基于犹豫直觉模糊语言集均值-标准差偏好距离的多属性决策研究
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摘要
在犹豫直觉模糊语言集和语言尺度函数的基础上定义了均值-标准差偏好的Hamming距离,并提出了基于犹豫直觉模糊语言集距离TOPSIS和TODIM的多属性决策方法,进一步利用这两种方法对实例问题建筑商的招标方案进行排序,并讨论了偏好参数对排序结果的灵敏度分析。为验证上述方法的有效性,与已有方法对同一实例的排序结果进行了比较分析。
In many multi-criteria decision making(MCDM)problems,due to the complexity and fuzziness of the decision making environment,many attributes should be assessed in a quantitative form.In this case,decision makers can't just use single-value linguistic term to express their preferences because they are hesitant with decision information,they often provide the hesitant intuitionistic fuzzy linguistic term set to depict the decision information.As far as we know,existing studies often used the subscript of linguistic terms directly in the process of operations,which can't consider the semantic environment.This may cause information distortion,but the linguistic scale function can solve this problem.Therefore,the Hamming distance of mean-standard deviation with preference between hesitant intuitionistic fuzzy linguistic term set based on linguistic scale function is defined,the related properties are also proved.Then the multiple attribute decision making method of TOPSIS and TODIM is proposed.These two methods can solve the ranking of alternatives effectively in multiple attribute decision making problems.Furthermore,in order to illustrate the feasibility and effectiveness,the same numerical example concerning construction company bidding schemes are sorted by using these two methods.Finally,the sensitivity analysis of the preference parameters on the ranking result and comparision analysis with other method are also discussed.
In many multi-criteria decision making(MCDM)problems,due to the complexity and fuzziness of the decision making environment,many attributes should be assessed in a quantitative form.In this case,decision makers can't just use single-value linguistic term to express their preferences because they are hesitant with decision information,they often provide the hesitant intuitionistic fuzzy linguistic term set to depict the decision information.As far as we know,existing studies often used the subscript of linguistic terms directly in the process of operations,which can't consider the semantic environment.This may cause information distortion,but the linguistic scale function can solve this problem.Therefore,the Hamming distance of mean-standard deviation with preference between hesitant intuitionistic fuzzy linguistic term set based on linguistic scale function is defined,the related properties are also proved.Then the multiple attribute decision making method of TOPSIS and TODIM is proposed.These two methods can solve the ranking of alternatives effectively in multiple attribute decision making problems.Furthermore,in order to illustrate the feasibility and effectiveness,the same numerical example concerning construction company bidding schemes are sorted by using these two methods.Finally,the sensitivity analysis of the preference parameters on the ranking result and comparision analysis with other method are also discussed.
引文
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[2]Atanassov K T.Intuitionistic fuzzy sets[J].Fuzzy Sets&Systems,1986,20(1):87-96.
[3]梁昌勇,张恩桥,戚筱雯,等.一种评价信息不完全的混合型多属性群决策方法[J].中国管理科学,2009,17(4):126-132.
[4]乐琦.直觉模糊环境下考虑匹配意愿的双边匹配决策[J].中国管理科学,2017,25(6):161-168.
[5]Zadeh L A.The concept of a linguistic variable and its application to approximate reasoning—I[J].Information Sciences,1975,8(3):199-249.
[6]Zadeh L A.The concept of a linguistic variable and its application to approximate reasoning—II[J].Information Sciences,1975,8(4):301-357.
[7]Zadeh L A.The concept of a linguistic variable and its application to approximate reasoning-III[J].Information Sciences,1975,9(1):43-80.
[8]Herrera F,Herrera-Viedma E,Verdegay J L.A model of consensus in group decision making under linguistic assessments[J].Fuzzy Sets&Systems,1996,78(1):73-87.
[9]Herrera F,Herrera-Viedma E,Verdegay J L.Direct approach processes in group decision making using linguistic OWA operators[J].Fuzzy Sets and Systems,1996,79(2):175-190.
[10]Xu Zeshui.An approach based on the uncertain LOWG and induced uncertain LOWG operators to group decision making with uncertain multiplicative linguistic preference relations[J].Decision Support Systems,2006,41(2):488-499.
[11]Rodriguez R M, Martinez L,Herrera F.Hesitant fuzzy linguistic term sets for decision making[J].IEEE Transactions on Fuzzy Systems,2012,20(1):109-119.
[12]廖虎昌,缑迅杰,徐泽水.基于犹豫模糊语言集的决策理论与方法综述[J].系统工程理论与实践,2017,37(1):35-48.
[13]Liao Huchang,Xu Zeshui,Zeng Xiaojun,et al.Qualitative decision making with correlation coefficients of hesitant fuzzy linguistic term sets[J].KnowledgeBased Systems,2015,76:127-138.
[14]Beg I,Rashid T.Hesitant intuitionistic fuzzy linguistic term sets[J].Notes on Intuitionistic Fuzzy Set,2014,20(3):53-64.
[15]Xu Zeshui.Deviation measures of linguistic preference relations in group decision making[J].Omega,2005,33(3):249-254.
[16]Liao Huchang,Xu Zeshui,Zeng Xiaojun.Distance and similarity measures for hesitant fuzzy linguistic term sets and their application in multi-criteria decision making[J].Information Sciences,2014,271(3):125-142.
[17]Xu Zeshui.A method based on linguistic aggregation operators for group decision making with linguistic preference relations[J].Information Sciences,2004,166(1-4):19-30.
[18]Zhou Wei,Xu Zeshui,Chen Minghui.Preference relations based on hesitant-intuitionistic fuzzy information and their application in group decision making[J].Computers&Industrial Engineering,2015,87:163-175.
[19]徐泽水.基于语言标度中术语指标的多属性群决策法[J].系统工程学报,2005,20(1):84-88.
[20]Wang Jianqiang,Wu Jiating,Wang Jing,et al.Interval-valued hesitant fuzzy linguistic sets and their applications in multi-criteria decision-making problems[J].Information Sciences,2014,288:55-72.
[21]Kahneman D,Tversky A.Prospect theory:An analysis of decision under risk[J].Econometrica,1979,47(2):263-291.
[22]Xu Zeshui.Intuitionistic fuzzy aggregation operators[J].IEEE Transactions on Fuzzy Systems,2007,15(6):1179-1187.
[23]Faizi S,Rashid T,Zafar S.An outranking method for multi-criteria group decision making using hesitant intuitionistic fuzzy linguistic term sets[J].Journal of Intelligent&Fuzzy Systems,2017,32(3):2153-2164.
[24]梁昌勇,戚筱雯,丁勇,等.一种基于TOPSIS的混合型多属性群决策方法[J].中国管理科学,2012,20(4):109-117.
[25]Gomes L,Lima M.TODIM:Basics and application to multicriteria ranking of projects with environmental impacts[J].Foundations of Computing and Decision Sciences,1992,16(4):113-127.
[26]王坚强,李新娥.基于多值中智集的TODIM方法[J].控制与决策,2015,30(6):1139-1142.
[27]Roy B.The outranking approach and the foundations of Electre methods[J].Theory and Decision,1991,31(1):49-73.
[28]Greco S,Matarazzo B,Slowinski R.Rough sets theory for multicriteria decision analysis[J].European Journal of Operational Research,2001,129(1):1-47.
[2]Atanassov K T.Intuitionistic fuzzy sets[J].Fuzzy Sets&Systems,1986,20(1):87-96.
[3]梁昌勇,张恩桥,戚筱雯,等.一种评价信息不完全的混合型多属性群决策方法[J].中国管理科学,2009,17(4):126-132.
[4]乐琦.直觉模糊环境下考虑匹配意愿的双边匹配决策[J].中国管理科学,2017,25(6):161-168.
[5]Zadeh L A.The concept of a linguistic variable and its application to approximate reasoning—I[J].Information Sciences,1975,8(3):199-249.
[6]Zadeh L A.The concept of a linguistic variable and its application to approximate reasoning—II[J].Information Sciences,1975,8(4):301-357.
[7]Zadeh L A.The concept of a linguistic variable and its application to approximate reasoning-III[J].Information Sciences,1975,9(1):43-80.
[8]Herrera F,Herrera-Viedma E,Verdegay J L.A model of consensus in group decision making under linguistic assessments[J].Fuzzy Sets&Systems,1996,78(1):73-87.
[9]Herrera F,Herrera-Viedma E,Verdegay J L.Direct approach processes in group decision making using linguistic OWA operators[J].Fuzzy Sets and Systems,1996,79(2):175-190.
[10]Xu Zeshui.An approach based on the uncertain LOWG and induced uncertain LOWG operators to group decision making with uncertain multiplicative linguistic preference relations[J].Decision Support Systems,2006,41(2):488-499.
[11]Rodriguez R M, Martinez L,Herrera F.Hesitant fuzzy linguistic term sets for decision making[J].IEEE Transactions on Fuzzy Systems,2012,20(1):109-119.
[12]廖虎昌,缑迅杰,徐泽水.基于犹豫模糊语言集的决策理论与方法综述[J].系统工程理论与实践,2017,37(1):35-48.
[13]Liao Huchang,Xu Zeshui,Zeng Xiaojun,et al.Qualitative decision making with correlation coefficients of hesitant fuzzy linguistic term sets[J].KnowledgeBased Systems,2015,76:127-138.
[14]Beg I,Rashid T.Hesitant intuitionistic fuzzy linguistic term sets[J].Notes on Intuitionistic Fuzzy Set,2014,20(3):53-64.
[15]Xu Zeshui.Deviation measures of linguistic preference relations in group decision making[J].Omega,2005,33(3):249-254.
[16]Liao Huchang,Xu Zeshui,Zeng Xiaojun.Distance and similarity measures for hesitant fuzzy linguistic term sets and their application in multi-criteria decision making[J].Information Sciences,2014,271(3):125-142.
[17]Xu Zeshui.A method based on linguistic aggregation operators for group decision making with linguistic preference relations[J].Information Sciences,2004,166(1-4):19-30.
[18]Zhou Wei,Xu Zeshui,Chen Minghui.Preference relations based on hesitant-intuitionistic fuzzy information and their application in group decision making[J].Computers&Industrial Engineering,2015,87:163-175.
[19]徐泽水.基于语言标度中术语指标的多属性群决策法[J].系统工程学报,2005,20(1):84-88.
[20]Wang Jianqiang,Wu Jiating,Wang Jing,et al.Interval-valued hesitant fuzzy linguistic sets and their applications in multi-criteria decision-making problems[J].Information Sciences,2014,288:55-72.
[21]Kahneman D,Tversky A.Prospect theory:An analysis of decision under risk[J].Econometrica,1979,47(2):263-291.
[22]Xu Zeshui.Intuitionistic fuzzy aggregation operators[J].IEEE Transactions on Fuzzy Systems,2007,15(6):1179-1187.
[23]Faizi S,Rashid T,Zafar S.An outranking method for multi-criteria group decision making using hesitant intuitionistic fuzzy linguistic term sets[J].Journal of Intelligent&Fuzzy Systems,2017,32(3):2153-2164.
[24]梁昌勇,戚筱雯,丁勇,等.一种基于TOPSIS的混合型多属性群决策方法[J].中国管理科学,2012,20(4):109-117.
[25]Gomes L,Lima M.TODIM:Basics and application to multicriteria ranking of projects with environmental impacts[J].Foundations of Computing and Decision Sciences,1992,16(4):113-127.
[26]王坚强,李新娥.基于多值中智集的TODIM方法[J].控制与决策,2015,30(6):1139-1142.
[27]Roy B.The outranking approach and the foundations of Electre methods[J].Theory and Decision,1991,31(1):49-73.
[28]Greco S,Matarazzo B,Slowinski R.Rough sets theory for multicriteria decision analysis[J].European Journal of Operational Research,2001,129(1):1-47.