命题逻辑公式模糊软集语义及其在决策分析中的应用

doi:10.16451/j.cnki.issn1003-6059.201803002

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Abstract Soft propositional logic formulas based on a fuzzy soft set S=(F,A) of domain U are introduced, and the fuzzy soft semantics interpretation of soft propositional logic formulas is provided. A decision fuzzy information system is transformed into a decision fuzzy soft set, and a soft decision rule is expressed as an implication logic formula composed of some atomic formulas. The concepts of basic truth degree, condition truth and absolute truth are introduced. The availability and the rationality of soft decision rule are evaluated from different aspects, such as sufficiency and necessity. An extraction algorithm of typical decision rules based on the decision soft set and a recommendation algorithm based on soft decision analysis are proposed, and the practical examples and numerical experiment verify the effectiveness of the proposed algorithms.

Key words： Decision Fuzzy Information System Decision Fuzzy Soft Set Soft Logic Formula Soft Decision Rule Soft Truth Degree

Received: 26 October 2017

ZTFLH:

TP 391

Fund:Supported by Natural Science Foundation of Hunan Province(No.2016JJ6138,2017JJ2241,2017JJ3287), Social Sciences Fund Project of Hunan Province(No.16YBA329,13YBB205),Science Research Project of Education Department of Hunan Province(No.16B244), Science Research Project of Xiangnan University(No.2014XJ54)

Corresponding Authors: ZHANG Jialu, master, professor. His research interests include non-classical mathematical logics, approximate reasoning theory and intelligent information processing theory.

About author:: WU Xia, master, associate professor. Her research interests include non-classical mathe-matical logics and approximate reasoning theory.WANG Luda, Ph.D., engineer. His research interests include data analysis.

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Cite this article:

WU Xia,ZHANG Jialu,WANG Luda. Fuzzy Soft Set Semantics of Propositional Logic Formulas and Its Application to Decision Analysis[J]. , 2018, 31(3): 208-218.

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http://manu46.magtech.com.cn/Jweb_prai/EN/10.16451/j.cnki.issn1003-6059.201803002 OR http://manu46.magtech.com.cn/Jweb_prai/EN/Y2018/V31/I3/208

[1] MOLODTSOV D. Soft Set Theory-First Results. Computers and Mathematics with Applications, 1999, 37(4/5): 19-31.
[2] FENG F, LI C X, DAVVAZ B, et al. Soft Sets Combined with Fuzzy Sets and Rough Sets: A Tentative Approach. Soft Computing, 2010, 14(9): 899-911.
[3] FENG F, LIU X Y, LEOREANU-FOTEA V, et al. Soft Sets and Soft Rough Sets. Information Science, 2011, 181(6): 1125-1137.
[4] ALI M I. A Note on Soft Sets, Rough Soft Sets and Fuzzy Soft Sets. Applied Soft Computing, 2011, 11(4): 3329-3332.
[5] ALI M I, SHABIR M. Logic Connectives for Soft Sets and Fuzzy Soft Sets. IEEE Transactions on Fuzzy Systems, 2014, 22(6): 1431-1442.
[6] JIANG Y C, TANG Y, CHEN Q M, et al. Extending Soft Sets with Description Logics. Computers and Mathematics with Applications, 2010, 59(6): 2087-2096.
[7] ZHAN J M, LIU Q, HERAWAN T. A Novel Soft Rough Set: Soft Rough Hemirings and Corresponding Multicriteria Group Decision Making. Applied Soft Computing, 2017, 54: 393-402.
[8] ROY A R, MAJI P K. A Fuzzy Soft Set Theoretic Approach to Decision Making Problems. Journal of Computational and Applied Mathematics, 2007, 203(2): 412-418.
[9] JIANG Y C, LIU H, TANG Y, et al. Semantic Decision Making Using Ontology-Based Soft Sets. Mathematical and Computer Mode-lling, 2011, 53(5): 1140-1149.
[10] 耿生玲,李永明,刘震.关联规则挖掘的软集包含度方法.电子学报, 2013, 41(4): 804-809.
(GENG S L, LI Y M, LIU Z. An Approach to Association Rules Mining Using Inclusion Degree of Soft Sets. Acta Electronica Sinica, 2013, 41(4): 804-809.)
[11] MUSHRIF M M, SENGUPTA S, RAY A K. Texture Classification Using a Novel, Soft Set Theory Based Classification Algorithm // Proc of the 7th Asian Conference on Computer Vision. Berlin, Germany: Springer, 2006, I: 246-254.
[12] KALAYATHANKAL S J, SINGH G S. A Fuzzy Soft Flood Alarm Model. Mathematics and Computers in Simulation, 2010, 80(6): 887-893.
[13] MAJI P K, ROY A R, BISWAS R. An Application of Soft Sets in a Decision Making Problem. Computers and Mathematics with Applications, 2002, 44(8/9): 1077-1083.
[14] MA X L, LIU Q, ZHAN J M. A Survey of Decision Making Me-thods Based on Certain Hybrid Soft Set Models. Artificial Intelligence Review, 2017, 47(4): 507-530.
[15] ZHAN J M, ALI M I, MEHMOOD N. On a Novel Uncertain Soft Set Model: Z-soft Fuzzy Rough Set Model and Corresponding Decision Making Methods. Applied Soft Computing, 2017, 56: 446-457.
[16] 余力,刘鲁.电子商务个性化推荐研究.计算机集成制造系统, 2004, 10(10): 1306-1313.
(YU L, LIU L. Research on Personalized Recommendations in E-business. Computer Integrated Manufacturing Systems, 2004, 10(10): 1306-1313)
[17] 许海玲,吴潇,李晓东,等.互联网推荐系统比较研究.软件学报, 2009, 20(2): 350-362.
(XU H L, WU X, LI X D, et al. Comparison Study of Internet Recommendation Systems. Journal of Software, 2009, 20(2): 350-362.)
[18] 李聪,梁昌勇,马丽.基于领域最近邻的协同过滤推荐算法.计算机研究与发展, 2008, 45(9): 1532-1538.
(LI C, LIANG C Y, MA L. A Collaborative Filtering Recommendation Algorithm Based on Domain Nearest Neighbor. Journal of Computer Research and Development, 2008, 45(9): 1532-1538.)
[19] 周彤,张家录.随机信息系统属性相关性及在知识约简中的应用.计算机工程与应用, 2011, 47(14): 140-142.
(ZHOU T, ZHANG J L. Relativity of Attributes in Random Information Systems and Its Application to Knowledge Reduction. Computer Engineering and Applications, 2011, 47(14): 140-142.)
[20] 张文修,梁怡,吴伟志.信息系统与知识发现.北京:科学出版社, 2003.
(ZHANG W X, LIANG Y, WU W Z. Information Systems and Knowledge Discoveries. Beijing, China: Science Press, 2003.)
[21] 胡宝清.模糊集理论基础.第2版.武汉:武汉大学出版社, 2010.
(HU B Q. Foundation of Fuzzy Sets Theory. 2nd Edition. Wuhan, China: Wuhan University Press, 2010.)
[22] ZHANG J L, WU X, LIU X L. Approximation Reasoning Models Based on Random Variables Sequence. Journal of Intelligent & Fuzzy Systems, 2014, 26(3): 1465-1479.
[23] 张家录,陈雪刚,赵晓东.经典命题逻辑的概率语义及其应用.计算机学报, 2014, 37(8): 1775-1785.
(ZHANG J L, CHEN X G, ZHAO X D. Theory of Probability Se-
mantics of Classical Propositional Logic and Its Application. Chinese Journal of Computers, 2014, 37(8): 1775-1785.)
[24] 吴霞,张家录.随机模糊环境下的命题逻辑真度理论.模式识别与人工智能, 2017, 30(4): 289-301.
(WU X, ZHANG J L. Truth Theory of Proposition Logic under Random Fuzzy Environment. Pattern Recognition and Artificial Intelligence, 2017, 30(4): 289-301.)
[25] KIM J K, CHO Y H, KIM W J, et al. A Personalized Recommendation Procedure for Internet Shopping Support. Electronic Commerce Research and Applications, 2002, 1(3/4): 301-313.
[26] FENG F, AKRAM M, DAVVAZ B J, et al. Attribute Analysis of Information Systems Based on Elementary Soft Implications. Knowledge-Based Systems, 2014, 70: 281-292.