三支决策模型及其研究现状分析
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摘要
三支决策是由Yao等人基于决策粗糙集理论模型,进一步结合决策情景而提出的一种决策理论。它成功地为粗糙集的正域、负域和边界域合理地赋予了语义解释,分别对应实际决策中的接受、拒绝和延迟决策。三支决策理论自提出以来,随即得到诸多学者关注并对其进行了完善和拓展,其已在多领域得到广泛应用。详细介绍三支决策的背景及基本理论模型,总结国内外关于三支决策的研究现状及进展,最后对三支决策未来研究方向进行了展望。
Based on decision-theoretic rough sets and practical situation, the concept of three-way decisions is a kind of decision theory proposed by Yao et al. With the aid of this theory, the positive, negative and boundary regions of rough sets are given a new semantic explanation, which correspond to the notions of acceptance,rejection and deferment in decision making, respectively. Since the raise of three-way decisions, it has attracted many scholars' attentions and it is improved and expanded to many fields. In this paper, we firstly introduce the background and basic theoretical models of the three-way decisions. Then, we can review the current research status and progress of this topic. Finally, we look forward to the future research trends.
Based on decision-theoretic rough sets and practical situation, the concept of three-way decisions is a kind of decision theory proposed by Yao et al. With the aid of this theory, the positive, negative and boundary regions of rough sets are given a new semantic explanation, which correspond to the notions of acceptance,rejection and deferment in decision making, respectively. Since the raise of three-way decisions, it has attracted many scholars' attentions and it is improved and expanded to many fields. In this paper, we firstly introduce the background and basic theoretical models of the three-way decisions. Then, we can review the current research status and progress of this topic. Finally, we look forward to the future research trends.
引文
[1]PAWLAK Z.Rough set[J].International Journal of Computer and Information Sciences,1982,11(5):341-356.
[2]YAO Y Y,WONG S K.A decision theoretic framework for approximating concepts[J].International Journal of Man-Machine Studies,1992,37(6):793-809.
[3]YAO Y Y.Three-way decision:An interpretation of rules in rough set theory[J].Information Sciences,2010,180(3):341-353.
[4]YAO Y Y.Three-way decisions with probabilistic rough sets[J].Information Sciences,2010,180(3):341-353.
[5]贾修一,商琳,周献中,等.三支决策理论与应用[M].南京:南京大学出版社,2012.
[6]刘盾.三支决策与粒计算[M].北京:科学出版社,2013.
[7]于洪.三支决策:复杂问题求解方法与实践[M].北京:科学出版社,2015.
[8]梁德翠.模糊环境下基于决策粗糙集的决策方法研究[D].成都:西南交通大学,2014.
[9]YAO Y,ZHAO Y.Attribute reduction in decisiontheoretic rough set models[J].Information Sciences,2008,178(17):3356-3373.
[10]YAO Y.Probabilistic rough set approximations[J].International Journal of Approximate Reasoning,2008,49(2):255-271.
[11]YAO Y.The superiority of three-way decisions in probabilistic rough set models[J].Information Sciences,2011,181(6):1080-1096.
[12]JIA X,LIAO W,TANG Z,et al.Minimum cost attribute reduction in decision-theoretic rough set models[J].Information Sciences,2013,219(1):151-167.
[13]QIANY,ZHANG H,SANG Y,et al.Multigranulation decision-theoretic rough sets[J].International Journal of Approximate Reasoning,2014,55(1):225-237.
[14]LIU D,LI T,LIANG D.Incorporating logistic regression to decision-theoretic rough sets for classifications[J].International Journal of Approximate Reasoning,2014,55(1):197-210.
[15]LIANG D,LIU D.Deriving three-way decisions from intuitionistic fuzzy decision-theoretic rough sets[J].Information Sciences,2015,300:28-48.
[16]LIANG D,PEDRYCZ W,LIU D,et al.Three-way decisions based on decision-theoretic rough sets under linguistic assessment with the aid of group decision making[J].Applied Soft Computing,2015,29:256-269.
[17]LIU D,LIANG D,WANG C.A novel three-way decision model based on incomplete information system[J].Knowledge-Based Systems,2016,91:32-45.
[18]YAO Y,ZHOU B.Naive Bayesian Rough Sets[C]//International Conference on Rough Set and Knowledge Technology.Berlin:Springer-Verlag,2010:719-726.
[19]JIA X,TANG Z,LIAO W,et al.On an optimization representation of decision-theoretic rough set model[J].International Journal of Approximate Reasoning,2014,55(1):156-166.
[20]贾修一,商琳,陈家骏.决策风险最小化属性约简[J].计算机科学与探索,2011,5(2):155-160.
[21]贾修一,李伟湋,商琳,等.一种自适应求三枝决策中决策阈值的算法[J].电子学报,2011,39(11):2520-2525.
[22]张贤勇,杨霁琳,唐孝.三支决策与三支关注的双量化集成[J].模式识别与人工智能,2017,30(5):394-402.
[23]汪璐,贾修一,顾雁囡.三支决策贝叶斯网络分类器[J].南京大学学报:自然科学,2016,52(5):833-843.
[24]YU H,CHU S,YANG D.Autonomous knowledgeoriented clustering using decision-theoretic rough set theory[C].International Conference on Rough Set and Knowledge Technology.Berlin:Springer-Verlag,2010:687-694.
[25]HERBERT J P,YAO J T.Game-theoretic risk analysis in decision-theoretic rough sets[C]//International Conference on Rough Set and Knowledge Technology.Berlin:Springer-Verlag,2008:132-139.
[26]HERBERT J P,YAO J T.Game-theoretic rough sets[J].Fundamenta Informaticae,2011,108(3-4):267-286.
[27]HERBERT J P,YAO J T.Analysis of data-driven parameters in game-theoretic rough sets[C]//International Conference on Rough Sets and Knowledge Technology.Berlin:Springer-Verlag,2011:447-456.
[28]YAO Y,DENG X.Sequential three-way decisions with probabilistic rough sets[J].Information Sciences,2010,180(3):341-353.
[29]DENG X,YAO Y.An information-theoretic interpretation of thresholds in probabilistic rough sets[C]//International Conference on Rough Sets and Knowledge Technology.Berlin:Springer-Verlag,2012:369-378.
[30]AZAM N,YAO J.Analyzing uncertainties of probabilistic rough set regions with game-theoretic rough sets[J].International Journal of Approximate Reasoning,2014,55(1):142-155.
[31]LIANG D,LIU D,Pedrycz W,et al.Triangular fuzzy decision-theoretic rough sets[J].International Journal of Approximate Reasoning,2013,54(8):1087-1106.
[32]LIU D,LI T R,LI H X.A multiple-category classification approach with decision-theoretic rough sets[J].Fundamenta Informaticae,2012,115(2-3):173-188.
[33]LIU D,LI T R,LIANG D C.Three-way government decision analysis with decision-theoretic rough sets[J].International Journal of Uncertainty,Fuzziness and KnowledgeBased Systems,2012,20(1):119-132.
[34]LIU D,LI T R,LIANG D C.Decision-theoretic rough sets with probabilistic distribution[C]//International Conference on Rough Sets and Knowledge Technology.Berlin:SpringerVerlag,2012:389-398.
[35]刘盾,李天瑞,李华雄.区间决策粗糙集[J].计算机科学,2012,39(7):178-214.
[36]刘盾,李天瑞,梁德翠.模糊数决策粗糙集[J].计算机科学,2012,39(12):25-29.
[37]LIU D,LI T R,RUAN D.Probabilistic model criteria with decision-theoretic rough sets[J].Information Sciences,2011,181(17):3709-3722.
[38]LIANG D,XU Z,LIU D.Three-way decisions based on decision-theoretic rough sets with dual hesitant fuzzy information[J].Information Sciences,2017,396:127-143.
[39]LIANG D,LIU D,KOBINA A.Three-way group decisions with decision-theoretic rough sets[J].Information Sciences,2016,345:46-64.
[40]LIANG D,LIU D.A novel risk decision making based on decision-theoretic rough sets under hesitant fuzzy information[J].IEEE Transactions on Fuzzy Systems,2015,23(2):237-247.
[41]张燕平,邹慧锦,赵姝.基于CCA的代价敏感三支决策模型[J].南京大学学报:自然科学,2015,51(2):447-452.
[42]张楠,姜丽丽,岳晓冬,等.效用三支决策模型[J].智能系统学报,2016,11(4):459-468.
[43]ZHANG Q,XIA D,WANG G.Three-way decision model with two types of classification errors[J].Information Sciences,2017,420:431-453.
[44]LI HUAXIONG,ZHOU XIANZHONG.Risk decision making based on decision-theoretic rough set:A threeway view decision model[J].International Journal of Computational Intelligence Systems,2011,4(1):1-11.
[45]陈刚,刘秉权,吴岩.求三支决策最优阈值的新算法[J].计算机应用,2012,32(8):2212-2215.
[46]徐久成,刘洋洋,杜丽娜,等.基于三支决策的支持向量机增量学习方法[J].计算机科学,2015,42(6):82-87.
[47]徐久成,杜丽娜,刘洋洋.三支决策与Vague集[J].小型微型计算机系统,2016,37(7):1464-1468.
[48]刘盾,梁德翠.广义三支决策与狭义三支决策[J].计算机科学与探索,2017,11(3):502-510.
[49]于洪,毛传凯.基于k-means的自动三支决策聚类方法[J].计算机应用,2016,36(8):2061-2065.
[50]薛占熬,朱泰隆,薛天宇,等.基于直觉模糊集的三支决策模型[J].计算机科学,2016,43(6):283-288.
[51]薛占熬,刘杰,朱泰隆,等.基于覆盖的Sugeno测度粗糙集模型及其三支决策[J].计算机科学,2016,43(3):285-290.
[52]王磊,黄河笑,吴兵,等.基于主题与三支决策的文本情感分析[J].计算机科学,2015,42(6):93-96.
[53]周哲,商琳.一种基于动态词典和三支决策的情感分析方法[J].山东大学学报:工学版,2015,45(1):19-23.
[54]朱艳辉,田海龙,刘璟,等.基于三支决策的新闻情感关键句识别方法[J].山西大学学报:自然科学版,2015,38(4):595-600.
[55]YAO Y.Rough sets and three-way decisions[C]//International Conference on Rough Sets and Knowledge Technology.2015:62-73.
[56]YAO Y.Three-way decisions and cognitive computing[J].Cognitive Computation,2016,8(4):543-554.
[57]LI M,WANG G.Approximate concept construction with three-way decisions and attribute reduction in incomplete contexts[J].Knowledge-Based Systems,2016,91:165-178.
[58]李美争,王国胤.三支近似概念格中基于对象-概念辨识矩阵的属性约简方法[J].控制与决策,2016,31(10):1779-1784.
[59]SAVCHENKO A V.Fast multi-class recognition of piecewise regular objects based on sequential three-way decisions and granular computing[J].Knowledge-Based Systems,2016,91:252-262.
[60]ZHANG H Y,YANG S Y,MA J M.Ranking interval sets based on inclusion measures and applications to three-way decisions[J].Knowledge-Based Systems,2016,91:62-70.
[61]PETERS J F,RAMANNA S.Proximal three-way decisions:Theory and applications in social networks[J].Knowledge-Based Systems,2016,91:4-15.
[62]HU B Q,WONG H,YIU K F C.On two novel types of three-way decisions in three-way decision spaces[J].International Journal of Approximate Reasoning,2017,82:285-306.
[63]LANG G,MIAO D,CAI M.Three-way decision approaches to conflict analysis using decision-theoretic rough set theory[J].Information Sciences,2017,406:185-207.
[64]LI X,SUN B,SHE Y,et al.Generalized matroids based on three-way decision models[J].International Journal of Approximate Reasoning,2017,90:192-207.
[65]HAO C,LI J,FAN M,et al.Optimal scale selection in dynamic multi-scale decision tables based on sequential threeway decisions[J].Information Sciences,2017,415:213-232.
[2]YAO Y Y,WONG S K.A decision theoretic framework for approximating concepts[J].International Journal of Man-Machine Studies,1992,37(6):793-809.
[3]YAO Y Y.Three-way decision:An interpretation of rules in rough set theory[J].Information Sciences,2010,180(3):341-353.
[4]YAO Y Y.Three-way decisions with probabilistic rough sets[J].Information Sciences,2010,180(3):341-353.
[5]贾修一,商琳,周献中,等.三支决策理论与应用[M].南京:南京大学出版社,2012.
[6]刘盾.三支决策与粒计算[M].北京:科学出版社,2013.
[7]于洪.三支决策:复杂问题求解方法与实践[M].北京:科学出版社,2015.
[8]梁德翠.模糊环境下基于决策粗糙集的决策方法研究[D].成都:西南交通大学,2014.
[9]YAO Y,ZHAO Y.Attribute reduction in decisiontheoretic rough set models[J].Information Sciences,2008,178(17):3356-3373.
[10]YAO Y.Probabilistic rough set approximations[J].International Journal of Approximate Reasoning,2008,49(2):255-271.
[11]YAO Y.The superiority of three-way decisions in probabilistic rough set models[J].Information Sciences,2011,181(6):1080-1096.
[12]JIA X,LIAO W,TANG Z,et al.Minimum cost attribute reduction in decision-theoretic rough set models[J].Information Sciences,2013,219(1):151-167.
[13]QIANY,ZHANG H,SANG Y,et al.Multigranulation decision-theoretic rough sets[J].International Journal of Approximate Reasoning,2014,55(1):225-237.
[14]LIU D,LI T,LIANG D.Incorporating logistic regression to decision-theoretic rough sets for classifications[J].International Journal of Approximate Reasoning,2014,55(1):197-210.
[15]LIANG D,LIU D.Deriving three-way decisions from intuitionistic fuzzy decision-theoretic rough sets[J].Information Sciences,2015,300:28-48.
[16]LIANG D,PEDRYCZ W,LIU D,et al.Three-way decisions based on decision-theoretic rough sets under linguistic assessment with the aid of group decision making[J].Applied Soft Computing,2015,29:256-269.
[17]LIU D,LIANG D,WANG C.A novel three-way decision model based on incomplete information system[J].Knowledge-Based Systems,2016,91:32-45.
[18]YAO Y,ZHOU B.Naive Bayesian Rough Sets[C]//International Conference on Rough Set and Knowledge Technology.Berlin:Springer-Verlag,2010:719-726.
[19]JIA X,TANG Z,LIAO W,et al.On an optimization representation of decision-theoretic rough set model[J].International Journal of Approximate Reasoning,2014,55(1):156-166.
[20]贾修一,商琳,陈家骏.决策风险最小化属性约简[J].计算机科学与探索,2011,5(2):155-160.
[21]贾修一,李伟湋,商琳,等.一种自适应求三枝决策中决策阈值的算法[J].电子学报,2011,39(11):2520-2525.
[22]张贤勇,杨霁琳,唐孝.三支决策与三支关注的双量化集成[J].模式识别与人工智能,2017,30(5):394-402.
[23]汪璐,贾修一,顾雁囡.三支决策贝叶斯网络分类器[J].南京大学学报:自然科学,2016,52(5):833-843.
[24]YU H,CHU S,YANG D.Autonomous knowledgeoriented clustering using decision-theoretic rough set theory[C].International Conference on Rough Set and Knowledge Technology.Berlin:Springer-Verlag,2010:687-694.
[25]HERBERT J P,YAO J T.Game-theoretic risk analysis in decision-theoretic rough sets[C]//International Conference on Rough Set and Knowledge Technology.Berlin:Springer-Verlag,2008:132-139.
[26]HERBERT J P,YAO J T.Game-theoretic rough sets[J].Fundamenta Informaticae,2011,108(3-4):267-286.
[27]HERBERT J P,YAO J T.Analysis of data-driven parameters in game-theoretic rough sets[C]//International Conference on Rough Sets and Knowledge Technology.Berlin:Springer-Verlag,2011:447-456.
[28]YAO Y,DENG X.Sequential three-way decisions with probabilistic rough sets[J].Information Sciences,2010,180(3):341-353.
[29]DENG X,YAO Y.An information-theoretic interpretation of thresholds in probabilistic rough sets[C]//International Conference on Rough Sets and Knowledge Technology.Berlin:Springer-Verlag,2012:369-378.
[30]AZAM N,YAO J.Analyzing uncertainties of probabilistic rough set regions with game-theoretic rough sets[J].International Journal of Approximate Reasoning,2014,55(1):142-155.
[31]LIANG D,LIU D,Pedrycz W,et al.Triangular fuzzy decision-theoretic rough sets[J].International Journal of Approximate Reasoning,2013,54(8):1087-1106.
[32]LIU D,LI T R,LI H X.A multiple-category classification approach with decision-theoretic rough sets[J].Fundamenta Informaticae,2012,115(2-3):173-188.
[33]LIU D,LI T R,LIANG D C.Three-way government decision analysis with decision-theoretic rough sets[J].International Journal of Uncertainty,Fuzziness and KnowledgeBased Systems,2012,20(1):119-132.
[34]LIU D,LI T R,LIANG D C.Decision-theoretic rough sets with probabilistic distribution[C]//International Conference on Rough Sets and Knowledge Technology.Berlin:SpringerVerlag,2012:389-398.
[35]刘盾,李天瑞,李华雄.区间决策粗糙集[J].计算机科学,2012,39(7):178-214.
[36]刘盾,李天瑞,梁德翠.模糊数决策粗糙集[J].计算机科学,2012,39(12):25-29.
[37]LIU D,LI T R,RUAN D.Probabilistic model criteria with decision-theoretic rough sets[J].Information Sciences,2011,181(17):3709-3722.
[38]LIANG D,XU Z,LIU D.Three-way decisions based on decision-theoretic rough sets with dual hesitant fuzzy information[J].Information Sciences,2017,396:127-143.
[39]LIANG D,LIU D,KOBINA A.Three-way group decisions with decision-theoretic rough sets[J].Information Sciences,2016,345:46-64.
[40]LIANG D,LIU D.A novel risk decision making based on decision-theoretic rough sets under hesitant fuzzy information[J].IEEE Transactions on Fuzzy Systems,2015,23(2):237-247.
[41]张燕平,邹慧锦,赵姝.基于CCA的代价敏感三支决策模型[J].南京大学学报:自然科学,2015,51(2):447-452.
[42]张楠,姜丽丽,岳晓冬,等.效用三支决策模型[J].智能系统学报,2016,11(4):459-468.
[43]ZHANG Q,XIA D,WANG G.Three-way decision model with two types of classification errors[J].Information Sciences,2017,420:431-453.
[44]LI HUAXIONG,ZHOU XIANZHONG.Risk decision making based on decision-theoretic rough set:A threeway view decision model[J].International Journal of Computational Intelligence Systems,2011,4(1):1-11.
[45]陈刚,刘秉权,吴岩.求三支决策最优阈值的新算法[J].计算机应用,2012,32(8):2212-2215.
[46]徐久成,刘洋洋,杜丽娜,等.基于三支决策的支持向量机增量学习方法[J].计算机科学,2015,42(6):82-87.
[47]徐久成,杜丽娜,刘洋洋.三支决策与Vague集[J].小型微型计算机系统,2016,37(7):1464-1468.
[48]刘盾,梁德翠.广义三支决策与狭义三支决策[J].计算机科学与探索,2017,11(3):502-510.
[49]于洪,毛传凯.基于k-means的自动三支决策聚类方法[J].计算机应用,2016,36(8):2061-2065.
[50]薛占熬,朱泰隆,薛天宇,等.基于直觉模糊集的三支决策模型[J].计算机科学,2016,43(6):283-288.
[51]薛占熬,刘杰,朱泰隆,等.基于覆盖的Sugeno测度粗糙集模型及其三支决策[J].计算机科学,2016,43(3):285-290.
[52]王磊,黄河笑,吴兵,等.基于主题与三支决策的文本情感分析[J].计算机科学,2015,42(6):93-96.
[53]周哲,商琳.一种基于动态词典和三支决策的情感分析方法[J].山东大学学报:工学版,2015,45(1):19-23.
[54]朱艳辉,田海龙,刘璟,等.基于三支决策的新闻情感关键句识别方法[J].山西大学学报:自然科学版,2015,38(4):595-600.
[55]YAO Y.Rough sets and three-way decisions[C]//International Conference on Rough Sets and Knowledge Technology.2015:62-73.
[56]YAO Y.Three-way decisions and cognitive computing[J].Cognitive Computation,2016,8(4):543-554.
[57]LI M,WANG G.Approximate concept construction with three-way decisions and attribute reduction in incomplete contexts[J].Knowledge-Based Systems,2016,91:165-178.
[58]李美争,王国胤.三支近似概念格中基于对象-概念辨识矩阵的属性约简方法[J].控制与决策,2016,31(10):1779-1784.
[59]SAVCHENKO A V.Fast multi-class recognition of piecewise regular objects based on sequential three-way decisions and granular computing[J].Knowledge-Based Systems,2016,91:252-262.
[60]ZHANG H Y,YANG S Y,MA J M.Ranking interval sets based on inclusion measures and applications to three-way decisions[J].Knowledge-Based Systems,2016,91:62-70.
[61]PETERS J F,RAMANNA S.Proximal three-way decisions:Theory and applications in social networks[J].Knowledge-Based Systems,2016,91:4-15.
[62]HU B Q,WONG H,YIU K F C.On two novel types of three-way decisions in three-way decision spaces[J].International Journal of Approximate Reasoning,2017,82:285-306.
[63]LANG G,MIAO D,CAI M.Three-way decision approaches to conflict analysis using decision-theoretic rough set theory[J].Information Sciences,2017,406:185-207.
[64]LI X,SUN B,SHE Y,et al.Generalized matroids based on three-way decision models[J].International Journal of Approximate Reasoning,2017,90:192-207.
[65]HAO C,LI J,FAN M,et al.Optimal scale selection in dynamic multi-scale decision tables based on sequential threeway decisions[J].Information Sciences,2017,415:213-232.