基于IVHFWHM算子的犹豫关联多属性决策方法
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摘要
针对决策属性为区间犹豫模糊数(IVHFN)且属性间相互关联的多属性决策(MADM)问题,提出一种基于区间犹豫模糊加权Heronian平均(IVHFWHM)算子的新型决策方法。同时基于IVHFN运算法则和Heronian平均(HM)算子,提出了区间犹豫模糊Heronian平均(IVHFHM)算子和IVHFWHM算子。研究了IVHFHM算子的置换不变性、幂等性、单调性、有界性和参数对称性等性质。建立基于IVHFWHM算子的多属性决策模型,通过MADM数值实验验证了模型的可行性与有效性。
With respect to the problems of multiple attribute decision-making in which the attribute values are in the form of interval-valued hesitant fuzzy numbers( IVHFN) and attributes are associated with each other. This paper proposed a novel decision-making method based on interval-valued hesitant fuzzy weighted Heronian mean( IVHFWHM) operator. According to the IVHFN's operational laws and Heronian mean( HM) operator,it proposed interval-valued hesitant fuzzy Heronian mean( IVHFHM) operator and IVHFWHM operator. Then,it studied the IVHFHM's properties of permutation invariance,idempotent,monotonicity,boundedness and parameter symmetry. This paper constructed a multiple attribute decision-making model based on IVHFWHM operator. Finally,it provided a numerical example of MADM problem to illustrate the effectiveness and feasibility of the proposed operator.
With respect to the problems of multiple attribute decision-making in which the attribute values are in the form of interval-valued hesitant fuzzy numbers( IVHFN) and attributes are associated with each other. This paper proposed a novel decision-making method based on interval-valued hesitant fuzzy weighted Heronian mean( IVHFWHM) operator. According to the IVHFN's operational laws and Heronian mean( HM) operator,it proposed interval-valued hesitant fuzzy Heronian mean( IVHFHM) operator and IVHFWHM operator. Then,it studied the IVHFHM's properties of permutation invariance,idempotent,monotonicity,boundedness and parameter symmetry. This paper constructed a multiple attribute decision-making model based on IVHFWHM operator. Finally,it provided a numerical example of MADM problem to illustrate the effectiveness and feasibility of the proposed operator.
引文
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[12]王晓楠,巨永锋,高婷.基于犹豫模糊H-平均的交通流模型选择方法[J].计算机工程与应用,2017,53(13):134-140.(WangXiaonan,Ju Yongfeng,Gao Ting. Method of traffic flow model selectionbased on hesitant fuzzy Heronian mean[J]. Computer Engineeringand Applications,2017,53(13):134-140.)
[13]周晓辉,姚俭,徐磊,等.区间直觉模糊几何Heronian平均算子及其应用[J].系统工程,2016,34(4):140-146.(Zhou Xiaohui,YaoJian,Xu lei,et al. Interval-valued intuitionistic fuzzy geometric Hero-nian means and its application[J]. Systems Engineering,2016,34(4):140-146.)
[14]林显宁.基于犹豫语言H-几何算子的信息安全系统选择[J].计算机工程与应用,2017,53(13):174-180.(Lin Xianning. Selec-tion method of information security system based on hesitant linguisticHeronian geometric operator[J]. Computer Engineering and Appli-cations,2017,53(13):174-180.)
[15]Xia Meimei,Xu Zeshui. Hesitant fuzzy information aggregationin deci-sion making[J]. International Journal of Approximate Reaso-ning,2011,52(3):395-407.
[16]Xu Zeshui,Da Q L. The uncertain OWA operator[J]. InternationalJournal of Intelligence System,2002,23(17):699-775.
[2] Torra V. Hesitant fuzzy sets[J]. International Journal of IntelligentSystems,2010,25(6):529-539.
[3] Chen Na,Xu Zeshui,Xia Meimei. Interval-valued hesitant preferencerelations and their application to group decision making[J]. Know-ledge-Based Systems,2013,37(22):528-540.
[4] Wei Guiwu,Zhao Xiaofei,Lin Rui. Some hesitant interval-valued fuzzyaggregation operators and their applications to multiple attribute deci-sion making[J]. Knowledge-Based Systems,2013,46(7):43-53.
[5]于倩,侯福均,翟玉冰,等.区间犹豫模糊ELECTRE多属性决策方法及应用[J].运筹与管理,2015,24(6):16-24.(Yu Qian,HouFujun,Zhai Yubing,et al. Electre-based measure for multi-attributedecision making using interval-valused hesitant fuzzy set[J]. Opera-tions Research and Management Science,2015,24(6):16-24.)
[6]周晓辉,姚俭.区间直觉梯形模糊几何Heronian平均算子及应用[J].计算机工程与应用,2016,52(9):39-43.(Zhou Xiaohui,YaoJian. Interval-valued intuitionistic trapezoidal fuzzy geometric Heronianmeans operator and its application[J]. Computer Engineering andApplications,2016,52(9):39-43.)
[7] Beliakov G,Pradera A,Calvo T. Aggregation functions:a guide forpractitioners[M]. Berlin:Springer,2007.
[8] Sykora S. Mathematical means and average:generalized heronianmeans[D].[S. l.]:Sykora S Stan’s Library,2009.
[9] Sykora S. Generalized Heronian means II[D].[S. l.]:Sykora SStan’s Library,2009.
[10]Liu H Z,Pei D W. HOWA operator and its application to multi-attri-bute decision making[J]. Journal of Zhejiang Sci-Tech Universi-ty,2012,25:138-142.
[11]于倩,侯福均.犹豫模糊语言Heronian平均算子在多属性决策中的应用[J].运筹与管理,2016,25(2):90-97.(Yu Qian,Hou Fu-jun. Hesitant fuzzy linguistic Heronian mean operators and their appli-cation to multiple attribute decision making[J]. Operations Re-search and Management Science,2016,25(2):90-97.)
[12]王晓楠,巨永锋,高婷.基于犹豫模糊H-平均的交通流模型选择方法[J].计算机工程与应用,2017,53(13):134-140.(WangXiaonan,Ju Yongfeng,Gao Ting. Method of traffic flow model selectionbased on hesitant fuzzy Heronian mean[J]. Computer Engineeringand Applications,2017,53(13):134-140.)
[13]周晓辉,姚俭,徐磊,等.区间直觉模糊几何Heronian平均算子及其应用[J].系统工程,2016,34(4):140-146.(Zhou Xiaohui,YaoJian,Xu lei,et al. Interval-valued intuitionistic fuzzy geometric Hero-nian means and its application[J]. Systems Engineering,2016,34(4):140-146.)
[14]林显宁.基于犹豫语言H-几何算子的信息安全系统选择[J].计算机工程与应用,2017,53(13):174-180.(Lin Xianning. Selec-tion method of information security system based on hesitant linguisticHeronian geometric operator[J]. Computer Engineering and Appli-cations,2017,53(13):174-180.)
[15]Xia Meimei,Xu Zeshui. Hesitant fuzzy information aggregationin deci-sion making[J]. International Journal of Approximate Reaso-ning,2011,52(3):395-407.
[16]Xu Zeshui,Da Q L. The uncertain OWA operator[J]. InternationalJournal of Intelligence System,2002,23(17):699-775.