基于集对信息粒空间的三支决策模型及应用

doi:10.11959/j.issn.1000-436x.2016242

通信学报 ›› 2016, Vol. 37 ›› Issue (Z1): 15-24.doi: 10.11959/j.issn.1000-436x.2016242

基于集对信息粒空间的三支决策模型及应用

张春英^1,²,王立亚^1,²(),李明霞^1,²,刘保相^1,²

¹ 华北理工大学理学院，河北唐山 063009
² 河北省数据科学与应用重点实验室，河北唐山 063009

出版日期:2016-10-25 发布日期:2017-01-17
基金资助:
国家自然科学基金资助项目;国家自然科学基金资助项目;河北省自然科学基金资助项目;华北理工大学青年科学研究基金资助项目

Model of three-way decision based on the space of set pair information granule and its application

Chun-ying ZHANG^1,²,Li-ya WANG^1,²(),Ming-xia LI^1,²,Bao-xiang LIU^1,²

¹ College of Science,North China University of Science and Technology,Tangshan 063009,China
² Key Laboratory of Data Science and Application of Hebei Province,Tangshan 063009,China

Online:2016-10-25 Published:2017-01-17
Supported by:
The National Natural Science Foundation of China;The National Natural Science Foundation of China;The Natural Science Founda-tion of Hebei Province;The Science Foundation for Young Scientists of North China University of Science and Technology

摘要/Abstract

摘要：

通过对现有三支决策理论和方法的分析，提出基于集对信息粒空间的三支决策模型，以及从对立统一的集对论观点，对三支决策的内涵和外延加以诠释。首先，分析集对信息粒空间的结构，分为正同粒、负反粒和差异；其次，将集对信息粒按照所设定的阈值划分为3个互不相交的正同域、负反域和差异域，并基于这3个域给出决策损失函数的计算方法，给出决策算法流程；最后在风险投资评估中运用集对信息粒空间上的三支决策方法对风险投资进行评估决策，取得了较好的决策效果。

关键词: 集对粒空间, 广义三支决策, 狭义三支决策, 集对关联

Abstract:

Through the analysis of the existing theory and method of three-way decision,model of three-way decision based on the space of set pair information granule was proposed,which was to explain the intension and extension of three-way decision on the view of unity of opposites.Firstly the space structure of set pair information granule can be di-vided into positive granule,negative granule,different granule,which were similar and slightly different with three re-gions of generalized three-way decision.The three kinds of information granules in set pair information granule space were built based on certain positive degree,negative degree and different degree.Secondly,according to the given threshold,set pair information granule is divided into mutually disjointing positive region,negative region and different region.Based on these three regions,the computing method of decision loss function is put forward,and the process of decision-making algorithm is obtained use the three-way decision method of set pair information granule space to evalu-ate and make decision on risk investment,then good decision results have been achieved.

Key words: set pair granule space, generalized three-way decision, narrow three-way decision,, set pair association

张春英,王立亚,李明霞,刘保相. 基于集对信息粒空间的三支决策模型及应用[J]. 通信学报, 2016, 37(Z1): 15-24.

Chun-ying ZHANG,Li-ya WANG,Ming-xia LI,Bao-xiang LIU. Model of three-way decision based on the space of set pair information granule and its application[J]. Journal on Communications, 2016, 37(Z1): 15-24.

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		实体的客观状态
决策动作
决策动作
	属于		不属于
接受决策	λ_PP		λ_PN
延迟决策	λ_BP		λ_BN
拒绝决策	λ_NP		λ_NN

				u₁₁						u₁₂						u₁₃						u₁₄
指标
指标
	e₁	e₂	e₃	e₄	e₁	v₁₁	e₁	e₂	e₃	e₄	e₁	v₁₂	e₁	e₂	e₃	e₄	e₁	v₁₃	e₁	e₂	e₃	e₄	e₅	e₁₄
p₁	1	0	1	?	1	1	0	?	0	?	1	0	0	1	?	1	1	1	1	?	?	1	1	1
p₂	1	1	0	1	0	0	?	1	1	1	0	1	1	?	1	0	1	1	?	?	1	0	1	1
p₃	0	1	?	0	1	0	1	0	?	1	1	1	0	1	0	?	0	0	1	?	0	?	0	0
p₄	?	0	0	?	1	0	1	0	0	?	0	0	1	1	?	1	?	1	?	?	?	1	?	1
p₅	1	?	1	1	1	1	1	1	0	1	1	1	0	0	?	0	0	0	1	1	?	0	0	1
p₆	?	1	1	0	1	1	1	1	?	0	1	1	1	0	1	?	1	1	?	1	1	?	1	1
p₇	0	1	1	1	1	1	1	0	1	?	1	1	0	1	0	?	0	0	1	?	1	?	1	1
p₈	1	0	?	?	0	0	0	0	?	0	1	0	1	1	1	?	1	1	?	?	1	?	1	1
p	1	1	1	?	0	?	0	0	?	0	?	?	?	1	0	1	?	?	?	?	0	1	?	？

p_n	u₁₁下的集对关联度	u₁₂下的集对关联度	u₁₃下的集对关联度	u₁₄下的集对关联度
p₁	0.6+0i+0.4j	0.2+0.6i+0.2j	0.4+0.6i+0j	0.4+0.6i+0j
p₂	0.6+0.2i+0.2j	0+0.6i+0.4j	0+0.6i+0.4j	0.4+0.2i+0.4j
p₃	0.2+0.4i+0.4j	0.4+0.2i+0.4j	0.4+0.6i+0j	0.4+0.6i+0j
p₄	0.2+0.4i+0.4j	0.2+0.6i+0.2j	0.6+0.4i+0j	0.8+0.2i+0j
p₅	0.4+0.4i+0.2j	0+0.4i+0.6j	0+0.6i+0.4j	0+0.8i+0.2j
p₆	0.4+0.4i+0.2j	0.4+0.2i+0.4j	0+0.6i+0.4j	0.2+0.6i+0.2j
p₇	0.4+0.2i+0.4j	0.2+0.6i+0.2j	0.4+0.6i+0j	0.2+0.6i+0.2j
p₈	0.4+0.2i+0.4j	0.8+0.2i+0j	0.2+0.6i+0.2j	0.4+0.4i+0.2j

	实体的客观状态
决策动作
决策动作
	属于X	不属于X
接受决策	0	17
延迟决策	9	2
拒绝决策	15	0

			U₁
指标
指标
	u₁₁	u₁₂	u₁₃	u₁₄	v₁
p₁	1	0	1	1	1
p₂	0	1	1	1	1
p₃	0	1	0	0	0
p₄	0	0	1	1	1
p₅	1	1	0	1	1
p₆	1	1	1	1	1
p₇	1	1	0	1	1
p₈	0	0	1	1	1
p	—	0	1	1	?

基于集对信息粒空间的三支决策模型及应用

Model of three-way decision based on the space of set pair information granule and its application

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