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《山东大学学报(理学版)》 ›› 2023, Vol. 58 ›› Issue (9): 94-104.doi: 10.6040/j.issn.1671-9352.0.2022.430

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不完备邻域加权多粒度决策理论粗糙集及三支决策

王茜1,2(),张贤勇1,2,*()   

  1. 1. 四川师范大学数学科学学院, 四川 成都 610066
    2. 四川师范大学智能信息与量子信息研究所, 四川 成都 610066
  • 收稿日期:2022-08-19 出版日期:2023-09-20 发布日期:2023-09-08
  • 通讯作者: 张贤勇 E-mail:2055778250@qq.com;xianyongzh@sina.com
  • 作者简介:王茜(1997—), 女, 硕士研究生, 研究方向为粗糙集与粒计算. E-mail: 2055778250@qq.com
  • 基金资助:
    四川省科技计划项目(2021YJ0085);四川省科技计划项目(2022ZYD0001)

Incomplete neighborhood weighted multi-granularity decision-theoretic rough sets and three-way decision

Qian WANG1,2(),Xianyong ZHANG1,2,*()   

  1. 1. School of Mathematical Sciences, Sichuan Normal University, Chengdu 610066, Sichuan, China
    2. Institute of Intelligent Information and Quantum Information, Sichuan Normal University, Chengdu 610066, Sichuan, China
  • Received:2022-08-19 Online:2023-09-20 Published:2023-09-08
  • Contact: Xianyong ZHANG E-mail:2055778250@qq.com;xianyongzh@sina.com

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摘要：

关注粒度间差异性和不平衡性, 利用粒度分类能力挖掘粒度权重, 从而构建两种基于粒度加权策略的粗糙集模型实施相关的三支决策。首先, 根据边界域对知识划分的影响定义粒度重要度并诱导粒度权重, 融合权重与条件概率提出不完备邻域加权多粒度决策理论粗糙集, 得到三支决策。然后, 考虑属性的特定限制, 建立不完备邻域加权限制多粒度决策理论粗糙集, 得到相关性质与相互关系。最后, 利用可变三支决策进行实例分析与数据实验, 证实新模型的合理性与优越性。关于不完备邻域多粒度决策理论粗糙集, 两种加权模型优化改进与系统扩张了对应的基础模型, 有利于相关数据分析与决策制定。

关键词: 不完备邻域信息系统, 多粒度粗糙集, 决策理论粗糙集, 三支决策, 粒度重要度

Abstract:

Concerning the differences and imbalances of granularities, the classification capacity of granularity is considered to mine the granularity weight, and two rough set models based on the granularity weighting strategy are constructed to implement three-way decision. At first, the granularity significance is defined by the influence of boundary region for knowledge classification, and it induces the granularity weight; by fusing the granularity weights and condition probabilities, incomplete neighborhood weighted multi-granularity decision-theoretic rough sets are modeled to establish three-way decision. Then considering the specific restriction of important attribute, incomplete neighborhood weighted-restrictive multi-granularity decision-theoretic rough sets are further proposed, and relevant properties and mutual relationships are acquired. At last, example demonstrations and data experiments are performed by variable three-way decision, and the rationality and superiority of new models are verified. Regarding incomplete neighborhood multi-granularity decision-theoretic rough sets, the two weighted models optimally improve and systematically extend corresponding basic models, and they facilitate relevant data analysis and decision making.

Key words: incomplete neighborhood information system, multi-granularity rough set, decision-theoretic rough set, three-way decision, granularity significance

中图分类号: 

  • TP18

表1

三好学生测评信息表"

U A B C class
a1 a2 b1 b2 c1 c2
u1 0.47 0.66 0.76 0.61 0.43 0.31 0
u2 0.73 0.62 0.54 0.76 0.56 0.44 1
u3 0.21 * 0.35 0.26 0.46 0.59 0
u4 0.76 0.61 0.87 0.67 0.26 0.19 1
u5 0.45 0.54 0.67 * 0.75 0.66 0
u6 0.88 0.78 0.34 0.47 0.56 0.62 1
u7 0.17 0.23 0.45 0.36 0.45 0.52 0
u8 0.95 0.86 0.76 0.64 0.67 * 1
u9 0.65 0.57 * 0.57 0.34 0.27 0
u10 0.87 0.81 0.88 0.76 0.47 0.58 1
u11 * 0.64 0.62 0.59 0.54 0.62 0
u12 0.31 0.46 0.46 0.71 0.74 0.65 1

表2

三好学生测评代价函数"

Γ X ~X
aP $\tilde{\lambda}_{\mathrm{PP}}=[0，0.2]$ $\tilde{\lambda}_{\mathrm{PN}}=[0.8，1.2]$
aB $\tilde{\lambda}_{\mathrm{BP}}=[0.2，0.6]$ $\tilde{\lambda}_{\mathrm{BN}}=[0.3，0.6]$
aN $\tilde{\lambda}_{\mathrm{NP}}=[0.8，1.2]$ $\tilde{\lambda}_{\mathrm{NN}}=[0.2，0.4]$

表3

乐观、悲观、平均多粒度决策理论粗糙集模型三支区域"

模型 k值 POS(X)；NEG(X)；BND(X)
乐观 0.0 {u2, u4, u6, u8, u10}；{u1, u3, u5, u7, u9, u11, u12}；Ø
0.2 {u2, u4, u6, u8, u10}；{u1, u3, u5, u7, u9, u11, u12}；Ø
0.4 {u2, u4, u6, u8, u10}；{u1, u3, u5, u7, u9, u11, u12}；Ø
0.6 {u2, u4, u6, u8, u10}；{u1, u3, u5, u7, u9, u11, u12}；Ø
0.8 {u2, u4, u6, u8, u10}；{u1, u3, u5, u7, u9, u11, u12}；Ø
1.0 {u2, u4, u6, u8, u10}；{u1, u3, u5, u7, u9, u11, u12}；Ø
悲观 0.0 Ø；{u2, u4, u6, u8, u10, u12}；{u1, u3, u5, u7, u9, u11}
0.2 Ø；{u2, u4, u6, u8, u10, u12}；{u1, u3, u5, u7, u9, u11}
0.4 {u4}；{u2, u6, u8, u10, u12}；{u1, u3, u5, u7, u9, u11}
0.6 {u4}；{u2, u6, u8, u10, u12}；{u1, u3, u5, u7, u9, u11}
0.8 {u4}；{u2, u6, u8, u10, u12}；{u1, u3, u5, u7, u9, u11}
1.0 {u4}；{u2, u6, u8, u10, u12}；{u1, u3, u5, u7, u9, u11}
平均 0.0 {u2, u4, u6, u10}；{u1, u5, u8, u9, u11, u12}；{u3, u7}
0.2 {u2, u4, u6, u10}；{u5, u8, u9, u11, u12}；{u1, u3, u7}
0.4 {u2, u4, u6, u10}；{u5, u8, u9, u11, u12}；{u1, u3, u7}
0.6 {u2, u4, u6, u8, u10}；{u5, u9, u11, u12}；{u1, u3, u7}
0.8 {u2, u4, u6, u8, u10}；{u5, u11, u12}；{u1, u3, u7, u9}
1.0 {u2, u4, u6, u8, u10}；{u5, u11, u12}；{u1, u3, u7, u9}

表4

两种加权多粒度决策理论粗糙集模型的三支区域"

模型 k值 $\left(\operatorname{Sig}_{A}(X)，\operatorname{Sig}_{B}(X)，\operatorname{Sig}_{C}(X)\right)$ $\operatorname{POS}(X) ; \operatorname{NEG}(X) ; \operatorname{BND}(X)$
加权 0.0 (0.5, 0.5, 0.333) {u2, u4, u6, u10}；{u3, u5, u8, u9, u11, u12}；{u1, u7}
0.2 (0.5, 0.5, 0.333) {u2, u4, u6, u10}；{u5, u8, u9, u11, u12}；{u1, u3, u7}
0.4 (0.583, 0.5, 0.667) {u2, u4, u6, u8, u10}；{u5, u9, u11, u12}；{u1, u3, u7}
0.6 (0.583, 0.5, 0.667) {u2, u4, u6, u8, u10}；{u5, u11, u12}；{u1, u3, u7, u9}
0.8 (0.333, 0.286, 0.381) {u2, u4, u6, u8, u10}；{u5, u11, u12}；{u1, u3, u7, u9}
1.0 (0.32, 0.32, 0.36) {u2, u4, u6, u8, u10}；{u5, u11, u12}；{u1, u3, u7, u9}
加权限制 0.0 (0.5, 0.5, 0.333) {u2, u4, u10}；{u5, u8, u12}；{u1, u3, u6, u7, u9, u11}
0.2 (0.5, 0.5, 0.333) {u2, u4, u10}；{u5, u8, u12}；{u1, u3, u6, u7, u9, u11}
0.4 (0.583, 0.5, 0.667) {u2, u4, u8, u10}；{u5, u12}；{u1, u3, u6, u7, u9, u11}
0.6 (0.583, 0.5, 0.667) {u2, u4, u8, u10}；{u5, u12}；{u1, u3, u6, u7, u9, u11}
0.8 (0.333, 0.286, 0.381) {u2, u4, u8, u10}；{u5, u12}；{u1, u3, u6, u7, u9, u11}
1.0 (0.32, 0.32, 0.36) {u2, u4, u8, u10}；{u5, u12}；{u1, u3, u6, u7, u9, u11}

表5

UCI数据集描述"

编号 数据集 对象数 条件属性数 决策类数
(a) Wine 178 13 3
(b) Wpbc 198 33 2
(c) Wdbc 569 30 2
(d) Sonar 208 60 2

表6

代价函数"

Γ X ~X
aP $\tilde{\lambda}_{\mathrm{PP}}=[0，0]$ $\tilde{\lambda}_{\mathrm{PN}}=[0.9，1.1]$
aB $\tilde{\lambda}_{\mathrm{BP}}=[0.15，0.35]$ $\tilde{\lambda}_{\mathrm{BN}}=[0.02，0.22]$
aN $\tilde{\lambda}_{\mathrm{NP}}=[0.26，0.46]$ $\tilde{\lambda}_{\mathrm{NN}}=[0，0]$

图1

三种多粒度决策理论粗糙集模型正区域大小变化"

图2

三种多粒度决策理论粗糙集模型边界域大小变化"

图3

三种多粒度决策理论粗糙集模型负区域大小变化"

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