Uncertain linguistic generalized weighted Heronian mean operator and its application in decision making

doi:10.3969/j.issn.1000-1565.2023.02.001

Abstract

Abstract: In practical multiple-attribute decision making problems, sometimes there are correlations between attributes, and attribute values are given in the form of uncertain language. In order to solve the multiple-attribute decision making problems with correlations between attributes in uncertain linguistic environment, the uncertain linguistic generalized weighted Heronian mean(ULGWHM)operator is given, and its properties are studied, including idempotency, boundedness, monotonicity, permutation and limit properties. Then a multiple-attribute decision making method based on this operator is presented. Finally, the feasibility of multiple-attribute decision making method based on ULGWHM operator is illustrated by an example.

Key words: multiple-attribute decision making, attribute association, Heronian mean, uncertain linguistic generalized weighted Heronian mean

CLC Number:

C934

HU Ximei, YANG Shuxia, TIAN Dazeng. Uncertain linguistic generalized weighted Heronian mean operator and its application in decision making[J]. Journal of Hebei University(Natural Science Edition), 2023, 43(2): 113-120.

References

[1] 郭子雪,张运通,田雨,等.基于直觉模糊多属性决策的逆向物流供应商选择[J].河北大学学报(自然科学版), 2021, 41(6): 638-644. DOI:10.3969/j.issn.1000-1565.2021.06.002.
[2] 章玲,周德群.基于关联的多属性决策分析理论研究综述[J].管理评论, 2008, 20(5): 51-57. DOI:10.14120/j.cnki.cn11-5057/f.2008.05.010.
[3] 刘卫锋,常娟,杜迎雪.(语言)Heronian平均算子及其决策应用[J].中国管理科学, 2017, 25(4): 174-183. DOI:10.16381/j.cnki.issn1003-207x.2017.04.021.
[4] YU D J. Intuitionistic fuzzy geometric Heronian mean aggregation operators[J]. Appl Soft Comput, 2013, 13(2): 1235-1246. DOI:10.1016/j.asoc.2012.09.021.
[5] 施明华,肖庆宪.直觉模糊幂Heronian平均算子及其在多属性决策中的应用[J].系统工程理论与实践, 2018, 38(4): 971-982. DOI:10.12011/1000-6788(2018)04-0971-12.
[6] 赵辉,屈微璐,邱玮婷,等.区间直觉不确定语言几何Heronian平均算子及其在多属性群决策中的应用[J].数学的实践与认识, 2018, 48(17): 187-197.
[7] 周晓辉,姚俭,徐磊,等.区间直觉模糊几何Heronian平均算子及其应用[J].系统工程, 2016, 34(4): 140-146.
[8] 王娟,金智新.三角犹豫模糊Heronian平均算子及其在多属性决策中的应用[J].运筹与管理, 2019, 28(11): 68-76. DOI:10.12005/orms.2019.0250.
[9] HU X M, YANG S X, ZHU Y R. Multiple attribute decision-making based on three-parameter generalized weighted heronian mean[J]. Mathematics, 2021, 9(12): 1363. DOI:10.3390/math9121363.
[10] HU X M, YANG S X, ZHU Y R. Multiple attribute decision making based on linguistic generalized weighted heronian mean[J]. Symmetry, 2021, 13(7): 1191. DOI:10.3390/sym13071191.
[11] 徐泽水.不确定多属性决策方法及应用[M].北京: 清华大学出版社, 2004.
[12] XU Z S. Uncertain linguistic aggregation operators based approach to multiple attribute group decision making under uncertain linguistic environment[J]. Inf Sci, 2004, 168(1/2/3/4): 171-184. DOI:10.1016/j.ins.2004.02.003.
[13] 姬欢,裴道武.不确定语言Hero平均算子及其在多属性群决策中的应用[J].浙江理工大学学报(自然科学版), 2016, 35(2): 317-321. DOI:10.3969/j.issn.1673-3851.2016.03.027.
[14] LIU X D, ZHU J J, LIU G D, et al. A multiple attribute decision making method based on uncertain linguistic heronian mean[J]. Math Probl Eng, 2013, 2013: 597671. DOI:10.1155/2013/597671.
[15] XU Z S. A method based on linguistic aggregation operators for group decision making with linguistic preference relations[J]. Inf Sci, 2004, 166(1/2/3/4): 19-30. DOI:10.1016/j.ins.2003.10.006.
[16] 徐泽水,达庆利.区间数排序的可能度法及其应用[J].系统工程学报, 2003, 18(1): 67-70. DOI:10.3969/j.issn.1000-5781.2003.01.011.
[17] 徐泽水.模糊互补判断矩阵排序的一种算法[J].系统工程学报, 2001, 16(4): 311-314. DOI:10.3969/j.issn.1000-5781.2001.04.012.
[18] BULLEN P S. Handbook of means and their inequalities[M]. Dordrecht: Springer Netherlands, 2003. DOI:10.1007/978-94-017-0399-4. (