单值Neutrosophic sets环境下基于参照系数的VIKOR方法
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摘要
模糊集的提出极大拓宽了多属性决策理论,但无法处理不一致和不连续信息,单值中智集(single-valued neutrosophic sets)的提出弥补了这一不足。本文把单值中智集的三个参数投影到坐标轴上形成三维空间,并把VIKOR方法拓展到该环境下。为了使得VIKOR方法同时考虑正理想解和负理想解对方案的影响,本文提出参照系数的概念并将其引入到原始VIKOR方法中,并通过参照系数的变动探究不同参照标准对排序及最佳妥协解的影响。通过对比分析验证方法的有效性和可行性。对比结果表明,不同的参照标准下,得到的排序及最佳妥协解不同。最后,把所提方法用到实际问题中。
The proposed single-valued neutrosophic sets make up for the shortcomings of fuzzy sets that cannot handle inconsistent and discontinuous information.The study regards three parameters of singlevalued neutrosophic sets as three coordinates to generate a 3 Ddimension,and extends VIKOR method to single-valued neutrosophic sets environment.The ranking of original VIKOR method is based on the closeness between alternatives and the positive ideal solution(PIS).Namely the optimal compromise solution is the closest to PIS.However,in the 3 Dspace consists of single-valued neutrosophic sets,the closest distance between the alternative and PIS does not mean that it is the farthest from the negative ideal solution(NIS).That is,the ranking and the optimal compromise solution are different when take the closeness between alternatives and PIS as baseline compared with the closeness between alternatives and NIS.Different preference of decision makers for reference standard lead to different results which cause confusion in the decision making.The existing research does not propose some advices to solve the problem.For this reason,the concept of reference coefficient(RC)is proposed and the closeness between alternatives and NIS is introduced into original VIKOR method and the influence of different RC is explored on the ranking and the optimal compromise solution.In order to verify the effectiveness of the improved method,the result of the paper are compared with those of the existing literature.The result shows that the changes of RC have an impact on the ranking and the optimal compromise solution.It is more reasonable for decision makers to consider the results of different RC comprehensively.VIKOR method based on the reference coefficient amends the use of original VIKOR method under the imprecision environment which is an extension of VIKOR method.The research result shows that it is a reasonable ranking method.
The proposed single-valued neutrosophic sets make up for the shortcomings of fuzzy sets that cannot handle inconsistent and discontinuous information.The study regards three parameters of singlevalued neutrosophic sets as three coordinates to generate a 3 Ddimension,and extends VIKOR method to single-valued neutrosophic sets environment.The ranking of original VIKOR method is based on the closeness between alternatives and the positive ideal solution(PIS).Namely the optimal compromise solution is the closest to PIS.However,in the 3 Dspace consists of single-valued neutrosophic sets,the closest distance between the alternative and PIS does not mean that it is the farthest from the negative ideal solution(NIS).That is,the ranking and the optimal compromise solution are different when take the closeness between alternatives and PIS as baseline compared with the closeness between alternatives and NIS.Different preference of decision makers for reference standard lead to different results which cause confusion in the decision making.The existing research does not propose some advices to solve the problem.For this reason,the concept of reference coefficient(RC)is proposed and the closeness between alternatives and NIS is introduced into original VIKOR method and the influence of different RC is explored on the ranking and the optimal compromise solution.In order to verify the effectiveness of the improved method,the result of the paper are compared with those of the existing literature.The result shows that the changes of RC have an impact on the ranking and the optimal compromise solution.It is more reasonable for decision makers to consider the results of different RC comprehensively.VIKOR method based on the reference coefficient amends the use of original VIKOR method under the imprecision environment which is an extension of VIKOR method.The research result shows that it is a reasonable ranking method.
引文
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[13]赵树平,梁昌勇,罗大伟.基于VIKOR和诱导广义直觉梯形模糊Choquet积分算子的多属性群决策方法[J].中国管理科学,2016,(6):132-142.
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[15]谭春桥,贾媛.基于证据理论和前景理论的犹豫-直觉模糊语言多准则决策方法[J].控制与决策,2017,32(2):333-339.
[16]江文奇.三角模糊数型多准则群决策的VIKOR扩展方法[J].控制与决策,2015,(6):1059-1064.
[17]Zhang Nian,Wei Guiwu.Extension of VIKOR method for decision making problem based on hesitant fuzzy set[J].Applied Mathematical Modelling,2013,37(7):4938-4947.
[18]Kim Y,Chung E S.Fuzzy VIKOR approach for assessing the vulnerability of the water supply to climate change and variability in South Korea[J].Applied Mathematical Modelling,2013,37(22):9419-9430.
[19]李庆胜,刘思峰.基于灰色关联的灰色犹豫模糊VIKOR方法[J].数学的实践与认识,2015,(18):119-126.
[20]索玮岚.基于扩展VIKOR的不确定语言多属性群决策方法[J].控制与决策,2013,(9):1431-1435.
[21]刘凯宁,樊治平,李永海.考虑多因素关联情形的企业发展战略选择的SDV方法[J].管理学报,2014,11(12):1766-1774.
[22]Smarandache F.A unifying field in logics:Neutrsophic logic.Neutrosophy,neutrosophic set,neutrosophic probability(fourth edition).[J].Journal of Molecular Biology,2003,332(2):489-503.
[23]Peng Juanjuan,Wang Jianqiang,Zhang Hongyu,et al.An outranking approach for multi-criteria decisionmaking problems with simplified neutrosophic sets[J].Applied Soft Computing,2014,25(C):336-346.
[24]Ye Jun.Improved cosine similarity measures of simplified neutrosophic sets for medical diagnoses[J].Artificial Intelligence in Medicine,2014,63(3):171-179.
[25]Liu Peide,Wang Yumei.Multiple attribute decisionmaking method based on single-valued neutrosophic normalized weighted Bonferroni mean[J].Neural Computing&Applications,2014,25(7-8):2001-2010.
[26]Ye Jun,Fu Jing.Multi-period medical diagnosis method using a single valued neutrosophic similarity measure based on tangent function[J].Computer Methods&Programs in Biomedicine,2016,123:142-149.
[27]Biswas P,Pramanik S,Giri B C.TOPSIS method for multi-attribute group decision-making under single-valued neutrosophic environment[J].Neural Computing&Applications,2016,27(3):727-737.
[28]Hu Junhua,Pan Li,Chen Xiaohong.An interval neutrosophic projection-based VIKOR method for selecting doctors[J].Cognitive Computation,2017,9(6):801-816.
[29]Wang Haibin,Smarandache F,Sunderraman R.Single valued neutrosophic sets[C]//Proceedings of the 8th Joint Conference on Information Science,Salt Lake City,USA,July 21-26,2005.
[30]Ye Jun.Vector similarity measures of simplified neutrosophic sets and their application in multicriteria decision making[J].International Journal of Fuzzy Systems,2014,16(2):204-211.
[31]Ye Jun.A multicriteria decision-making method using aggregation operators for simplified neutrosophic sets[J].Journal of Intelligent&Fuzzy Systems,2014,26(5):2459-2466.
[32]Peng Juanjuan,Wang Jianqiang,Zhang Hongyu,et al.An outranking approach for multi-criteria decision-making problems with simplified neutrosophic sets[J].Applied Soft Computing,2014,25(C):336-346.
[33]Peng Juanjuan,Wang Jianqiang,Wang Jing,et al.Simplified neutrosophic sets and their applications in multi-criteria group decision-making problems[J].International Journal of Systems Science,2016,47(2):2342-2358.
[34]Majumdar P,Samanta S K.On similarity and entropy of neutrosophic sets[J].Journal of Intelligent&Fuzzy Systems Applications in Engineering&Technology,2014,26(3):1245-1252.
[35]Zadeh L A.Fuzzy sets[J].Information&Control,1965,8(3):338-353.
[36]Atanassov K T.Intuitionistic fuzzy sets[J].Fuzzy Sets&Systems,1986,20(1):87-96.
[37]Gorzaczany M B.A method of inference in approximate reasoning based on interval-valued fuzzy sets[J].Fuzzy Sets&Systems,1987,21(1):1-17.
[38]Atanassov K,Gargov G.Interval valued intuitionistic fuzzy sets[J].Fuzzy Sets&Systems,1989,31(3):343-349.
[39]Torra V.Hesitant fuzzy sets[J].International Journal of Intelligent Systems,2010,25(6):529-539.
[40]Yang Yingjie,Chiclana F.Consistency of 2Dand 3Ddistances of intuitionistic fuzzy sets[J].Expert Systems with Applications,2012,39(10):8665-8670.
[41]Cao Qingwei,Wu Jian,Liang Changyong.An intuitionsitic fuzzy judgement matrix and TOPSIS integrated multi-criteria decision making method for green supplier selection[J].Journal of Intelligent&Fuzzy Systems,2015,28(1):117-126.
[42]Zhang Nian,Wei Guiwu.Extension of VIKOR method for decision making problem based on hesitant fuzzy set[J].Applied Mathematical Modelling,2013,37(7):4938-4947.
[2]Falcone G,Luca A D,Stillitano T,et al.Assessment of environmental and economic impacts of vine-growing combining life cycle assessment,life cycle costing and multicriterial analysis[J].Sustainability,2016,8(8):793.
[3]Hu Kuanghua,Chen Fuhsiang,Tzeng Gwo hiung.E-valuating the improvement of sustainability of sports industry policy based on MADM[J].Sustainability,2016,8(7)606.
[4]Vucˇijak B,Kurtagic′S M,Silajdzˇic′I.Multicriteria decision making in selecting best solid waste management scenario:A municipal case study from Bosnia and Herzegovina[J].Journal of Cleaner Production,2015,130:166-174.
[5]Chen Tingyu.Remoteness index-based pytha-gorean fuzzy VIKOR methods with a generalized distance measure for multiple criteria decision analysis[J].Information Fusion,2017,41:129-150.
[6]Zhang Junling,Hegde G,Shang Jennifer,et al.Evaluating emergency response solutions for sustainable community development by using fuzzy multi-criteria group decision making approaches:IVDHF-TOPSIS and IVDHF-VIKOR[J].Sustainability,2016,8(4):291.
[7]Ghadikolaei A S,Parkouhi S V.A resilience approach for supplier selection:Using fuzzy analytic network process and grey VIKOR techniques[J].Journal of Cleaner Production,2017,161:431-451.
[8]袁宇,关涛,闫相斌,等.基于混合VIKOR方法的供应商选择决策模型[J].控制与决策,2014,(3):551-560.
[9]方曦,李治东,熊焰,等.基于模糊VIKOR法的企业决策情报评价及应用[J].情报理论与实践,2015,38(3):49-52.
[10]Liao Huchang,Xu Zeshui.Subtraction and division operations over hesitant fuzzy sets[J].Journal of Intelligent&Fuzzy Systems,2014,27(1):65-72.
[11]江文奇.基于FVIKOR的三角模糊数型准则决策方法[J].控制与决策,2016,31(7):1330-1334.
[12]Wu Zhibin,Ahmad J,Xu Jiuping.A group decision making framework based on fuzzy VIKOR approach for machine tool selection with linguistic information[J].Applied Soft Computing,2016,42(C):314-324.
[13]赵树平,梁昌勇,罗大伟.基于VIKOR和诱导广义直觉梯形模糊Choquet积分算子的多属性群决策方法[J].中国管理科学,2016,(6):132-142.
[14]江文奇.基于前景理论和VIKOR的风险型模糊多准则决策方法[J].控制与决策,2014,(12):2287-2291.
[15]谭春桥,贾媛.基于证据理论和前景理论的犹豫-直觉模糊语言多准则决策方法[J].控制与决策,2017,32(2):333-339.
[16]江文奇.三角模糊数型多准则群决策的VIKOR扩展方法[J].控制与决策,2015,(6):1059-1064.
[17]Zhang Nian,Wei Guiwu.Extension of VIKOR method for decision making problem based on hesitant fuzzy set[J].Applied Mathematical Modelling,2013,37(7):4938-4947.
[18]Kim Y,Chung E S.Fuzzy VIKOR approach for assessing the vulnerability of the water supply to climate change and variability in South Korea[J].Applied Mathematical Modelling,2013,37(22):9419-9430.
[19]李庆胜,刘思峰.基于灰色关联的灰色犹豫模糊VIKOR方法[J].数学的实践与认识,2015,(18):119-126.
[20]索玮岚.基于扩展VIKOR的不确定语言多属性群决策方法[J].控制与决策,2013,(9):1431-1435.
[21]刘凯宁,樊治平,李永海.考虑多因素关联情形的企业发展战略选择的SDV方法[J].管理学报,2014,11(12):1766-1774.
[22]Smarandache F.A unifying field in logics:Neutrsophic logic.Neutrosophy,neutrosophic set,neutrosophic probability(fourth edition).[J].Journal of Molecular Biology,2003,332(2):489-503.
[23]Peng Juanjuan,Wang Jianqiang,Zhang Hongyu,et al.An outranking approach for multi-criteria decisionmaking problems with simplified neutrosophic sets[J].Applied Soft Computing,2014,25(C):336-346.
[24]Ye Jun.Improved cosine similarity measures of simplified neutrosophic sets for medical diagnoses[J].Artificial Intelligence in Medicine,2014,63(3):171-179.
[25]Liu Peide,Wang Yumei.Multiple attribute decisionmaking method based on single-valued neutrosophic normalized weighted Bonferroni mean[J].Neural Computing&Applications,2014,25(7-8):2001-2010.
[26]Ye Jun,Fu Jing.Multi-period medical diagnosis method using a single valued neutrosophic similarity measure based on tangent function[J].Computer Methods&Programs in Biomedicine,2016,123:142-149.
[27]Biswas P,Pramanik S,Giri B C.TOPSIS method for multi-attribute group decision-making under single-valued neutrosophic environment[J].Neural Computing&Applications,2016,27(3):727-737.
[28]Hu Junhua,Pan Li,Chen Xiaohong.An interval neutrosophic projection-based VIKOR method for selecting doctors[J].Cognitive Computation,2017,9(6):801-816.
[29]Wang Haibin,Smarandache F,Sunderraman R.Single valued neutrosophic sets[C]//Proceedings of the 8th Joint Conference on Information Science,Salt Lake City,USA,July 21-26,2005.
[30]Ye Jun.Vector similarity measures of simplified neutrosophic sets and their application in multicriteria decision making[J].International Journal of Fuzzy Systems,2014,16(2):204-211.
[31]Ye Jun.A multicriteria decision-making method using aggregation operators for simplified neutrosophic sets[J].Journal of Intelligent&Fuzzy Systems,2014,26(5):2459-2466.
[32]Peng Juanjuan,Wang Jianqiang,Zhang Hongyu,et al.An outranking approach for multi-criteria decision-making problems with simplified neutrosophic sets[J].Applied Soft Computing,2014,25(C):336-346.
[33]Peng Juanjuan,Wang Jianqiang,Wang Jing,et al.Simplified neutrosophic sets and their applications in multi-criteria group decision-making problems[J].International Journal of Systems Science,2016,47(2):2342-2358.
[34]Majumdar P,Samanta S K.On similarity and entropy of neutrosophic sets[J].Journal of Intelligent&Fuzzy Systems Applications in Engineering&Technology,2014,26(3):1245-1252.
[35]Zadeh L A.Fuzzy sets[J].Information&Control,1965,8(3):338-353.
[36]Atanassov K T.Intuitionistic fuzzy sets[J].Fuzzy Sets&Systems,1986,20(1):87-96.
[37]Gorzaczany M B.A method of inference in approximate reasoning based on interval-valued fuzzy sets[J].Fuzzy Sets&Systems,1987,21(1):1-17.
[38]Atanassov K,Gargov G.Interval valued intuitionistic fuzzy sets[J].Fuzzy Sets&Systems,1989,31(3):343-349.
[39]Torra V.Hesitant fuzzy sets[J].International Journal of Intelligent Systems,2010,25(6):529-539.
[40]Yang Yingjie,Chiclana F.Consistency of 2Dand 3Ddistances of intuitionistic fuzzy sets[J].Expert Systems with Applications,2012,39(10):8665-8670.
[41]Cao Qingwei,Wu Jian,Liang Changyong.An intuitionsitic fuzzy judgement matrix and TOPSIS integrated multi-criteria decision making method for green supplier selection[J].Journal of Intelligent&Fuzzy Systems,2015,28(1):117-126.
[42]Zhang Nian,Wei Guiwu.Extension of VIKOR method for decision making problem based on hesitant fuzzy set[J].Applied Mathematical Modelling,2013,37(7):4938-4947.