一种Vague软集的模糊综合评判模型
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摘要
针对基于模糊矩阵的模糊综合评判多级运算比较繁琐的问题,该文提出和构建了基于Vague软集的模糊综合评判模型。将评语集和因素集统一至Vague软集的论域和参数集中,采用Vague软集相似度量代替模糊综合评判矩阵,使得计算过程由多级计算变换为一级计算,避免了矩阵运算和矩阵维数发生变化带来的问题。计算实例对比表明:该模型能够得到正确的综合评价结果,提出的依据Vague软集相似度量构建的模糊综合评判模型,实现了在避免矩阵运算的同时,保证了综合评价结果的正确性。
According to the problems of complicated multistage operation in that fuzzy comprehensive evaluation based on fuzzy matrix,a fuzzy comprehensive evaluation model based on Vague soft sets is proposed and constructed.Conceptually,the commentary set and the factor set are unified to the universe and the parameter set of Vague soft sets.In the calculation,the fuzzy comprehensive evaluation matrix is replaced by the similarity measure of Vague soft sets.This leads to the process of computing that transforms from multilevel to one level computing,and avoids the problems caused by matrix operation and matrix dimension change.Case comparison shows that the proposed and constructed model is able to obtain the correct comprehensive evaluation results.The proposed fuzzy comprehensive evaluation model based on similarity measure of Vague soft sets,realized in avoiding matrix operation at the same time,ensures the validity of the comprehensive evaluation results.
According to the problems of complicated multistage operation in that fuzzy comprehensive evaluation based on fuzzy matrix,a fuzzy comprehensive evaluation model based on Vague soft sets is proposed and constructed.Conceptually,the commentary set and the factor set are unified to the universe and the parameter set of Vague soft sets.In the calculation,the fuzzy comprehensive evaluation matrix is replaced by the similarity measure of Vague soft sets.This leads to the process of computing that transforms from multilevel to one level computing,and avoids the problems caused by matrix operation and matrix dimension change.Case comparison shows that the proposed and constructed model is able to obtain the correct comprehensive evaluation results.The proposed fuzzy comprehensive evaluation model based on similarity measure of Vague soft sets,realized in avoiding matrix operation at the same time,ensures the validity of the comprehensive evaluation results.
引文
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[7]张彦蕊,黄冬梅.基于AHP和模糊综合评判的生活垃圾处理模式评价[J].数学的实践与认识,2014,44(3):55-61.(ZHANG Yanrui,HUANG Dongmei.Evaluationof MSW disposal pattern based on AHP and fuzzymethods[J].Journal of Mathematics in Practice andTheory,2014,44(3):55-61.)
[8]霍攀,曹丽文,田艳凤.AHP与模糊评判法在垃圾填埋场选址中的应用对比[J].环境工程,2015,33(3):131-135.(HUO Pan,CAO Liwen,TIAN Yanfeng.Applicationand comparison of AHP and fuzzy evaluation method inlandfill siting[J].Environmental Engineering,2015,33(3):131-135.)
[9]GAU W L,BUEHRER D J.Vague sets[J].IEEETransactions on Systems,Man and Cybernetics,1993,23(2):610-614.
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[11]XU W,MA J,WANG S Y,et al.Vague soft sets andtheir properties[J].Computer and Mathematics withApplications,2010,59(2):787-794.
[12]邓维斌,许昌林,樊自甫.基于Vague集相似度量的多准则模糊决策方法[J].系统工程理论与实践,2014,34(4):981-990.(DENG Weibin,XU Changlin,FANZifu.Multi-criteria fuzzy decision making method basedon similarity measures between Vague sets[J].Systems Engineering-Theory &Practice,2014,34(4):981-990.)
[13]黎雯,周廷刚,张伟.GIS空间分析与模糊综合评判在银行ATM网点选址中的应用[J].测绘科学,2008,33(1):229-231.(LI Wen,ZHOU Tinggang,ZHANGWei.The application of spatial analysis of GIS andfuzzy synthetic evaluation in site location of ATMnetwork[J].Science of Surveying and Mapping,2008,33(1):229-231.)
[14]BIGAND A,COLOT O.Fuzzy filter based on interval-valued fuzzy sets for image filtering[J].Fuzzy Sets andSystems,2010,161(1):96-117.
[15]WANG C,QU A J.Entropy,similarity measure anddistance measure of Vague soft sets and their relations[J].Information Sciences,2013,244(7):92-106.
[16]彭立,杨武年,刘汉湖,等.基于RS和GIS的地震移民选址空间决策研究与实现[J].西南大学学报(自然科学版),2011,33(3):96-103.(PENG Li,YANGWunian,LIU Hanhu,et al.Study on spatial decision-making of site selection for earthquake-inducedmigration using remote sensing and GIS technology[J].Journal of Southwest University(Natural ScienceEdition),2011,33(3):96-103.)
[17]何雅琴,李杰.基于AHP的城市突发公共事件交通应急等级判定[J].公路交通科技,2013,30(3):136-140.(HE Yaqin,LI Jie.Grading of traffic emergencyresponse to urban emergency based on AHP[J].Journalof Highway and Transportation Research andDevelopment,2013,30(3):136-140.)
[2]季佳佳,赵冬玲,杨建宇,等.基于多层次模糊综合评判法的土地变更调查数据质量评价研究[J].中国土地科学,2015,29(4):90-96.(JI Jiajia,ZHAO Dongling,YANG Jianyu,et al.Quality assessment of landchanging investigation data based on multi-level basedon fuzzy comprehensive evaluation method[J].ChinaLand Sciences,2015,29(4):90-96.)
[3]黄晶晶,付正飞,罗朝晖,等.武汉市垃圾填埋场选址适宜性区划研究[J].环境工程,2015,33(9):105-108.(HUANG Jingjing,FU Zhengfei,LUO Zhaohui,et al.Study on suitability zoning for the site selection oflangfill in Wuhan city[J].Environmental Engineering,2015,33(9):105-108.)
[4]郭兆夏,梁轶,王景红,等.GIS技术支持下的陕西核桃精细化气候适宜性区划[J].干旱地区农业研究,2015,33(1):194-198.(GUO Zhaoxia,LIANG Yi,WANGJinghong,et al.Climate regionalization for walnut plantin Shanxi province based on GIS[J].AgriculturalResearch in the Arid Areas,2015,33(1):194-198.)
[5]刘志祥,冯凡,王剑波,等.模糊综合评判法在矿山岩体质量分级中的应用[J].武汉理工大学学报,2014,36(1):129-134.(LIU Zhixiang,FENG Fan,WANGJianbo,et al.Application of fuzzy synthesis assessmentmethod on classification of rock mass in mine[J].Journalof Wuhan University of Technology,2014,36(1):129-134.)
[6]潘润秋,刘珺,宋丹妤.基于模糊综合分析法的农用地分等方法[J].农业工程学报,2014,30(18):257-265.(PAN Runqiu,LIU Jun,SONG Danyu.Agriculturalland classification based on fuzzy comprehensiveanalysis[J].Transactions of the Chinese Society ofAgricultural Engineering,2014,30(18):257-265.)
[7]张彦蕊,黄冬梅.基于AHP和模糊综合评判的生活垃圾处理模式评价[J].数学的实践与认识,2014,44(3):55-61.(ZHANG Yanrui,HUANG Dongmei.Evaluationof MSW disposal pattern based on AHP and fuzzymethods[J].Journal of Mathematics in Practice andTheory,2014,44(3):55-61.)
[8]霍攀,曹丽文,田艳凤.AHP与模糊评判法在垃圾填埋场选址中的应用对比[J].环境工程,2015,33(3):131-135.(HUO Pan,CAO Liwen,TIAN Yanfeng.Applicationand comparison of AHP and fuzzy evaluation method inlandfill siting[J].Environmental Engineering,2015,33(3):131-135.)
[9]GAU W L,BUEHRER D J.Vague sets[J].IEEETransactions on Systems,Man and Cybernetics,1993,23(2):610-614.
[10]MOLODTSOVD D.Soft set theory:first results[J].Computer and Mathematics with Applications,1999,37(4-5):19-31.
[11]XU W,MA J,WANG S Y,et al.Vague soft sets andtheir properties[J].Computer and Mathematics withApplications,2010,59(2):787-794.
[12]邓维斌,许昌林,樊自甫.基于Vague集相似度量的多准则模糊决策方法[J].系统工程理论与实践,2014,34(4):981-990.(DENG Weibin,XU Changlin,FANZifu.Multi-criteria fuzzy decision making method basedon similarity measures between Vague sets[J].Systems Engineering-Theory &Practice,2014,34(4):981-990.)
[13]黎雯,周廷刚,张伟.GIS空间分析与模糊综合评判在银行ATM网点选址中的应用[J].测绘科学,2008,33(1):229-231.(LI Wen,ZHOU Tinggang,ZHANGWei.The application of spatial analysis of GIS andfuzzy synthetic evaluation in site location of ATMnetwork[J].Science of Surveying and Mapping,2008,33(1):229-231.)
[14]BIGAND A,COLOT O.Fuzzy filter based on interval-valued fuzzy sets for image filtering[J].Fuzzy Sets andSystems,2010,161(1):96-117.
[15]WANG C,QU A J.Entropy,similarity measure anddistance measure of Vague soft sets and their relations[J].Information Sciences,2013,244(7):92-106.
[16]彭立,杨武年,刘汉湖,等.基于RS和GIS的地震移民选址空间决策研究与实现[J].西南大学学报(自然科学版),2011,33(3):96-103.(PENG Li,YANGWunian,LIU Hanhu,et al.Study on spatial decision-making of site selection for earthquake-inducedmigration using remote sensing and GIS technology[J].Journal of Southwest University(Natural ScienceEdition),2011,33(3):96-103.)
[17]何雅琴,李杰.基于AHP的城市突发公共事件交通应急等级判定[J].公路交通科技,2013,30(3):136-140.(HE Yaqin,LI Jie.Grading of traffic emergencyresponse to urban emergency based on AHP[J].Journalof Highway and Transportation Research andDevelopment,2013,30(3):136-140.)
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