基于中智犹豫模糊灰关联投影的动态多属性决策方法及应用
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摘要
构建了基于灰关联投影的中智犹豫模糊多属性决策模型.针对评价值为中智模糊数且属性和时序权重均未知的动态多属性决策问题,根据中智模糊集的距离测度构建决策矩阵,计算各时段的方案指标数列与理想方案数列对应元素间的距离.构建基于灰关联度总偏差最小的非线性规划模型,确定属性权重,从而求得灰关联投影值.应用指数衰减模型计算时序权重,对方案各时段灰关联投影值进行加权集成,得到综合灰关联投影值,并据此对方案排序择优.应用该模型对四个中国大学评价体系的稳定性进行了分析,证明了模型的有效性.
In this paper, a fuzzy multiple attribute decision making model based on grey relational projection method is constructed. To solve the dynamic MADM problem with neutrosophic numbers and attribute-time series weight unknown, a decision matrix is constructed based on the distance measure of neutrosophic fuzzy sets. The distance between corresponding elements of the scheme to be evaluated and the ideal is calculated. The attribute weights are determined by constructing a nonlinear programming model based on the minimum total deviation of grey correlation degree and the grey relational projection value is obtained.The time series weights are determined by the exponential decay model. The priority of the schemes is preferred according to order of the comprehensive grey relational projection values which are calculated by integrating the grey relational projection values in each period of the scheme. The model proposed in this paper is used to analyze the stability of four Chinese university evaluation systems and its validity is proved.
In this paper, a fuzzy multiple attribute decision making model based on grey relational projection method is constructed. To solve the dynamic MADM problem with neutrosophic numbers and attribute-time series weight unknown, a decision matrix is constructed based on the distance measure of neutrosophic fuzzy sets. The distance between corresponding elements of the scheme to be evaluated and the ideal is calculated. The attribute weights are determined by constructing a nonlinear programming model based on the minimum total deviation of grey correlation degree and the grey relational projection value is obtained.The time series weights are determined by the exponential decay model. The priority of the schemes is preferred according to order of the comprehensive grey relational projection values which are calculated by integrating the grey relational projection values in each period of the scheme. The model proposed in this paper is used to analyze the stability of four Chinese university evaluation systems and its validity is proved.
引文
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[4] Torra V. Hesitant fuzzy sets[J]. International Journal of Intelligent System, 2010, 25(6):529-539.
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[8] Hanafy I M, Salama A A, Mahfouz K M. Correlation coefficients of neutrosophic sets by centroid method[J]. International Journal of Probability&Statistics, 2013, 2(1):9-12.
[9] Majumdar P, Samanta S K. On similarity and entropy of neutrosophic sets[J]. Journal of Intelligent&Fuzzy Systems, 2014, 26(3):1245-1252.
[10] Jun Ye. Multicriteria decision-making method using the correlation coefficient under single-valued neutrosophic environment[J]. International Journal of General Systems, 2013, 42(4):386-394.
[11] Ye J. Single valued neutrosophic cross-entropy for multicriteria decision making problems[J]. Applied Mathematical Modelling, 2014, 38(3):1170-1175.
[12] Ye J. Similarity measures between interval neutrosophic sets and their applications in multicriteria decision-making[J]. Journal of Intelligent&Fuzzy Systems, 2014, 26(1):165-172.
[13] Broumi S, Smarandache F. Several similarity measures of neutrosophic sets[J]. Neutrosophic Sets&Systems, 2013, 1(1).
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[16] Bhowmik M, Pal M. Intuitionistic neutrosophic set[J]. Journal of Computing&Information Science in Engineering, 2014, 4(2):142-152.
[17] Dey P P, Pramanik S, Giri B C. Generalized neutrosophic soft multi-attribute group decision making based on TOPSIS[J]. Critical Review, 2015.
[18] Liu P, Zhang L. The Extended VIKOR Method for Multiple Criteria Decision Making Problem Based on Neutrosophic Hesitant Fuzzy Set[J]. 2015.
[19] Ye J. Some aggregation operators of interval neutrosophic linguistic numbers for multiple attribute decision making[J]. Journal of Intelligent&Fuzzy Systems, 2014:2231-2241.
[20] Broumi S, Ye J, Smarandache F. An extended topsis method for multiple attribute decision making based on interval neutrosophic uncertain linguistic variables[J]. Neutrosophic Sets&Systems, 2015,8.
[21] Biswas P, Pramanik S, Giri B C. GRA Method of Multiple Attribute Decision Making with Single Valued Neutrosophic Hesitant Fuzzy Set Information[M]//New Trends in Neutrosophic Theory and Applications, 2016.
[22] Liu C F, Luo Y S. New aggregation operators of single-valued neutrosophic hesitant fuzzy set and their application in multi-attribute decision making[J]. Pattern Analysis&Applications, 2017(1):1-11.
[23]王玉美.基于区间中智数的信息集成算子研究[D].山东财经大学,2015.
[24]滕飞.基于区间中智不痛定语言变量的信息集成算子研究[D].山东财经大学,2016.
[25]韩莉莉,魏翠萍.基于单值中智集Choquet积分算子的群决策方法[J].运筹学学报,2017(02):110-118.
[26]崔西希,吴成茂.快速空间邻域信息的中智模糊聚类分割算法[J].电视技术,2016(08):1-7.
[27]吴成茂,上官若愚.嵌入隐马尔科夫随机场的中智模糊聚类算法[J].西安电子科技大学学报,2017(06):103-108+121.
[28]杨永伟,张饶蕾,郭静.基于犹豫中智集的多属性决策方法[J].模糊系统与数学,2017(02):114-122.
[29]刘培德,李洪刚,王鹏,刘俊麟.基于区间中智集的ELECTRE方法及其在多属性决策中的应用[J].山东财经大学学报,2016(02):80-87.
[30]刘舂芳,罗跃生.区间中智集的熵与相似度及其应用[J].模糊系统与数学,2016(03):91-96.
[31]刘培德,柳溪,徐隆.基于云模型的区间中智数多属性群决策TOPSIS方法[J].经济与管理评论,2016(03):73-78.
[32]毛军军,姚登宝,王翠翠,等.基于时序模糊软集的群决策方法[J].系统工程理论与实践,2014, 34(1):182-189.
[33]国兆亮.2010-2011年《美国新闻与世界报道》大学排行方法及指标体系[J].华北电力大学学报(社会科学版),2011(1):120-123.
[2] Atanassov K. Intuitionistic fuzzy sets[J]. Fuzzy Sets and Systems, 1986, 20:87-96.
[3] Torra V, Narukawa Y. On hesitant fuzzy sets and decision[C]//In The 18th IEEE InternationalConference on Fuzzy Systems, Jeju Island, Korea, 2009. 1378-1382.
[4] Torra V. Hesitant fuzzy sets[J]. International Journal of Intelligent System, 2010, 25(6):529-539.
[5] Zhu B, Xu Z, Xia M. Dual hesitant fuzzy sets[J]. Journal of Applied Mathematics, 2012,(11):2607-2645.
[6] Smarandache F. A unifying field in logics. neutrosophy:Neutrosophic probability, set and logic[M].Rehoboth:American Press, 1999.
[7] Wang H, Smarandache F, Sunderraman R. Single valued neutrosophic sets[J]. Review of the Air Force Academy, 2010, 10.
[8] Hanafy I M, Salama A A, Mahfouz K M. Correlation coefficients of neutrosophic sets by centroid method[J]. International Journal of Probability&Statistics, 2013, 2(1):9-12.
[9] Majumdar P, Samanta S K. On similarity and entropy of neutrosophic sets[J]. Journal of Intelligent&Fuzzy Systems, 2014, 26(3):1245-1252.
[10] Jun Ye. Multicriteria decision-making method using the correlation coefficient under single-valued neutrosophic environment[J]. International Journal of General Systems, 2013, 42(4):386-394.
[11] Ye J. Single valued neutrosophic cross-entropy for multicriteria decision making problems[J]. Applied Mathematical Modelling, 2014, 38(3):1170-1175.
[12] Ye J. Similarity measures between interval neutrosophic sets and their applications in multicriteria decision-making[J]. Journal of Intelligent&Fuzzy Systems, 2014, 26(1):165-172.
[13] Broumi S, Smarandache F. Several similarity measures of neutrosophic sets[J]. Neutrosophic Sets&Systems, 2013, 1(1).
[14] Wang H. Interval neutrosophic sets and logic:theory and applications in computing[J]. Computer Science, 2005, 65(4):vi,87.
[15] Maji P K. A neutrosophic soft set approach to a decision making problem[J]. Ann Fuzzy Math Inform, 2013(2):313-319.
[16] Bhowmik M, Pal M. Intuitionistic neutrosophic set[J]. Journal of Computing&Information Science in Engineering, 2014, 4(2):142-152.
[17] Dey P P, Pramanik S, Giri B C. Generalized neutrosophic soft multi-attribute group decision making based on TOPSIS[J]. Critical Review, 2015.
[18] Liu P, Zhang L. The Extended VIKOR Method for Multiple Criteria Decision Making Problem Based on Neutrosophic Hesitant Fuzzy Set[J]. 2015.
[19] Ye J. Some aggregation operators of interval neutrosophic linguistic numbers for multiple attribute decision making[J]. Journal of Intelligent&Fuzzy Systems, 2014:2231-2241.
[20] Broumi S, Ye J, Smarandache F. An extended topsis method for multiple attribute decision making based on interval neutrosophic uncertain linguistic variables[J]. Neutrosophic Sets&Systems, 2015,8.
[21] Biswas P, Pramanik S, Giri B C. GRA Method of Multiple Attribute Decision Making with Single Valued Neutrosophic Hesitant Fuzzy Set Information[M]//New Trends in Neutrosophic Theory and Applications, 2016.
[22] Liu C F, Luo Y S. New aggregation operators of single-valued neutrosophic hesitant fuzzy set and their application in multi-attribute decision making[J]. Pattern Analysis&Applications, 2017(1):1-11.
[23]王玉美.基于区间中智数的信息集成算子研究[D].山东财经大学,2015.
[24]滕飞.基于区间中智不痛定语言变量的信息集成算子研究[D].山东财经大学,2016.
[25]韩莉莉,魏翠萍.基于单值中智集Choquet积分算子的群决策方法[J].运筹学学报,2017(02):110-118.
[26]崔西希,吴成茂.快速空间邻域信息的中智模糊聚类分割算法[J].电视技术,2016(08):1-7.
[27]吴成茂,上官若愚.嵌入隐马尔科夫随机场的中智模糊聚类算法[J].西安电子科技大学学报,2017(06):103-108+121.
[28]杨永伟,张饶蕾,郭静.基于犹豫中智集的多属性决策方法[J].模糊系统与数学,2017(02):114-122.
[29]刘培德,李洪刚,王鹏,刘俊麟.基于区间中智集的ELECTRE方法及其在多属性决策中的应用[J].山东财经大学学报,2016(02):80-87.
[30]刘舂芳,罗跃生.区间中智集的熵与相似度及其应用[J].模糊系统与数学,2016(03):91-96.
[31]刘培德,柳溪,徐隆.基于云模型的区间中智数多属性群决策TOPSIS方法[J].经济与管理评论,2016(03):73-78.
[32]毛军军,姚登宝,王翠翠,等.基于时序模糊软集的群决策方法[J].系统工程理论与实践,2014, 34(1):182-189.
[33]国兆亮.2010-2011年《美国新闻与世界报道》大学排行方法及指标体系[J].华北电力大学学报(社会科学版),2011(1):120-123.