概率犹豫模糊算法及其网络舆情预测模型选择
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摘要
针对区间犹豫模糊集在描述决策信息时会导致决策信息重要性程度损失这一问题,构建了一种基于概率区间犹豫模糊几何算子的新的多属性群决策模型。引入了概率区间犹豫模糊集的概念,将Archimedean范数引入到概率区间犹豫模糊环境下,定义了新的概率区间犹豫模糊运算法则;运用新的运算法则,提出了概率区间犹豫模糊有序加权几何(Probabilistic Interval-Valued Hesitant Fuzzy Ordered Weighted Geometric,PIVHFOWG)算子;讨论了PIVHFOWG算子的一些基本性质,并研究了其两种常见形式;在概率区间犹豫模糊信息环境下,建立了一种新的多属性群决策模型,且通过网络舆情预测系统的选择实例验证了提出的决策模型是可行的和有效的。
For the serious loss of important level of information when decision making information is described by intervalvalued hesitant fuzzy set, a new multi-attribute group decision making model is investigated on the basis of probabilistic interval-valued hesitant fuzzy geometric operator. Firstly, the concept of probabilistic interval-valued hesitant fuzzy set is introduced, and the new probabilistic interval-valued hesitant fuzzy operational laws are defined by using the Archimedean norm. Then, based on the defined operational laws, the Probabilistic Interval-Valued Hesitant Fuzzy Ordered Weighted Geometric(PIVHFOWG) operator is proposed. Furthermore, some basic properties of PIVHFOWG operator are discussed, and several common forms of PIVHFOWG operator are studied. Finally, a novel multi-attribute group decision making model is developed under the probabilistic interval-valued hesitant fuzzy information environment, and a numerical example about the network public opinion prediction system selection is provided to illustrate the effectiveness of the developed model.
For the serious loss of important level of information when decision making information is described by intervalvalued hesitant fuzzy set, a new multi-attribute group decision making model is investigated on the basis of probabilistic interval-valued hesitant fuzzy geometric operator. Firstly, the concept of probabilistic interval-valued hesitant fuzzy set is introduced, and the new probabilistic interval-valued hesitant fuzzy operational laws are defined by using the Archimedean norm. Then, based on the defined operational laws, the Probabilistic Interval-Valued Hesitant Fuzzy Ordered Weighted Geometric(PIVHFOWG) operator is proposed. Furthermore, some basic properties of PIVHFOWG operator are discussed, and several common forms of PIVHFOWG operator are studied. Finally, a novel multi-attribute group decision making model is developed under the probabilistic interval-valued hesitant fuzzy information environment, and a numerical example about the network public opinion prediction system selection is provided to illustrate the effectiveness of the developed model.
引文
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[5]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.
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[9]林杨,王应明,陈圣群.一种考虑区间直觉模糊集的多属性匹配决策方法[J].信息与控制,2016,45(2):204-210.
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[12]金飞飞,裴利丹,陈华友,等.区间犹豫模糊三角相似度及其多属性群决策[J].计算机工程与应用,2015,51(4):41-45.
[13]Liu B,Shen Y,Zhang W,et al.An interval-valued intuitionistic fuzzy principal component analysis modelbased method for complex multi-attribute large-group decision-making[J].European Journal of Operational Research,2015,245(1):209-225.
[14]鲁小云,俞惠芳.区间值犹豫模糊信息系统中的信息熵研究[J].小型微型计算机系统,2017,38(1):138-141.
[15]Jin F F,Ni Z W,Chen H Y.Interval-valued hesitant fuzzy Einstein prioritized aggregation operators and their applications to multi-attribute group decision making[J].Soft Computing,2016,20(5):1863-1878.
[16]Zhang Z M,Wu C.Weighted hesitant fuzzy sets and their application to multi-criteria decision making[J].British Journal of Mathematics&Computer Science,2014,4(8):1091-1123.
[17]Liu P.The aggregation operators based on Archimedean t-conorm and t-norm for single-valued neutrosophic numbers and their application to decision making[J].International Journal of Fuzzy Systems,2016,18(5):1-15.
[18]Xia M M,Xu Z S.Hesitant fuzzy information aggregation in decision making[J].International Journal of Approximate Reasoning,2011,52(3):395-407.
[19]Zhang Z,Wu C.Some interval-valued hesitant fuzzy aggregation operators based on Archimedean t-norm and tconorm with their application in multi-criteria decision making[J].Journal of Intelligent&Fuzzy Systems,2014,27(6):2737-2748.
[2]Atanassov K.Intuitionistic fuzzy sets[J].Fuzzy Sets and Systems,1986,20(1):87-96.
[3]Torra V.Hesitant fuzzy sets[J].International Journal of Intelligent Systems,2010,25(6):529-539.
[4]Atanassov K.Interval-valued intuitionistic fuzzy sets[J].Fuzzy Sets&Systems,1989,31(3):343-349.
[5]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.
[6]Wan S P,Dong J Y.Interval-valued intuitionistic fuzzy mathematical programming method for hybrid multi-criteria group decision making with interval-valued intuitionistic fuzzy truth degrees[J].Information Fusion,2015,26:49-65.
[7]Chen T Y.The inclusion-based TOPSIS method with interval-valued intuitionistic fuzzy sets for multiple criteria group decision making[J].Applied Soft Computing,2015,26:57-73.
[8]陈志旺,陈林,杨七,等.用区间直觉模糊集方法对属性权重未知的群求解其多属性决策[J].控制理论与应用,2014,31(8):1025-1033.
[9]林杨,王应明,陈圣群.一种考虑区间直觉模糊集的多属性匹配决策方法[J].信息与控制,2016,45(2):204-210.
[10]Meng F,Chen X.Interval-valued intuitionistic fuzzy multicriteria group decision making based on cross entropy and 2-additive measures[J].Soft Computing,2015,19(7):2071-2082.
[11]陈树伟,蔡丽娜.区间值犹豫模糊集[J].模糊系统与数学,2013,27(6):38-44.
[12]金飞飞,裴利丹,陈华友,等.区间犹豫模糊三角相似度及其多属性群决策[J].计算机工程与应用,2015,51(4):41-45.
[13]Liu B,Shen Y,Zhang W,et al.An interval-valued intuitionistic fuzzy principal component analysis modelbased method for complex multi-attribute large-group decision-making[J].European Journal of Operational Research,2015,245(1):209-225.
[14]鲁小云,俞惠芳.区间值犹豫模糊信息系统中的信息熵研究[J].小型微型计算机系统,2017,38(1):138-141.
[15]Jin F F,Ni Z W,Chen H Y.Interval-valued hesitant fuzzy Einstein prioritized aggregation operators and their applications to multi-attribute group decision making[J].Soft Computing,2016,20(5):1863-1878.
[16]Zhang Z M,Wu C.Weighted hesitant fuzzy sets and their application to multi-criteria decision making[J].British Journal of Mathematics&Computer Science,2014,4(8):1091-1123.
[17]Liu P.The aggregation operators based on Archimedean t-conorm and t-norm for single-valued neutrosophic numbers and their application to decision making[J].International Journal of Fuzzy Systems,2016,18(5):1-15.
[18]Xia M M,Xu Z S.Hesitant fuzzy information aggregation in decision making[J].International Journal of Approximate Reasoning,2011,52(3):395-407.
[19]Zhang Z,Wu C.Some interval-valued hesitant fuzzy aggregation operators based on Archimedean t-norm and tconorm with their application in multi-criteria decision making[J].Journal of Intelligent&Fuzzy Systems,2014,27(6):2737-2748.