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基于IITFN输入的复杂系统关联MAGDM方法

DOI: 10.3724/SP.J.1004.2014.01442, PP. 1442-1471

Keywords: 不确定性,区间直觉梯形模糊数,前景理论,多属性群决策,Choquet积分

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Abstract:

?区间直觉梯形模糊数(Interval-valuedintuitionistictrapezoidalfuzzynumber,IITFN)是刻画复杂系统不确定性的有效工具.基于进一步完善的IITFN运算规则,讨论其局部封闭性.由此定义IITFN几何Bonferroni平均算子,并验证该算子的相关性质.针对决策者及属性之间均存在关联作用且权重均未知的多属性群决策(Multi-attributegroupdecisionmaking,MAGDM)问题,提出基于前景混合区间直觉梯形几何Bonferroni(Prospecthybridinterval-valuedintuitionistictrapezoidalfuzzygeometricBonferroni,PHIITFGB)平均算子的关联多属性群决策方法.该方法首先通过依次定义IITFN的前景效应、前景价值函数和前景价值,获取前景价值矩阵;其次,将前景价值矩阵转化为前景记分函数矩阵,并综合运用基于灰关联深度系数的客观属性权重极大熵模型和基于2-可加模糊测度与Choquet积分联合的决策者权重确定模型,获取决策者权重及属性权重;再次,利用PHIITFGB算子集结各决策者的方案评估信息,结合决策者权重即可获取相应于各方案的综合前景价值;最后,计算综合前景记分价值函数,基于IITFN的序关系判别准则确定方案排序.案例验证决策方法的有效性和可行性.

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