基于模糊测度与累积前景理论的区间二型模糊多准则决策方法

针对准则值为区间二型模糊数且准则间存在关联关系的风险型多准则决策问题, 本文提出一种基于模糊测度理论与累积前景理论的区间二型模糊多准则决策方法。首先, 为全面反映准则间的关联关系, 本文提出Shapley区间二型模糊Choquet积分算子, 并证明该算子的一些性质。其次, 为反映专家行为偏好, 本文定义区间二型模糊前景效应与前景价值函数, 并提出累积前景Shapley区间二型模糊Choquet积分算子。然后, 为确定准则集的模糊测度, 本文建立基于区间二型模糊双向投影与Shapley函数的权重优化模型。在此基础上, 本文给出一种用于解决准则值为区间二型模糊数, 准则间存在关联关系, 专家存在风险偏好以及准则权重部分未知的多准则决策方法。最后, 通过风险投资实例佐证所提出的方法的适用性与科学性。

Interval Type-2 Fuzzy Muti-criteria Decision Making Method Based on Fuzzy Measures and Cumulative Prospect Theory

For risk muti-criteria decision making problems with interactive condition and interval type-2 fuzzyinformation, an interval type-2 fuzzy decision making method is proposed based on fuzzy measures theory and cumulative prospect theory. Firstly, in order to globally consider the interactions among the criteria, this paper proposes the Shapley interval type-2 fuzzy Choquet operator. Meanwhile, some desirable properties of this operator are studied. Then, to capture the diversities of risk attitudes and sensitivities among experts with limited relational behaviors, this paper defines the prospect effect and the prospect value function of interval type-2 fuzzy number, and proposes the cumulative prospect Shapley interval type-2 fuzzy Choquet operator. In addition, based on the defined bidirectional projection measures of interval type-2 fuzzy sets and the Shapley function, the models for the optimal fuzzy measures on a criteria set are established. After that, an approach to muti-criteria decision making with interaction condition, experts’ risk preference and incomplete weight information under interval type-2 fuzzy environment is developed. Finally, a practical example regarding risk investment is provided to demonstrate the applicability and validity of the developed approach.