9261-7 · doi:10.1007/s10726-011-9261-7
[35] DOI: 10.1016/j.ins.2003.10.006 · Zbl 1101.68849 · doi:10.1016/j.ins.2003.10.006
[36] DOI: 10.1142/S0218488504003211 · Zbl 1076.91508 · doi:10.1142/S0218488504003211
[37] DOI: 10.1016/j.ins.2011.01.028 · Zbl 1219.03064 · doi:10.1016/j.ins.2011.01.028
[38] DOI: 10.1002/int.20474 · Zbl 1211.94062 · doi:10.1002/int.20474
[39] DOI: 10.1016/j.knosys.2013.05.011 · doi:10.1016/j.knosys.2013.05.011
[40] DOI: 10.1080/09544829708907962 · doi:10.1080/09544829708907962
[41] DOI: 10.1016/j.ejor.2013.05.005 · Zbl 1317.91031 · doi:10.1016/j.ejor.2013.05.005
[42] DOI: 10.1016/j.ejor.2004.09.017 · Zbl 1091.90525 · doi:10.1016/j.ejor.2004.09.017
[43] Yu D.J., Journal of Computational Information Systems 7 (12) pp 4506– (2011)
[44] DOI: 10.1142/S0217595915500488 · doi:10.1142/S0217595915500488
[45] DOI: 10.1016/0020-0255(75)90036-5 · Zbl 0397.68071 · doi:10.1016/0020-0255(75)90036-5
[46] DOI: 10.1016/0020-0255(75)90046-8 · Zbl 0404.68074 · doi:10.1016/0020-0255(75)90046-8
[47] DOI: 10.1016/0020-0255(75)90017-1 · Zbl 0404.68075 · doi:10.1016/0020-0255(75)90017-1
[48] DOI: 10.1016/j.knosys.2014.02.006 · doi:10.1016/j.knosys.2014.02.006
[49] DOI: 10.1016/j.ins.2012.01.048 · Zbl 1250.91035 · doi:10.1016/j.ins.2012.01.048
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.