基于IITFN输入的复杂系统关联MAGDM方法

An Interdependent Multi-attribute Group Decision Making Method for Complex Systems Based upon Fuzzy Input with Interval-valued Intuitionistic Trapezoidal Fuzzy Numbers

区间直觉梯形模糊数(Interval-valued intuitionistic trapezoidal fuzzy number,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-attribute group decision making,MAGDM)问题,提出基于前景混合区间直觉梯形几何Bonferroni(Prospect hybrid interval-valued intuitionistic trapezoidal fuzzy geometric Bonferroni,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.

The interval-valued intuitionistic trapezoidal fuzzy number （IITFN） is an efficient tool for describing uncertainties of complex systems. In this paper, we propose the improved operational laws of IITFNs and discuss their partial closure property. Then an interval-valued intuitionistic trapezoidal fuzzy geometric Bonferroni mean operator is developed, and some relative properties of this operator are also investigated. With respect to a multi-attribute group decision making （MAGDM） problem, in which there are both interactions among decision-makers and attributes with both unknown decision-makers＇ weights and attributesr weights, an interdependent MAGDM method based on a prospect hybrid interval- valued intuitionistic trapezoidal fuzzy geometric Bonferroni （PHIITFGB） mean operator is proposed. Firstly, the prospect effect, prospect value function, and prospect value of IITFN are defined to obtain the prospect value matrixes. Secondly, the prospect value matrixes are transformed into the corresponding prospect score function matrixes, then a maximum entropy optimization model for determining the objective attribute weights based on a principle of grey correlation deep coefficient and a model for obtaining decision-maker weights based on the combination of 2-additive fuzzy measures and Choquet integral are integrated to determine the decision-makers＇ weights and attributes＇ weights. Thirdly, evaluations of all the alternatives derived from all the decision makers are aggregated by utilizing the PHIITFGB mean operator, and then the comprehensive prospect value corresponding to each alternative is obtained by integrating the decision-makers＇ weights. Finally, a ranking of alternatives is determined by calculating score functions of the alternatives. A practical example is given to illustrate the validity and feasibility of the proposed decision-making methods.