区间数相似度计算模型及其应用研究
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摘要
在工程与管理评价决策中用区间数刻画事物属性特征大小是一种符合认知模糊性和统计学原理的有效方法。用区间数相似度刻画不同区间数的相似性,在不确定环境下决策过程中具有十分重要的作用。事物属性在取值区间内所服从的分布,不仅能呈现取值的不确定性,而且可刻画评价者或评价群体的偏好和风险态度。文中定义区间数相似度为两独立随机变量取值于两个区间交集的概率,运用概率论的方法,构建了任意分布条件下区间数相似度计算模型,推广了以往学者的研究成果。然后,为了简化而又最大可能地保留评价与决策的信息,构建了三角型分布条件下区间数相似度计算模型,并将其与多属性决策TOPSIS方法相结合,构建了基于区间数相似度的多属性评价与决策方法,通过被决策单元与正、负理想解的每个属性的取值区间数相似度,建立综合评价矩阵,很好地实现了被决策单元的优劣排序。通过实例计算,充分验证了模型的可计算性,并呈现了三角型分布下区间数相似度计算模型刻画评价者或评价群体的偏好和风险态度的优良性。显然,该理论方法将在工程与管理评价决策中具有较好的应用价值。
It is an effective method to describe the feature size of object attributes by interval numbers in engineering and management evaluation decision-making,which conforms to cognitive fuzziness and statistical principles.The similarity of different interval numbers can be described by the similarity degree of interval numbers,which can show the degree of concentration of different evaluators( or evaluation groups) on the evaluation of the attributes of things.Based on the distribution of the object attribute in the range of values can not only show the uncertainty of the value,but also describe the characteristics of the preference and the risk attitude of the evaluator or the evaluation group.The similarity degree of interval numbers was first defined as the probability of two corresponding independent random variables valued in two intervals.Then,with the method of probability theory,the similarity degree calculation model of interval numbers under arbitrary distribution was constructed,which extended the research results of previous scholars.And in order to simplify and maximize the information of people's evaluation and decision,the similarity degree calculation model of interval numbers was constructed under the condition of triangulation distribution,and a multi-attribute evaluation and decision method based on the similarity of interval numbers was constructed. A comprehensive evaluation matrix was set up by the similarity degree of interval numbers of each attribute of the decision unit and the positive and negative ideal solutions,and the good and bad order of the decision unit was realized.The computability of the model was fully verified by the example calculation,and the similarity calculation model of the interval number in the triangular distribution was presented to describe the preference and the good quality of the risk attitude of the evaluator or the evaluation group. Obviously,the theory and method will have very good application value in engineering and management evaluation and decision making.
It is an effective method to describe the feature size of object attributes by interval numbers in engineering and management evaluation decision-making,which conforms to cognitive fuzziness and statistical principles.The similarity of different interval numbers can be described by the similarity degree of interval numbers,which can show the degree of concentration of different evaluators( or evaluation groups) on the evaluation of the attributes of things.Based on the distribution of the object attribute in the range of values can not only show the uncertainty of the value,but also describe the characteristics of the preference and the risk attitude of the evaluator or the evaluation group.The similarity degree of interval numbers was first defined as the probability of two corresponding independent random variables valued in two intervals.Then,with the method of probability theory,the similarity degree calculation model of interval numbers under arbitrary distribution was constructed,which extended the research results of previous scholars.And in order to simplify and maximize the information of people's evaluation and decision,the similarity degree calculation model of interval numbers was constructed under the condition of triangulation distribution,and a multi-attribute evaluation and decision method based on the similarity of interval numbers was constructed. A comprehensive evaluation matrix was set up by the similarity degree of interval numbers of each attribute of the decision unit and the positive and negative ideal solutions,and the good and bad order of the decision unit was realized.The computability of the model was fully verified by the example calculation,and the similarity calculation model of the interval number in the triangular distribution was presented to describe the preference and the good quality of the risk attitude of the evaluator or the evaluation group. Obviously,the theory and method will have very good application value in engineering and management evaluation and decision making.
引文
[1]胡启洲,张卫华.区间数理论的研究及其应用[M].北京:科学出版社,2010:15-17.
[2]许瑞丽,徐泽水.区间数相似度研究[J].数学的实践与认识,2007,37(24):1-8.
[3]CHUTIA R.Fuzzy risk analysis using similarity measure of interval-valued fuzzy numbers and its application in poultry farming[J].Applied Intelligence,2018,48(11):3928-3949.
[4]韩菁,叶顺心,柴建,等.基于后悔理论的混合型多属性案例决策方法[J].中国管理科学,2016,24(12):108-116.
[5]陆广地,吴陈.基于联系数伴随函数的区间数多属性决策[J].模糊系统与数学,2018,32(1):182-190.
[6]尤天慧,高美丽.一种考虑决策者风险偏好的区间数多属性决策方法[J].运筹与管理,2012,21(1):70-74.
[7]谢海.基于改进的相对优势度的区间数排序[J].科学技术与工程,2008,22(8):5983-5986.
[8]刘芬,郭躬德.基于区间相似度的模糊时间序列预测算法[J].计算机应用,2013,33(11):3052-3056.
[9]任凯.一种基于案例属性特征的区间相似度改进算法研究[J].控制与决策,2010,25(2):307-310.
[10]詹棠森,林卫中.基于数据最优分区间相似度算法及应用[J].数学的实践与认识,2009,39(20):31-34.
[11]冯秀珍,武高峰.基于区间相似度的动态服务协商模型[J].计算机工程,2011,37(5):267-269.
[12]程砚秋.基于区间相似度和序列比对的群组G1评价方法[J].中国管理科学,2015(增刊1):204-210.
[13]张萌,李国喜.区间条件下基于理想决策法与灰关联分析的供应商选择方法(英文)[J].中南大学学报(英文版),2018,25(5):1116-1128.
[14]魏方圆,黄德才.基于区间数的多维不确定性数据UID-DBSCAN聚类算法[J].计算机科学,2017,44(11A):442-447.
[15]黄智力.区间数型与三角模糊数型不确定多指标决策研究[D].厦门:厦门大学,2016.
[16]黄泽衢.基于模糊理论的应急采购决策研究[J].物流工程与管理,2016,38(5):66-68.
[17]兰继斌,胡明明,叶新苗.基于相似度的区间数排序[J].计算机工程与设计,2011,32(4):1419-1421.
[18]黄衍,王应明,杨隆浩,等.基于SBM区间模型的决策单元相似度[J].控制与决策,2017,32(11):2090-2098.
[19]HESAMIAN G. Measuring similarity and ordering based on interval type-2 fuzzy numbers[J]. IEEE Transactions on Fuzzy Systems,2017,25(4):788-798.
[20]CHEN S J,WANG Z Y,LI W R.Calculating the degree of similarity between interval-valued fuzzy numbers based on map distance[J].Lecture Notes in Engineering&Computer Science,2013,2202(1):7-12.
[21]李秉焱,王进朵,朱琳.基于相似度的区间数群决策方法[J].南昌工程学院学报,2013,32(4):5-8.
[22]LIU G F,GUO L,BAO Y.Multi-attribute decision making based on the similarity degree of ternary interval numbers[J].Advanced Materials Research,2014,926-930:3092-3095.
[23]姜艳萍,樊治平,袁娜.基于相似度计算的森林火灾应急响应方案选择方法[J].系统工程,2010(11):104-109.
[24]WANG H. A method of feature selection for continuous features base on similarity degrees of interval numbers[C]//International Conference on Information and Network Security.IET,2014:20-20.
[25]XIAO Y I,HAN J,ZHANG H,et al.Asynchronous track-to-track association algorithm based on similarity degree of interval-real sequence[J].Acta Aeronautica Et Astronautica Sinica,2015,36(4):1212-1220.
[26]孟志华.基于区间数相似度的企业运营绩效评价指标体系构建[J].统计与决策,2017(20):177-180.
[27]樊治平,宫贤斌,张全.区间数多属性决策中决策矩阵的规范化方法[J].东北大学学报(自然科学版),1999,20(3):326-329.
[2]许瑞丽,徐泽水.区间数相似度研究[J].数学的实践与认识,2007,37(24):1-8.
[3]CHUTIA R.Fuzzy risk analysis using similarity measure of interval-valued fuzzy numbers and its application in poultry farming[J].Applied Intelligence,2018,48(11):3928-3949.
[4]韩菁,叶顺心,柴建,等.基于后悔理论的混合型多属性案例决策方法[J].中国管理科学,2016,24(12):108-116.
[5]陆广地,吴陈.基于联系数伴随函数的区间数多属性决策[J].模糊系统与数学,2018,32(1):182-190.
[6]尤天慧,高美丽.一种考虑决策者风险偏好的区间数多属性决策方法[J].运筹与管理,2012,21(1):70-74.
[7]谢海.基于改进的相对优势度的区间数排序[J].科学技术与工程,2008,22(8):5983-5986.
[8]刘芬,郭躬德.基于区间相似度的模糊时间序列预测算法[J].计算机应用,2013,33(11):3052-3056.
[9]任凯.一种基于案例属性特征的区间相似度改进算法研究[J].控制与决策,2010,25(2):307-310.
[10]詹棠森,林卫中.基于数据最优分区间相似度算法及应用[J].数学的实践与认识,2009,39(20):31-34.
[11]冯秀珍,武高峰.基于区间相似度的动态服务协商模型[J].计算机工程,2011,37(5):267-269.
[12]程砚秋.基于区间相似度和序列比对的群组G1评价方法[J].中国管理科学,2015(增刊1):204-210.
[13]张萌,李国喜.区间条件下基于理想决策法与灰关联分析的供应商选择方法(英文)[J].中南大学学报(英文版),2018,25(5):1116-1128.
[14]魏方圆,黄德才.基于区间数的多维不确定性数据UID-DBSCAN聚类算法[J].计算机科学,2017,44(11A):442-447.
[15]黄智力.区间数型与三角模糊数型不确定多指标决策研究[D].厦门:厦门大学,2016.
[16]黄泽衢.基于模糊理论的应急采购决策研究[J].物流工程与管理,2016,38(5):66-68.
[17]兰继斌,胡明明,叶新苗.基于相似度的区间数排序[J].计算机工程与设计,2011,32(4):1419-1421.
[18]黄衍,王应明,杨隆浩,等.基于SBM区间模型的决策单元相似度[J].控制与决策,2017,32(11):2090-2098.
[19]HESAMIAN G. Measuring similarity and ordering based on interval type-2 fuzzy numbers[J]. IEEE Transactions on Fuzzy Systems,2017,25(4):788-798.
[20]CHEN S J,WANG Z Y,LI W R.Calculating the degree of similarity between interval-valued fuzzy numbers based on map distance[J].Lecture Notes in Engineering&Computer Science,2013,2202(1):7-12.
[21]李秉焱,王进朵,朱琳.基于相似度的区间数群决策方法[J].南昌工程学院学报,2013,32(4):5-8.
[22]LIU G F,GUO L,BAO Y.Multi-attribute decision making based on the similarity degree of ternary interval numbers[J].Advanced Materials Research,2014,926-930:3092-3095.
[23]姜艳萍,樊治平,袁娜.基于相似度计算的森林火灾应急响应方案选择方法[J].系统工程,2010(11):104-109.
[24]WANG H. A method of feature selection for continuous features base on similarity degrees of interval numbers[C]//International Conference on Information and Network Security.IET,2014:20-20.
[25]XIAO Y I,HAN J,ZHANG H,et al.Asynchronous track-to-track association algorithm based on similarity degree of interval-real sequence[J].Acta Aeronautica Et Astronautica Sinica,2015,36(4):1212-1220.
[26]孟志华.基于区间数相似度的企业运营绩效评价指标体系构建[J].统计与决策,2017(20):177-180.
[27]樊治平,宫贤斌,张全.区间数多属性决策中决策矩阵的规范化方法[J].东北大学学报(自然科学版),1999,20(3):326-329.