基于概率PS-粗糙集的动态三支决策及应用
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摘要
在实际应用中,集合是动态变化的,包括元素的迁入和迁出.双向概率PS-粗糙集既考虑集合的动态特性,又考虑知识库中统计信息的粗集理论.在深入分析概率PS-粗糙集理论及其性质的基础上提出了基于双向概率PS-粗糙集的动态三支决策模型,以解决集合动态变化下的三支决策问题.首先,根据双向概率PS-粗糙集的上下近似得到概率PS-正域、负域和边界域,给出了双向概率PS-粗糙集的三支决策规则,并分析了三种规则的置信度与错误率的计算方法与性质;其次,定义了决策度量函数与决策损失函数,并基于贝叶斯决策论的最小风险决策规则,给出了参数阈值的计算方法;最后,讨论了此动态模型的决策性质,并通过元素迁入和迁出的实例证明了模型的正确性与可行性.
In practice,the set is dynamic,including elements moving in and moving out.The bidirectional transfer probabilistic PS-rough sets not only take into account the dynamic characteristics of the set but the rough sets theory of statistical information in the knowledge base.In order to solve the issue of three way decisions under set's dynamic changing,the model of three way decisions model based on bidirectional transfer probabilistic PS-rough sets was put forward.Firstly,according to the upper and lower approximation of bidirectional transfer probabilistic PS-rough sets,the probabilistic PS-positive region,negative region and boundary region were got,the rules of three way decisions on the bidirectional transfer probabilistic PS-rough sets were given,and the computing method and its properties of con-fidence coefficient and error rate were analyzed.Then,decision metric function and decision loss function of three-way decision based on bidirectional transfer probabilistic PS-rough sets were defined,and the estimation method of the threshold value based on the minimum risk decision rules of Bayesian decision theory was given.Finally,the decision properties of the dynamic model were discussed;the correctness and feasibility of the model were proved by an example of moving in and moving out of elements.
In practice,the set is dynamic,including elements moving in and moving out.The bidirectional transfer probabilistic PS-rough sets not only take into account the dynamic characteristics of the set but the rough sets theory of statistical information in the knowledge base.In order to solve the issue of three way decisions under set's dynamic changing,the model of three way decisions model based on bidirectional transfer probabilistic PS-rough sets was put forward.Firstly,according to the upper and lower approximation of bidirectional transfer probabilistic PS-rough sets,the probabilistic PS-positive region,negative region and boundary region were got,the rules of three way decisions on the bidirectional transfer probabilistic PS-rough sets were given,and the computing method and its properties of con-fidence coefficient and error rate were analyzed.Then,decision metric function and decision loss function of three-way decision based on bidirectional transfer probabilistic PS-rough sets were defined,and the estimation method of the threshold value based on the minimum risk decision rules of Bayesian decision theory was given.Finally,the decision properties of the dynamic model were discussed;the correctness and feasibility of the model were proved by an example of moving in and moving out of elements.
引文
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[2]姚一豫.三支决策研究的若干问题.刘盾,李天瑞,苗夺谦等.三支决策与粒计算.北京:科学出版社,2013:1-13.(Yao Y Y.Several issues in studies on three-way decisions.Liu D,Li T R,Miao D Q,et al,Three-way decision and granular computing.Beijing:Science Press,2013:1-13.)
[3]Hu B Q.Three-way decisions space and three-way decisions.Information Sciences,2014,281:21-52.
[4]Ziarko W.Variable precision rough set model.Journal of Computer and System Sciences,1993,46(1):39-59.
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[8]张燕平,邹慧锦,邢航等.CCA三支决策模型的边界域样本处理.计算机科学与探索,2014,8(5):593-600.(Zhang Y P,Zou H J,Xing H,et al,Dealing with samples in boundary regions of three-way decisions model based on CCA.Journal of Frontiers of Computer Science and Technology,2014,8(5):593-600.)
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[11]李明霞,刘保相,张春英.三支决策空间下的区间参数优化模型及应用.计算机科学,2017,44(1):84-89.(Li M X,Liu B X,Zhang C Y.Interval parameters optimization model under three-way decisions space and its application.Computer Science,2017,44(1):84-89.)
[12]张春英,王立亚,李明霞等.基于集对信息粒空间的三支决策模型及应用.通信学报,2016,37(Z1):2016242.(Zhang C Y,Wang L Y,Li M X,et al.Model of three-way decision based on the space of set pair information granule and its application.Journal on Communications,2016,37(Z1):2016242.)
[13]赵艳君,张春英.双向迁移概率PS-粗糙集模型及应用.计算机工程与应用,2012,48(14):148-151.(Zhao Y J,Zhang C Y.Model and application of bidirectional transfer probabilistic PS-rough sets.Computer Engineering and Applications,2012,48(14):148-151.)
[14]史开泉,赵建立.函数S-粗集与隐藏规律安全-认证.中国科学E辑:信息科学,2008,38(8):1234-1243.(Shi K Q,Zhao J L.Function Srough sets and hidden rules-Safety Certification.China Science Series E:Information Sciences,2008,38(8):1234-1243.)
[15]史开泉,姚炳学.函数S-粗集与规律辨识.中国科学E辑:信息科学,2008,38(4):553-564.(Shi K Q,Yao B X.The identification function S-rough sets and rules.China Science Series E:Information Sciences,2008,38(04):553-564.)
[16]史开泉.函数S-粗集.山东大学学报(理学版),2005,40(1):1-6,10.(Shi K Q.Function S-rough sets.Journal of Shandong University(Natural Science),2005,40(1):1-6,10.)
[17]史开泉,崔玉泉.变异S-粗集与它的变异结构.山东大学学报(理学版),2004,39(5):52-57.(Shi K Q,Cui Y Q.Variation S-rough sets and its variation structure.Journal of Shandong University(Natural Science),2004,39(5):52-57.)
[2]姚一豫.三支决策研究的若干问题.刘盾,李天瑞,苗夺谦等.三支决策与粒计算.北京:科学出版社,2013:1-13.(Yao Y Y.Several issues in studies on three-way decisions.Liu D,Li T R,Miao D Q,et al,Three-way decision and granular computing.Beijing:Science Press,2013:1-13.)
[3]Hu B Q.Three-way decisions space and three-way decisions.Information Sciences,2014,281:21-52.
[4]Ziarko W.Variable precision rough set model.Journal of Computer and System Sciences,1993,46(1):39-59.
[5]Slezak D.Rough sets and Bayes factor.In:Peters J F,Skowron A.Transactions on rough setsⅢ.Springer Berlin Heidelberg,2005:202-229.
[6]Slezak D,Ziarko W.The investigation of the Bayesian rough set model.International Journal of Approximate Reasoning,2005,40(1-2):81-91.
[7]张燕平,邹慧锦,赵姝.基于CCA的代价敏感三支决策模型.南京大学学报(自然科学),2015,51(2):447-452.(Zhang Y P,Zou H J,Zhao S.Cost-sensitive three-way decisions model based on CCA.Journal of Nanjing University(Natural Sciences),2015,51(2):447-452.)
[8]张燕平,邹慧锦,邢航等.CCA三支决策模型的边界域样本处理.计算机科学与探索,2014,8(5):593-600.(Zhang Y P,Zou H J,Xing H,et al,Dealing with samples in boundary regions of three-way decisions model based on CCA.Journal of Frontiers of Computer Science and Technology,2014,8(5):593-600.)
[9]Qi J J,Qian T,Wei L.The connections between three-way and classical concept lattices.Knowledge-Based Systems,2016,91:143-151.
[10]王立亚,张春英,刘保相.基于区间概念格的三支决策动态策略调控模型.计算机工程与应用,2016,52(24):80-84,101.(Wang L Y,Zhang C Y,Liu B X.Dynamic strategy regulation model of three-way decisions based on interval concept lattice and its application.Computer Engineering and Applications,2016,52(24):80-84,101.)
[11]李明霞,刘保相,张春英.三支决策空间下的区间参数优化模型及应用.计算机科学,2017,44(1):84-89.(Li M X,Liu B X,Zhang C Y.Interval parameters optimization model under three-way decisions space and its application.Computer Science,2017,44(1):84-89.)
[12]张春英,王立亚,李明霞等.基于集对信息粒空间的三支决策模型及应用.通信学报,2016,37(Z1):2016242.(Zhang C Y,Wang L Y,Li M X,et al.Model of three-way decision based on the space of set pair information granule and its application.Journal on Communications,2016,37(Z1):2016242.)
[13]赵艳君,张春英.双向迁移概率PS-粗糙集模型及应用.计算机工程与应用,2012,48(14):148-151.(Zhao Y J,Zhang C Y.Model and application of bidirectional transfer probabilistic PS-rough sets.Computer Engineering and Applications,2012,48(14):148-151.)
[14]史开泉,赵建立.函数S-粗集与隐藏规律安全-认证.中国科学E辑:信息科学,2008,38(8):1234-1243.(Shi K Q,Zhao J L.Function Srough sets and hidden rules-Safety Certification.China Science Series E:Information Sciences,2008,38(8):1234-1243.)
[15]史开泉,姚炳学.函数S-粗集与规律辨识.中国科学E辑:信息科学,2008,38(4):553-564.(Shi K Q,Yao B X.The identification function S-rough sets and rules.China Science Series E:Information Sciences,2008,38(04):553-564.)
[16]史开泉.函数S-粗集.山东大学学报(理学版),2005,40(1):1-6,10.(Shi K Q.Function S-rough sets.Journal of Shandong University(Natural Science),2005,40(1):1-6,10.)
[17]史开泉,崔玉泉.变异S-粗集与它的变异结构.山东大学学报(理学版),2004,39(5):52-57.(Shi K Q,Cui Y Q.Variation S-rough sets and its variation structure.Journal of Shandong University(Natural Science),2004,39(5):52-57.)