Computer Science ›› 2018, Vol. 45 ›› Issue (2): 135-139.

### Study on Three-way Decisions Based on Intuitionistic Fuzzy Probability Distribution

XUE Zhan-ao, XIN Xian-wei, YUAN Yi-lin and LV Min-jie

• Online:2018-02-15 Published:2018-11-13

Abstract: The fusion of intuitionistic fuzzy sets theory and possibility theory is a hot spot for dealing with uncertain questions.This paper proposed a three-way decisions model based on the probability distribution of intuitionistic fuzzy probability measurement (IFPM).First of all,the intuitionistic fuzzy decision space and the possibility distribution of the space were defined,and the properties of them were proved.Then,the calculation method of possibility means value for domain object membership degree and the non-membership degree was given.Thirdly,by analyzing the relationship possibility mean value of domain object membership degree and the non-membership degree between decision threshold,its probability distribution was discussed.Thus the three-way decisions model based on the probability distribution to the possibility distribution of transformation relations was expanded.An IFPM decision-making risk calculation method was given.Finally,this paper provided the formulas and analyzed the dynamic decision process of the three-way decisions through analyzing the changing of IFPM under different domain elements,and validated the effectiveness of the model through examples.

 [1] ZADEH L A.Fuzzy sets[J].Information & Control,1965,8(65):338-353. [2] ATANSSOV K T.Intuitionistic fuzzy sets[J].Fuzzy sets and Systems,1986,20(1):87-96. [3] MENG F,CHEN X.Entropy and similarity measure of Atanas-sov’s intuitionistic fuzzy sets and their application to pattern recognition based on fuzzy measures[J].Pattern Analysis and Applications,2016,19(1):11-20. [4] ZHOU L.On Atanassov’s Intuitionistic Fuzzy Sets in the Complex Plane and the Field of Intuitionistic Fuzzy Numbers[J].IEEE Transactions on Fuzzy Systems,2016,24(2):253-259. [5] SONG Y,WANG X,LEI L,et al.A novel similarity measure on intuitionistic fuzzy sets with its applications[J].Applied Intelligence,2015,42(2):252-261. [6] XUE Z A,SI X M,ZHU T L,et al.Study on model of covering-based rough intuitionistic fuzzy sets[J].Computer Science,2016,43(1):44-48,68.(in Chinese) 薛占熬,司小朦,朱泰隆,等.覆盖粗糙直觉模糊集模型的研究[J].计算机科学,2016,43(1):44-48,68. [7] ZADEH L A.Possibility theory and its application to information analysis[C]∥Proceedings of International Colloquium on Information Theory.Cachan:Juillet,1978:173-182. [8] DUBOIS D,ESTEVA F,GODO5 L,et al.An information-based discussion of vagueness[C]∥The 10th IEEE International Conference on Fuzzy Systems,2001.IEEE,2001:781-784. [9] JI L N.Research on fusion theory of possibility distribution and its engineer application[D].Taiyuan:North University of China,2015.(in Chinese) 吉琳娜.可能性分布合成理论及其工程应用研究[D].太原:中北大学,2015. [10] ZADEH L A.A note on modal logic and possibility theory[J].Information Sciences,2014,279:908-913. [11] PAWLAK Z.Rough sets[J].International Journal of Computer &Information Sciences,1982,11(5):341-356. [12] YAO Y Y,WONG S K M,LINGRAS P.A decision- theoretic rough set model[C]∥Proceedings of the 5th International Symposium on Methodologies for Intelligent Systems.Tennessee:North-Holland,1990:17-25. [13] ZIARKO W.Variable precision rough set model[J].Journal of Computer and System Sciences,1993,46(1):39-59. [14] SLE D,ZIARKO W.The investigation of the Bayesian rough set model[J].International Journal of Approximate Reasoning,2005,40(1):81-91. [15] YAO Y Y.Probabilistic rough set approximations[J].International Journal of Approximate Reasoning,2008,49(2):255-271. [16] YAO Y.Three-Way Decision:An Interpretation of Rules inRough Set Theory[C]∥International Conference on Rough Sets and Knowledge Technology.Springer-Verlag,2009:642-649. [17] YAO Y Y.Three-way decisions with probabilistic rough sets[J].Information Sciences,2010,180(3):341-353. [18] LIU D,LI T,LIANG D.Three-way Decisions in dynamic decision-theoretic rough sets[C]∥International Conference on Rough Sets and Knowledge Technology.Springer Berlin Heidelberg,2013:291-301. [19] ZHANG Y P,ZOU H J,ZHAO S.Cost-sensitive Three-way Decisions model based on CAA[J].Journal of NanJing University(Natural Sciences),2015,51(2):447-452.(in Chinese) 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(自然科学版),2015,51(2):447-452. [20] XUE Z A,ZHU T L,XUE T Y,et al.Three-way Decisionsmodel based on intuitionistic fuzzy sets[J].Computer Science,2016,43(6):285-288,297.(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,2016,43(6):285-288,297. [21] YU H,WANG G Y,LI T Y,et al.Three-way decisions:Me-thods and practices for complex problem solving[M].Beijing:Science Press,2015:20-48.(in Chinese) 于洪,王国胤,李天瑞,等.三支决策:复杂问题求解方法与实践[M].北京:科学出版社,2015:20-48. [22] YAO Y Y.Three-Way Decisions and Cognitive Computing[J].Cognitive Computation,2016(4):1-12. [23] 刘盾,李天瑞,苗夺谦,等.三支决策和粒计算[M].北京:科学出版社,2013:1-13. [24] KLIR G J,BEHZAD P,GEOREG J,et al.Probability-possibility transformations:a comparison[J].International Journal of Ge-neral Systems,1993,21(3):291-310. [25] DUBOIS D,PRADE H,SANDRI S.On Possibility Probability Transformations[M]∥Fuzzy Logic.Netherlands:Springer,1997:103-112.
 No related articles found!
Viewed
Full text

Abstract

Cited

Shared
Discussed