基于多伴随直觉模糊粗糙集的三支决策

南京大学学报(自然科学版) ›› 2017, Vol. 53 ›› Issue (6): 1081–.

基于多伴随直觉模糊粗糙集的三支决策

赵天娜1，米据生1*，解　滨2，梁美社1，3

出版日期:2017-11-27 发布日期:2017-11-27
作者简介:1.河北师范大学数学与信息科学学院，石家庄，050024；
2.河北师范大学信息技术学院，石家庄，050024；
3．石家庄职业技术学院，石家庄，050081
基金资助:
基金项目：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)，河北省教育厅创新基金(sj2015001)，河北师范大学研究生创新项目基金(CXZZSS2017046)
收稿日期：2017－08－30
*通讯联系人，E－mail：mijsh@263.net

Three－way decisions with multi－adjoint intuitionistic fuzzy rough sets

Zhao Tianna1，Mi Jusheng1*，Xie Bin2，Liang Meishe1，3

Online:2017-11-27 Published:2017-11-27
About author:1.College of Mathematics and Information Science，Hebei Normal University，Shijiazhuang，050024，China；
2．College of Information Technology，Hebei Normal University，Shijiazhuang，050024，China；
3．Shijiazhuang Vocational Technology Institute，Shijiazhuang，050081，China

摘要/Abstract

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－theoretic rough set provides a new perspective to handle decision－making problems under uncertainty and risk.Three－way decision with decision－theoretic rough sets，generated by Bayesian decision theory，is a typical risk decision method.Traditional intuitionistic fuzzy rough set uses a pair of triangular norm and implication operator to construct the logical operator，which does not consider the difference between attributes.However，multi－adjoint intuitionistic fuzzy rough set constructs the logical operator using several adjoint triples，which better reflects the user preferences.In this paper，multi－adjoint intuitionistic fuzzy rough set is proposed，and three－way decision with multi－adjoint intuitionistic fuzzy rough sets is formulated.First，we define an multi－adjoint fuzzy rough set，and construct the optimistic multi－adjoint fuzzy rough set in order to deal with the complicated calculation of intuitionistic fuzzy value.As the determination of loss function is one of the key steps in the decision process，we then calculate the loss function by using the degree of membership and the degree of nonmembership.The event objects were assessed through the loss functions.And then，we construct corresponding three way decision model，and induce the three－way decision in order to make decisions with the minimum risk of loss and get the risk of the corresponding decision.The structure of the expected loss function synthetically considers the support and the nonsupport，which can effectively reflect the real life situation and meet user’s preferences.Finally，an example of medical diagnosis is employed to verify the effectiveness of the proposed model.

赵天娜1，米据生1*，解　滨2，梁美社1，3. 基于多伴随直觉模糊粗糙集的三支决策[J]. 南京大学学报(自然科学版), 2017, 53(6): 1081–.

Zhao Tianna1，Mi Jusheng1*，Xie Bin2，Liang Meishe1，3. Three－way decisions with multi－adjoint intuitionistic fuzzy rough sets[J]. Journal of Nanjing University(Natural Sciences), 2017, 53(6): 1081–.

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