直觉模糊数决策粗糙集

doi:10.11896/j.issn.1002-137X.2018.02.044

摘要/Abstract

摘要： 决策粗糙集模型的代价函数不包含模糊概念,不能够细腻地描述包含模糊信息的决策。针对上述不足,首先将模型中精确值的代价函数拓展为直觉模糊数,构建直觉模糊数决策粗糙集模型。然后,通过分析基于直觉模糊数下、上理想的决策预期代价函数,形成保守、激进、可变的决策策略和相应的决策规则,并分析其相关数学性质。最后,通过对战略目标防空部署策略的风险分析来说明模型的具体应用过程。

关键词: 决策粗糙集,代价函数,直觉模糊数,下理想,上理想

Abstract: The cost function of decision-theoretic rough set does not include fuzzy concept,which can not describe the decision of the fuzzy information discreetly.For the above shortage,firstly,the concept of precise value of loss function was generalized to intuitionistic fuzzy numbers and the intuitionistic fuzzy numbers decision-theoretic rough set was established.Then,the expected loss with intuitionistic fuzzy numbers based on down-ideal and up-ideal was analyzed.The strategies based on conservatism,activism and variable semantics were described and decision rules were derived.The corresponding propositions of the intuitionistic fuzzy numbers decision-theoretic rough sets were analyzed.Finally,an example of disposition schemes for strategic target air-defense operation was given to illuminate the proposed model in applications.

Key words: Decision-theoretic rough sets,Loss function,Intuitionistic fuzzy numbers,Down-ideal,Up-ideal

陈玉金,李续武. 直觉模糊数决策粗糙集[J]. 计算机科学, 2018, 45(2): 254-260. https://doi.org/10.11896/j.issn.1002-137X.2018.02.044

CHEN Yu-jin and LI Xu-wu. Intuitionistic Fuzzy Numbers Decision-theoretic Rough Sets[J]. Computer Science, 2018, 45(2): 254-260. https://doi.org/10.11896/j.issn.1002-137X.2018.02.044

参考文献

[1] YAO Y Y,WONG S K M,LINGRAS P.A decision-theoreticrough set model[C]∥Proceedings of the 5th International Symposium on Methodologies for Intelligent Systems.North-Holland,1990:17-25.
[2] PAWLAK Z.Rough sets [J].International Journal of Computer and Information Sciences,1982,11(5):341-356.
[3] PAWLAK Z.Rudiments of rough sets [J].Information Science,2007,177(1):3-27.
[4] YANG X P,YAO J T.Modeling multi-agent three-way deci-sions with decision-theoretic rough sets[J].Fundamental Informaticae,2012,5(2-3):157-171.
[5] LI F,MIAO D Q,LIU C H,et al.Image segmentation algorithm based on the decision-theoretic rough set model[J].CAAI Transactions on Intelligent Systems,2014,9(2):143-147.(in Chinese) 李峰,苗夺谦,刘财辉,等.基于决策粗糙集的图像分割[J].智能系统学报,2014,9(2):143-147.
[6] LI R,GAO C Y,ZHANG L Y.The distributed fault diagnosis of power networks based on bayesian rough set method[J].Journal of North China Electric Power University (Natural Science Edition),2010,7(3):1-7.(in Chinese) 栗然,高聪颖,张烈勇.基于粗糙集-贝叶斯方法的分布式电网故障诊断[J].华北电力大学学报(自然科学版),2010,7(3):1-7.
[7] MISHRA H,MISHRA A,SHIV B.In praise of vagueness:malleability of vague information as a performance-booster[J].Psychological Science,2011,22(6):733
[8] LIU D,LI T R,LIANG D C.Fuzzy Decision-theoretic RoughSets[J].Computer Science,2012,39(12):25-29.(in Chinese) 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.
[9] LIU D,LI T R,LI H X.Interval-valued Decision-theoreticRough Sets[J].Computer Science,2012,39(7):178-181.(in Chinese) 刘盾,李天瑞,李华雄.区间决策粗糙集[J].计算机科学,2012,39(7):178-181.
[10] LIANG D C,LIU D,WITOLD P,et al.Triangular fuzzy decision-theoretic rough sets[J].International Journal of Approximate Reasoning,2013,54(8):1087-1106.
[11] ZHONG Y H,ZHANG P X.Generalized trapezoidal decision-theoretic rough sets[J].Mathematics in Practice and Theory,2015,45(6):82-88.(in Chinese) 钟映竑,张培新.广义梯形模糊数决策粗糙集[J].数学的实践与认识,2015,5(6):82-88.
[12] LIANG D C,LIU D.Deriving three-way decisions from intuitionistic fuzzy decision-theoretic rough sets[J].Information Science,2015,300(C):28-48.
[13] LIANG D C,XU Z S,LIU D.Three-way decisions with intui-tionistic fuzzy decision-theoretic rough sets based on point ope-rators[J].Information Science,2017,375:183-201.
[14] XUE Z A,ZHU T L,XUE T Y,et al.Model of three-way decision theory based on intuitionistic fuzzy sets[J].Computer Science,2016,3(6):283-288.(in Chinese) 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,2016,3(6):283-288.
[15] BURILLO P,BUSTINCE H,MOHEDANO V.Some definition of intuitionistic fuzzy number[C]∥Fuzzy based expert systems.Bulgaria:fuzzy Bulgarian enthusiasts,1994:28-30.
[16] XU Z S,YAGER R R.Some geometric aggregation operatorsbased on intuitionistic fuzzy sets[J].International Journal of General Systems,2006,35(4):417-433.
[17] LV J H.The research of intuitionistic fuzzy numbers and its application in multi-attribute[D].Fuxin:Liaoning Technology University,2011.(in Chinese) 吕金辉.直觉模糊数的研究及在多属性决策中的应用[D].阜新:辽宁工程技术大学,2011.
[18] GUO S C,LV J H.The research of the intuitionistic fuzzy numbers[J].Fuzzy Systems and Mathematics,2013,27(5):11-20.(in Chinese) 郭嗣琮,吕金辉.直觉模糊数的研究[J].模糊系统与数学,2013,27(5):11-20.

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