基于多粒度二元语义信息的多属性群决策的赋权方法研究
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摘要
由于受客观事物自身的复杂性、不确定性以及人类思维的模糊性等因素的影响,实际的决策信息往往难以量化,而一般较好的选择是采用定性的语言形式来表示。在群决策中,由于不同的决策者对同一决策问题会依据其个人偏好提出不同语言短语数目(简称粒度)的语言评价集给出各自的语言评价信息,因此多粒度语言评价信息的群决策问题有着较高的实际应用价值。
本文主要针对决策信息为多粒度二元语义形式的多属性群决策问题,建立确定权重的目标规划模型以获取属性权重从而进行决策,主要工作概括如下：
第一章,首先介绍多粒度二元语义信息的多属性群决策问题研究的背景和国内外研究现状,最后给出本文的主要研究工作。
第二章,针对多粒度语言信息,采用二元语义信息形式并利用转换函数实现评价信息的一致化,分别建立基于相对熵和基于投影的关于二元语义信息的多目标规划,在权重信息不完全条件下确定出决策问题的客观属性权重,最后利用二元语义集结算子对各个方案的信息进行集结和方案择优。
第三章,针对多粒度区间语言信息,采用区间二元语义信息形式并利用转换函数实现评价信息的一致化,分别建立基于离差最大化和基于Topsis的关于区间二元语义信息的目标规划,且分别在权重信息完全未知和不完全未知的条件下,确定出决策问题的客观属性权重,最后分别利用区间二元语义可能度公式和各方案与正理想方案间的相对贴近度对各个方案的信息进行集结和择优。
第四章,综合主观赋权方法和客观赋权方法,对多粒度语言信息多属性群决策问题的属性权重进行组合赋权,提出一种基于离差平方和的组合赋权方法,从而得到组合权重。
第五章,通过对前三章中的四种客观赋权方法和组合赋权方法进行实例分析,说明这些方法是有效的和可行的。
第六章,对全文进行了总结,并对进一步的研究前景作了展望。
Practical decision information is hard to be quantified, because many facts such as complexity、uncertainty of things and the ambiguity of human thought always place restrictions on it. Using a specified language to express it is a better choice. In the process of group decision making, different decision-makers are likely to use linguistic terms of different granularity to describe the same object of decision-making based on his or her preference. So it is valuable to study multiple attribute group decision making problems with multi-granularity linguistic assessment information and application.
In this dissertation, some analysis and research on the preference information in the form of multi-granularity two-tuple linguistic information are carried out, then some multi-objective programming models are constructed in order to determine the attribute weights, and the responding decision making methods are given, main jobs are as follows:
In chapter 1, first of all, the author introduce the background and the current research situation of multiple attribute group decision making problems with multi-granularity two-tuple linguistic information, and point out the main research tasks of the article.
In chapter 2, two new methods are proposed for multiple attribute group decision making problems with multi-granularity linguistic assessment information, based on two-tuple linguistic information. Firstly, a transformation function is given to uniform the multi-granularity linguistic preference information into the form of two-tuple linguistic information in basic linguistic term set. Then, multi-objective programming models based on relative entropy and project method, by which the attribute weight information is incomplete, are established. By solving these models, the attribute weights can be determined. The two-tuple aggregation operator is utilized to aggregate the linguistic assessment information corresponding to each alternative in order to rank the alternatives and select the most desirable one(s).
In chapter 3, two new methods are proposed for multiple attribute group decision making problems with multi-granularity interval linguistic information, based on interval two-tuple linguistic information. Firstly, a transformation function is given to uniform the multi-granularity interval linguistic preference information into the form of interval two-tuple linguistic information in basic linguistic term set. Then, multi-objective programming models based on maximizing deviation and TOPS IS method, by which the attribute weight information is completely unknown or partly unknown, are established. By solving these models, the attribute weights can be determined. The interval two-tuple aggregation operator is utilized to aggregate the linguistic assessment information corresponding to each alternative. The possibility degree of interval two-tuple linguistic information and the relative closeness degrees between each alternative and idea alternative are utilized to the result of aggregation in order to rank the alternatives and select the most desirable one(s).
In chapter 4, a new combination weighting method is proposed for multiple attribute group decision making problems with multi-granularity linguistic assessment information. Based on sum of square deviates, an optimal combination weights model is proposed in order to make full use of information, which is contained in the subjective weighting methods and the objective weighting methods. By solving this model, the attribute weights can be determined.
In chapter 5, the example analysis of objective weighting methods and combination weighting methods, which are put forward in the last three chapters, is given to demonstrate the feasibility and practicability of the proposed methods.
In chapter 6, full text job is summed up, and the prospect of the research on multiple attribute group decision making based on multi-granularity two-tuple linguistic information is looking into the distance.
本文主要针对决策信息为多粒度二元语义形式的多属性群决策问题,建立确定权重的目标规划模型以获取属性权重从而进行决策,主要工作概括如下：
第一章,首先介绍多粒度二元语义信息的多属性群决策问题研究的背景和国内外研究现状,最后给出本文的主要研究工作。
第二章,针对多粒度语言信息,采用二元语义信息形式并利用转换函数实现评价信息的一致化,分别建立基于相对熵和基于投影的关于二元语义信息的多目标规划,在权重信息不完全条件下确定出决策问题的客观属性权重,最后利用二元语义集结算子对各个方案的信息进行集结和方案择优。
第三章,针对多粒度区间语言信息,采用区间二元语义信息形式并利用转换函数实现评价信息的一致化,分别建立基于离差最大化和基于Topsis的关于区间二元语义信息的目标规划,且分别在权重信息完全未知和不完全未知的条件下,确定出决策问题的客观属性权重,最后分别利用区间二元语义可能度公式和各方案与正理想方案间的相对贴近度对各个方案的信息进行集结和择优。
第四章,综合主观赋权方法和客观赋权方法,对多粒度语言信息多属性群决策问题的属性权重进行组合赋权,提出一种基于离差平方和的组合赋权方法,从而得到组合权重。
第五章,通过对前三章中的四种客观赋权方法和组合赋权方法进行实例分析,说明这些方法是有效的和可行的。
第六章,对全文进行了总结,并对进一步的研究前景作了展望。
Practical decision information is hard to be quantified, because many facts such as complexity、uncertainty of things and the ambiguity of human thought always place restrictions on it. Using a specified language to express it is a better choice. In the process of group decision making, different decision-makers are likely to use linguistic terms of different granularity to describe the same object of decision-making based on his or her preference. So it is valuable to study multiple attribute group decision making problems with multi-granularity linguistic assessment information and application.
In this dissertation, some analysis and research on the preference information in the form of multi-granularity two-tuple linguistic information are carried out, then some multi-objective programming models are constructed in order to determine the attribute weights, and the responding decision making methods are given, main jobs are as follows:
In chapter 1, first of all, the author introduce the background and the current research situation of multiple attribute group decision making problems with multi-granularity two-tuple linguistic information, and point out the main research tasks of the article.
In chapter 2, two new methods are proposed for multiple attribute group decision making problems with multi-granularity linguistic assessment information, based on two-tuple linguistic information. Firstly, a transformation function is given to uniform the multi-granularity linguistic preference information into the form of two-tuple linguistic information in basic linguistic term set. Then, multi-objective programming models based on relative entropy and project method, by which the attribute weight information is incomplete, are established. By solving these models, the attribute weights can be determined. The two-tuple aggregation operator is utilized to aggregate the linguistic assessment information corresponding to each alternative in order to rank the alternatives and select the most desirable one(s).
In chapter 3, two new methods are proposed for multiple attribute group decision making problems with multi-granularity interval linguistic information, based on interval two-tuple linguistic information. Firstly, a transformation function is given to uniform the multi-granularity interval linguistic preference information into the form of interval two-tuple linguistic information in basic linguistic term set. Then, multi-objective programming models based on maximizing deviation and TOPS IS method, by which the attribute weight information is completely unknown or partly unknown, are established. By solving these models, the attribute weights can be determined. The interval two-tuple aggregation operator is utilized to aggregate the linguistic assessment information corresponding to each alternative. The possibility degree of interval two-tuple linguistic information and the relative closeness degrees between each alternative and idea alternative are utilized to the result of aggregation in order to rank the alternatives and select the most desirable one(s).
In chapter 4, a new combination weighting method is proposed for multiple attribute group decision making problems with multi-granularity linguistic assessment information. Based on sum of square deviates, an optimal combination weights model is proposed in order to make full use of information, which is contained in the subjective weighting methods and the objective weighting methods. By solving this model, the attribute weights can be determined.
In chapter 5, the example analysis of objective weighting methods and combination weighting methods, which are put forward in the last three chapters, is given to demonstrate the feasibility and practicability of the proposed methods.
In chapter 6, full text job is summed up, and the prospect of the research on multiple attribute group decision making based on multi-granularity two-tuple linguistic information is looking into the distance.
引文
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[5]徐泽水,达庆利.区间数排序的可能度法及其应用[J].系统工程学报,2003,18(1)：67-70.
[6]徐泽水,孙在东.一类不确定型多属性决策问题的排序方法[J].管理科学学报,2002,5(3)：35-39.
[7]徐泽水.一种不确定型OWA算子及其在群决策中的应用[J].东南大学学报(自然科学版),2002,32(1)：147-150.
[8]Yager R R.OWA aggregation over a continuous interval argument with applications to decision making [J].IEEE Transactions on Systems, Man, and Cybernetics, partB,2004,34:1952-1963.
[9]徐泽水.拓展的C-OWA算子及其在不确定多属性决策中的应用[J].系统工程理论与实践,2005,25(11)：7-13.
[10]陈华友,刘金培,王慧.一类连续区间数据的有序加权调和(C-OWH)平均算子及其应用[J].系统工程理论与实践,2008,28(7)：86-92.
[11]徐泽水.基于期望值的模糊多属性决策法及其研究[J].系统工程理论与实践,2004,24(1)：109-113.
[12]周宏安,刘三阳.基于离差最大化模型的模糊多属性决策投影法[J].系统工程与电子技术,2007,29(5)：741-744.
[13]杨静,邱菀华.基于投影技术的三角模糊数型多属性决策方法研究[J].控制与决策,2009,24(4)：637-640.
[14]杨静,邱菀华.基于离差的模糊多属性决策法及其应用[J].系统工 程,2008,26(6)：107-110.
[15]Gu X-B,Zhu Q-X.Fuzzy multi-attribute decision-making method based on eigenvector of fuzzy attribute evaluation space [J].Decision Support Systems,2006,41(2):400-410.
[16]许叶军,达庆利.TFOWA算子及其在决策中的应用[J].东南大学学报(自然科学版),2006,36(6)：1034-1038.
[17]彭展声,李荣钧.模糊多属性决策的投影折衷方法[J].模糊系统与数学,2006,20(4)：86-90.
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