The Applications of Utility function and Entropy of Interval Type-2 Fuzzy Set in Risk Decision-Making

doi:10.12005/orms.2021.0151

Abstract

Abstract: Aiming at the problem of Multi-Attribute Decision Making (MADM) with Interval Type-2 Fuzzy Set (IT2FS) as the information environment, the IT2FS utility function is introduced, and the risk decision model based on IT2FS utility function, entropy and risk factor is proposed. Firstly, based on the idea of cut set, two kinds of IT2FS utility function formulas are proposed, which effectively extracts all the information of IT2FS, which is more scientific and effective than the previous ranking-valued formulae. Secondly, based on the proposed three uncertainty measures of IT2FS, three new uncertain measures are proposed. Based on these three uncertain measures, the IT2FS entropy formula is put forward for the deficiency of the original entropy metric. Thirdly, the introduction of risk preference factors reflects the different risk attitudes of decision makers and improves the range of risk preference factors. We construct a risk decision model based on utility function, entropy and risk preference factor. Finally, the results of an example analysis shows that the risk preference of decision makers in the risk decision model has an impact on the attribute weight and the ranking of the alternatives. The decision-making idea has certain reference functions for risk investment decision-making and risk management decision-making.

Key words: interval type-2 fuzzy set, utility function, entropy, risk preference factor, multi-attribute

摘要： 针对以区间二型模糊集(IT2FS)为信息环境的多属性决策(MADM)问题,引入IT2FS效用函数,并提出基于IT2FS效用函数,熵和风险因子的风险决策模型。首先基于截集思想提出两种IT2FS效用函数公式,有效提取了IT2FS全部信息,比以往的序值型公式更加科学有效。其次基于已提出的IT2FS三种不确定度量存在的问题提出三种新型不确定度量,并基于此三种不确定度量提出IT2FS熵公式弥补原有熵度量的不足。再次引入风险偏好因子反映决策者不同的风险态度,并改进风险偏好因子范围。构造基于效用函数,熵和风险偏好因子的风险决策模型。最后利用一个实例分析结果表明,该风险决策模型中决策者风险偏好对属性权重以及方案的排序存在影响,该决策思想对风险投资决策和风险管理决策均有一定的参考作用。

关键词: 区间二型模糊集, 效用函数, 熵, 风险偏好因子, 多属性决策

CLC Number:

F832.48

LI Ru-xia, HU Wen-xiu, QI Xiao-liang. The Applications of Utility function and Entropy of Interval Type-2 Fuzzy Set in Risk Decision-Making[J]. Operations Research and Management Science, 2021, 30(5): 102-109.

李茹霞, 扈文秀, 齐晓亮. 区间二型模糊集效用函数和熵在风险决策中的应用[J]. 运筹与管理, 2021, 30(5): 102-109.

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