基于多伴随直觉模糊粗糙集的三支决策

发布时间：2019-06-12 01:26

【摘要】：决策粗糙集提供了处理不确定数据和风险数据决策问题的一个新方法,基于决策粗糙集的三支决策理论是典型的风险决策理论的推广.传统的直觉模糊粗糙集采用一对三角模与蕴涵算子来构造逻辑算子,未考虑属性之间的差别,而多伴随直觉模糊粗糙集采用多个伴随对构造逻辑算子,更好地体现了用户偏好.构造了多伴随直觉模糊粗糙集模型,研究了基于多伴随直觉模糊粗糙集的三支决策.首先,定义了乐观多伴随直觉模糊粗糙集,并用于处理直觉模糊数的复杂计算问题;然后利用隶属函数和非隶属函数计算损失函数,通过期望损失函数对事件对象进行评估,进一步构造了相应的三支决策模型;基于期望损失函数值最小的原则诱导出三支决策,并得到相应决策的风险值.此模型中期望损失函数的构造是基于支持度与非支持度两种度量的综合讨论,考虑更全面,更能有效地反映实际生活情况,满足用户偏好.最后用医学诊断的例子来验证该模型的有效性.
[Abstract]:Decision rough set provides a new method to deal with uncertain data and risk data decision-making problem. The three-branch decision theory based on decision rough set is a generalization of typical risk decision theory. The traditional intuitionistic fuzzy rough set uses a pair of triangular modules and implication operators to construct logic operators, without considering the difference between attributes, while multiple adjoint pairs are used to construct logic operators in multiple adjoint fuzzy rough sets, which better reflects the user preference. The multi-adjoint intuitionistic fuzzy rough set model is constructed, and the three-branch decision based on multi-adjoint intuitionistic fuzzy rough set is studied. Firstly, the optimistic multi-adjoint intuitionistic fuzzy rough set is defined and used to deal with the complex calculation problem of intuitionistic fuzzy number. Then, the loss function is calculated by membership function and non-membership function, and the event object is evaluated by expected loss function, and the corresponding three-branch decision model is constructed. Based on the principle of minimum expected loss function, the three-branch decision is induced and the risk value of the corresponding decision is obtained. The construction of expected loss function in this model is based on the comprehensive discussion of support degree and non-support degree, which is more comprehensive and can reflect the actual life situation more effectively and meet the preferences of users. Finally, an example of medical diagnosis is used to verify the effectiveness of the model.
【作者单位】：河北师范大学数学与信息科学学院;河北师范大学信息技术学院;石家庄职业技术学院;
【基金】：国家自然科学基金(61573127,61502144,61300121) 河北省自然科学基金(A2014205157) 河北省大学创新团队训练项目基金(LIRC022) 河北高等教育基金(QN2016133) 河北师范大学博士基金(L2015B01);河北师范大学研究生创新项目基金(CXZZSS2017046) 河北省教育厅创新基金(sj2015001)
【分类号】：O159

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