《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (10): 1-6.

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外P-模糊集的截集与扩展粗集模型

1. 山东财经大学数学与数量经济学院, 山东 济南 250014
• 出版日期:2020-10-20 发布日期:2020-10-07
• 作者简介:郝秀梅(1965— ),女,博士,教授,研究方向为系统决策理论与方法. E-mail:hxm0912@126.com

Cut sets of outer P-fuzzy sets and extended rough sets models

HAO Xiu-mei, LIU Ji-qin

1. School of Mathematic and Quantitative Economics, Shandong University of Finance and Economics, Jinan 250014, Shandong, China
• Online:2020-10-20 Published:2020-10-07

Abstract: The P-fuzzy sets are a pair of inner and outer P-fuzzy sets. Inner and outer P-fuzzy sets are two different kinds of dynamic fuzzy sets. The cut sets method is frequently used in fuzzy sets discussed. The concepts of λ-cut sets, strong λ-cut sets, interval cut sets and cut sets granularity are proposed, and the cut sets and interval cut sets granularity theorems of outer P-fuzzy sets are discussed. Then, the interval cut sets decomposition theorems of outer P-fuzzy sets are given. By using the concept of the outer P-fuzzy rough membership function, four rough sets extended models are proposed such as FF) rough sets, (1F,0F) rough sets, FF)probability rough sets and FF) variable precision rough sets. The FF)rough sets theorems of the outer P-fuzzy sets are discussed. In the end, the quantitative characteristics and relationship theorem are given.

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 [1] ZADEH L A. Fuzzy sets[J]. Information and Control, 1965, 8(3):338-353.[2] DUBOIS D, PRADE B. The three senmantics of fuzzy sets[J]. Fuzzy Sets and Systems, 1997(90):141-150.[3] GRESCONI G, TURKSEN B. Canonical forms of fuzzy teuthoods by meta-theory based model logic[J]. Information Sciences, 2001(131):157-194.[4] 陈水利, 李敬功, 王向松. 模糊集理论及其应用[M]. 北京: 科学出版社, 2005: 10-19. CHEN Shuili, LI Jinggong, WANG Xiangsong. Fuzzy sets theory and applications[M]. Beijing: Science Press, 2005: 10-19.[5] 袁修久, 张文修. 模糊粗糙集的包含度和相似度[J]. 模糊系统与数学, 2005, 19(1):111-115. YUAN Xiujiu, ZHANG Wenxiu. The inclusion degree and similarity degree of fuzzy rough sets[J]. Fuzzy Systems and Mathematics, 2005, 19(1):111-115.[6] 史开泉, 李岐强. 双枝模糊决策与决策识别问题[J]. 中国工程科学, 2001,3(1):71-77. SHI Kaiquan, LI Qiqiang. Both-branch fuzzy decision and problems on decision discernment[J]. Engineering Science, 2001, 3(1):71-77.[7] 史开泉, 崔玉泉. 双枝模糊决策与决策加密-认证[J].中国科学(E), 2003,33(2):154-163. SHI Kaiquan, CUI Yuquan. Both-branch fuzzy decision and problems on decision encryption authentication[J]. Science in China(Series E), 2003, 33(2):154-163.[8] 闫立梅, 徐风生, 史开泉. P-模糊集(A(-overF),AF)及其应用[J]. 计算机科学,2011,38(5):194-198. YAN Limei, XU Fengsheng, SHI Kaiquan. P-fuzzy sets(A(-overF),AF)and its applications[J]. Computer Science, 2011, 38(5):194-198.[9] 史开泉. P-集合[J].山东大学学报(理学版), 2008, 43(11):77-84. SHI Kaiquan. P-sets[J]. Journal of Shandong University(Natural Science), 2008, 43(11):77-84.[10] 史开泉. P-集合与它的应用特征[J].计算机科学,2010,37(8):1-8. SHI Kaiquan. P-sets and its applied characteristics[J]. Computer Science, 2010, 37(8):1-8.[11] 闫立梅. 内P-模糊集并-分离及其属性特征[J].山东大学学报(理学版), 2012, 47(1):104-109. YAN Limei. Union-separation of an internal P-fuzzy set and its attribute characteristics[J]. Journal of Shandong University(Natural Science), 2012, 47(1):104-109.[12] 郝秀梅, 蒋秀青. 概率粗信息矩阵的结构特征[J].模糊系统与数学, 2017, 31(3):153-158. HAO Xiumei, JIANG Xiuqing. Structure characteristics on probability rough information matrix[J]. Fuzzy Systems and Mathematics, 2017, 31(3):153-158.[13] 郝秀梅, 李宁宁. P-信息隐藏挖掘的数量特征及应用[J]. 山东大学学报(理学版), 2019, 54(9):9-15. HAO Xiumei, LI Ningning. The quantitative characteristics and applications of P-information hidden mining[J]. Journal of Shandong University(Natural Science), 2019, 54(9):9-14.[14] 刘卫锋, 白雪. 粗糙模糊集的区间值水平分解定理[J]. 模糊系统与数学, 2016, 30(4):156-161. LIU Weifeng, BAI Xue. Interval-valued decomposition theorems of rough fuzzy sets[J]. Fuzzy Systems and Mathematics, 2016, 30(4):156-161.[15] 史开泉,崔玉泉. S-粗集与粗决策[M]. 北京: 科学出版社, 2005: 170-185. SHI Kaiquan, CUI Yuquan. S-rough sets and rough decision[M]. Beijing: Science Press, 2005: 170-185.[16] 张文修, 吴伟志, 梁吉业, 等. 粗糙集理论与方法[M]. 北京: 科学出版社, 2001: 132-155. ZHANG Wenxiu, WU Weizhi, LIANG Jiye, et al. Rough sets theory and method[M]. Beijing: Science Press, 2001: 132-155.[17] 史开泉. 大数据结构-逻辑特征与大数据规律, 山东大学学报(理学版), 2019, 54(2):1-29. SHI Kaiquan. Big data structure-logic characteristics and big data law[J]. Journal of Shandong University(Natural Science), 2019, 54(2):1-29.[18] HAO Xiumei, GUO Huifang, JIANG Xiuqing. Multi-attributes risk investment decision making based on dynamic probability rough sets[C] //Proceedings of the 2017 International Conference on Natural Computation, Fuzzy Systems and Knowledge Discovery. Guilin: IEEE, 2017: 2419-2423.
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