基于二元语义模糊语言偏好表示的群体决策方法研究
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摘要
随着社会的进步、科技发展、知识和信息量的急剧增长,需要决策的问题越来越复杂,而一个人的知识、经验等毕竟有限,单个个体仅凭自己的经验和智慧已无法掌握所有必要的知识和信息来解决面临的决策,决策者需要向多个专家进行咨询、依靠多位决策者的智慧和知识来解决问题,这就是群体决策。
由于群体决策中自身所具有的矛盾:个体理性与群体理性之间的矛盾;个体效用函数的可比性问题;对利益上存在冲突的群体决策,公平原则和效用原则是一个两难兼顾的问题;等等。群体决策中仍然有许多问题没有解决,需要进一步的理论和实证研究,这就使得群体决策仍然是心理学、管理学等学科领域的研究热点。
另外,在群体决策中专家对问题的直觉判断有时难以用精确数来表示,而用“好,很好”等这样模糊语言表示则更方便,模糊语言的使用使决策者能更准确表达自己的偏好。总之,由于信息的不完全或人们对信息的理解问题以及决策者自身知识的局限性,模糊性在决策中必然存在。
模糊语言偏好的表示有多种:区间数、三角模糊数、梯形模糊数、语言标度、二元语义等。模糊群体决策中使用不同的模糊偏好表示方法及集结方法将得到不同的决策结果。模糊群体决策并没有形成一套完整的体系。
因此,本文选择“基于二元语义模糊语言偏好表示的群体决策方法研究”作为选题,进行模糊群体决策方法的研究。该选题的研究将提高模糊群体决策的有效性和合理性,丰富模糊群体决策基础理论,充实决策方法库;在理论研究基础上构建的基于二院语义群体决策支持系统将有利于模糊群体决策方法在实践中的应用。因此,该选题具有一定的理论研究和实践应用研究意义。
本论文将对模糊语言偏好的表示方法、模糊判断矩阵的一致性判定、不完全信息决策、群体决策中决策权的分配与个体意见集结等方面进行研究。研究工作主要从以下四个方面进行:
(一)针对模糊语言偏好表达的准确性、决策处理过程中信息丢失少、操作规则等准则对各种模糊语言偏好表示及信息融合问题进行研究。选择合适的模糊语言偏好表示方法,为后续的研究打下坚实的基础。
(二)对模糊判断矩阵的正确性检验进行研究,以提高决策的有效性。本文对模糊判断矩阵的次序一致性判定方法进行进一步的研究,并对非次序一致性模糊判断矩阵的修正方法进行研究;研究模糊判断矩阵的基本一致性是否与模糊判断矩阵的阶数相关。
(三)不完全二元语义表示的决策方法研究。决策过程中,决策者有时可能对某些判断缺少把握或对某些敏感问题不想发表意见,决策者可能以残缺判断矩阵的方式来表达其偏好。因此,本文将对残缺二元语义判断矩阵下的不完全信息决策方法进行研究。
(四)对群体决策中的关键问题:群体思维的形成、决策权的确定、群体一致性的衡量等方面问题进行文献分析研究。并对基于二元语义的群体决策中专家的决策权的确定、个体意见的集结方法等群体决策问题进行研究,以提高模糊群体决策的合理性。
本文在研究过程中利用文献分析法、模糊层次分析法、计算机仿真方法、统计方法、比较分析法、熵权法、问卷调查法、案例分析法、面向对象程序设计方法等多种方法来进行相关内容的研究,研究过程中将定性方法与定量方法有机结合,理论方法与实际应用相结合。
对研究内容进行路线设计后,综合上述方法对研究内容进行了深入研究。本论文的主要创新点如下:
(一)在对次序一致性判断方法的文献分析基础上,提出了基于二元关系传递性的模糊判断矩阵次序一致性判断和修正指导方法。通过计算非传递性路径数及非传递性路径贡献数来指导专家对判断矩阵进行修正,从而提高专家的修正效率,丰富判断矩阵的次序一致性判断方法库。
(二)在进行MATLAB编程及模糊互补判断矩阵一致性理论研究的基础上,运用MATLAB,通过仿真生成10000个具次序一致性的3×3,4×4,5×5,6×6阶模糊判断矩阵,在计算其加性一致性值并进行均值、方差等统计分析后,得出不同阶模糊互补判断矩阵在不同置信度下加性一致性阈值,解决了模糊判断矩阵的基本一致性判定问题。
(三)在分析模糊互补判断矩阵特点和二元语义判断矩阵特点的基础上,借助模糊互补判断矩阵的特点证明了二元语义判断矩阵的加性一致性特点,利用加性传递性来估算缺失元素,从而提出了一种残缺二元语义判断矩阵中缺失元素的估算方法,为非完全信息决策提供一种解决方案。
(四)专家给出的判断矩阵中有些元素一致性程度高而有些元素一致性程度低,建议根据专家判断元素的直接信息与间接信息的相似性来确定专家的权重,并提出相应的个体意见集结方法、专家贡献度衡量方法和群体一致性衡量方法。同时,在理论研究基础上开发了一个基于二元语义的群体决策支持系统,方便模糊群体决策理论在实践中的应用。
最后,将本论文理论研究成果运用到中小板上市公司的绩效评价指标的构建中。用二元语义表示模型对绩效评价衡量指标的满意度调查、专家对绩效评价指标的比较等进行处理,得出中小板上市公司的绩效评价指标体系,根据该指标体系可以实现对上市公司运营情况的衡量,方便企业本身、股东和投资者了解中小板上市公司的绩效,进行有效决策。
通过对理论研究的运用,印证二元语义表示模型表示模糊语言偏好的方便性。同时,在中小板上市公司的绩效评价指标构建中,运用基于二元语义的决策支持系统进行非财务指标权重的群体决策评价,系统输入简单,处理结果可靠。同时,由于系统提供了初始化设置模块,扩展系统的应用范围。
With the development of science and technology, and with the rapid increasing of knowledge and information, the decision-making problem becomes more and more complicate, a decision-maker can not resolve it because of his/her limited experience and wisdom. The decision-maker need consult with other decision-makers to seek more knowledge and information to deal with the complicated situations. Group decision-making basically solicits opinions from experts and combines these judgments into a coherent group decision.
Group decision making is still the hot research issues in psychology and management research field that attracts scholars to study, because there are some contradictories in group decision-making, such as contradiction between individual rationality and group rationality, comparison between individual performance functions, the dilemma between effectiveness and unbiased regulation in conflicting group decision-making. There are still some questions in group decision-making need further theory study and case study.
Meanwhile, it is difficult for decision-makers to express their intuitionistic preferences using accurate numbers, it is easier for decision-maker to use fuzzy numbers to express. And the decision-makers can express their preferences more accurately with the fuzzy linguistic preferences. All in all, due to uncertainty information, the understanding problem and the limited knowledge of decision-makers, there exists fuzziness in decision-making.
There are many representation approaches for fuzzy linguistic preference, for example, interval-valued fuzzy number, triangular fuzzy number, trapezoidal fuzzy number, linguistic label and 2-tuple linguistic representation model. Fuzzy group decision-making using different fuzzy linguistic preference representation method and aggregating method gets different decision results. There is not a perfect system for fuzzy group decision-making.
Therefore, "Research on Group Decision Making Method under Fuzzy Linguistic Preference represented by 2-tuple Linguistic Representation model" was selected as the title of the dissertation. Researches on fuzzy group decision-making method were in progress to further study. The study will improve the effectiveness and rationality of fuzzy group decision-making, and will enrich the group decision-making theory and expand the method database for group decision-making. And the 2-tuple linguistic representation group decision-making system based on the theory research will simplify the application fuzzy group decision-making.
The paper mainly studied the following problems such as the representation method of fuzzy linguistic preference, the consistency of fuzzy judgment matrix, the decision-making method under incomplete information, and the group decision-making method. The research mainly focused on the following four points.
(1) Based on the criteria such as representation accuracy, information loss in processing, and operating research, different kinds of fuzzy representation methods and the confusion methods for different fuzzy linguistic preference representation were studied. And the suitable fuzzy linguistic preference representation method was selected, which set the foundation of the paper.
(2) The study on judging the accuracy of a fuzzy judgment matrix was undergone to improve the effectiveness of the decision-making. The paper investigated the judgment of ordinal consistency of a fuzzy judgment matrix and the revising approach for a fuzzy judgment matrix without ordinal consistency. It also researched the threshold of consistency index according to different matrix cardinality to reveal whether the threshold was the same regardless of matrix cardinality.
(3) Researches on decision-making under incomplete linguistic 2-tuple judgment matrix were carried out to enrich the method database for incomplete decision-making. When a decision-maker is not confident about some judgment or do not want to express their opinions, the decision-maker will give an incomplete fuzzy judgment matrix to show their preference.
(4) Key points of group decision-making such as decision power designating, the process of group thinking, and the measurement of consensus were analyzed. The decision power designating method and aggregating approaches were investigated for group decision-making using 2-tuple linguistic representation model to improve the rationality of fuzzy group decision-making.
Methods such as literature analysis, analytic hierarchy process, computer simulation, statistical analysis, analogous analysis, entropy method, questionnaire investigation, case study, object-oriented programming method and so on, were used in the research of the paper. Quantitative method and qualitative method was combined to deal with the study. And theories were applied to practical applications in the research.
After designing the study plan for the research content, the research was deeply carried out with the aid of the above method. The main new ideas of the paper are as follows:
(1) Based on the literature analysis on ordinal consistency and transitiveness theory of a binary relation, the paper proposed a new method to judge the ordinal consistency of a fuzzy judgment matrix. And a revising method was put forward, which was based on the concepts of non-transitive router number and non-transitive router contributing number. The new method will enrich the method database for ordinal consistency judgment and revising, and help the expert to improve his/her revising effectiveness.
(2) The paper simulated 10000 3×3, 4×4, 5×5, 6×6 ordinal consistent fuzzy judgment matrices. The average and the standard deviation of its consistency index were calculated. The conclusion was that the threshold of consistency index should be different with different confidence degree and matrix cardinality, which solved the judging problem for consistency of fuzzy judgment matrix.
(3) The properties of linguistic 2-tuple judgment matrix with additive consistency were studied based on the analysis of properties of fuzzy complementary judgment matrix and 2-tuple linguistic judgment matrix. The transitivity property of additive consistency was used to compute the indirect valued of an element. An estimating method was put forward to estimate the missing values in an incomplete linguistic 2-tuple judgment matrix, which provided a new solution for incomplete decision-making.
(4) A new method was used to designate the decision power of each decision maker under group decision-making using linguistic 2-tuple representation. The basic idea of the decision power designating was that the consistency of each element was not the same, thus the decision power of the decision-maker should not be given the same priority. The responding individual aggregating method, the measurement for contribution degree of the decision-makers and consensus were proposed. And the group decision-making support system under 2-tuple linguistic representation model was designed based on the researched theory.
In acquiring the performance framework for small and medium entrepreneur board listed companies, linguistic 2-tuple representation model was used to analyze the questionnaire about satisfied degree of the evaluation attributes and the linguistic 2-tuple matrices which were given by experts from different company. Thus the performance evaluation framework was build for small and medium entrepreneur board listed company.
The application of the theory indicated that the 2-tuple linguistic representation model was suitable for representing fuzzy linguistic preference. Meanwhile, during the building of company performance evaluation indicators, the group decision-making system based on 2-tuple linguistic representation model was used to manipulate the evaluation given by experts for non-financial indicators. The input of the system is simple and the processing result is reliable. The system has the initialization modular, which will expand the application range.
由于群体决策中自身所具有的矛盾:个体理性与群体理性之间的矛盾;个体效用函数的可比性问题;对利益上存在冲突的群体决策,公平原则和效用原则是一个两难兼顾的问题;等等。群体决策中仍然有许多问题没有解决,需要进一步的理论和实证研究,这就使得群体决策仍然是心理学、管理学等学科领域的研究热点。
另外,在群体决策中专家对问题的直觉判断有时难以用精确数来表示,而用“好,很好”等这样模糊语言表示则更方便,模糊语言的使用使决策者能更准确表达自己的偏好。总之,由于信息的不完全或人们对信息的理解问题以及决策者自身知识的局限性,模糊性在决策中必然存在。
模糊语言偏好的表示有多种:区间数、三角模糊数、梯形模糊数、语言标度、二元语义等。模糊群体决策中使用不同的模糊偏好表示方法及集结方法将得到不同的决策结果。模糊群体决策并没有形成一套完整的体系。
因此,本文选择“基于二元语义模糊语言偏好表示的群体决策方法研究”作为选题,进行模糊群体决策方法的研究。该选题的研究将提高模糊群体决策的有效性和合理性,丰富模糊群体决策基础理论,充实决策方法库;在理论研究基础上构建的基于二院语义群体决策支持系统将有利于模糊群体决策方法在实践中的应用。因此,该选题具有一定的理论研究和实践应用研究意义。
本论文将对模糊语言偏好的表示方法、模糊判断矩阵的一致性判定、不完全信息决策、群体决策中决策权的分配与个体意见集结等方面进行研究。研究工作主要从以下四个方面进行:
(一)针对模糊语言偏好表达的准确性、决策处理过程中信息丢失少、操作规则等准则对各种模糊语言偏好表示及信息融合问题进行研究。选择合适的模糊语言偏好表示方法,为后续的研究打下坚实的基础。
(二)对模糊判断矩阵的正确性检验进行研究,以提高决策的有效性。本文对模糊判断矩阵的次序一致性判定方法进行进一步的研究,并对非次序一致性模糊判断矩阵的修正方法进行研究;研究模糊判断矩阵的基本一致性是否与模糊判断矩阵的阶数相关。
(三)不完全二元语义表示的决策方法研究。决策过程中,决策者有时可能对某些判断缺少把握或对某些敏感问题不想发表意见,决策者可能以残缺判断矩阵的方式来表达其偏好。因此,本文将对残缺二元语义判断矩阵下的不完全信息决策方法进行研究。
(四)对群体决策中的关键问题:群体思维的形成、决策权的确定、群体一致性的衡量等方面问题进行文献分析研究。并对基于二元语义的群体决策中专家的决策权的确定、个体意见的集结方法等群体决策问题进行研究,以提高模糊群体决策的合理性。
本文在研究过程中利用文献分析法、模糊层次分析法、计算机仿真方法、统计方法、比较分析法、熵权法、问卷调查法、案例分析法、面向对象程序设计方法等多种方法来进行相关内容的研究,研究过程中将定性方法与定量方法有机结合,理论方法与实际应用相结合。
对研究内容进行路线设计后,综合上述方法对研究内容进行了深入研究。本论文的主要创新点如下:
(一)在对次序一致性判断方法的文献分析基础上,提出了基于二元关系传递性的模糊判断矩阵次序一致性判断和修正指导方法。通过计算非传递性路径数及非传递性路径贡献数来指导专家对判断矩阵进行修正,从而提高专家的修正效率,丰富判断矩阵的次序一致性判断方法库。
(二)在进行MATLAB编程及模糊互补判断矩阵一致性理论研究的基础上,运用MATLAB,通过仿真生成10000个具次序一致性的3×3,4×4,5×5,6×6阶模糊判断矩阵,在计算其加性一致性值并进行均值、方差等统计分析后,得出不同阶模糊互补判断矩阵在不同置信度下加性一致性阈值,解决了模糊判断矩阵的基本一致性判定问题。
(三)在分析模糊互补判断矩阵特点和二元语义判断矩阵特点的基础上,借助模糊互补判断矩阵的特点证明了二元语义判断矩阵的加性一致性特点,利用加性传递性来估算缺失元素,从而提出了一种残缺二元语义判断矩阵中缺失元素的估算方法,为非完全信息决策提供一种解决方案。
(四)专家给出的判断矩阵中有些元素一致性程度高而有些元素一致性程度低,建议根据专家判断元素的直接信息与间接信息的相似性来确定专家的权重,并提出相应的个体意见集结方法、专家贡献度衡量方法和群体一致性衡量方法。同时,在理论研究基础上开发了一个基于二元语义的群体决策支持系统,方便模糊群体决策理论在实践中的应用。
最后,将本论文理论研究成果运用到中小板上市公司的绩效评价指标的构建中。用二元语义表示模型对绩效评价衡量指标的满意度调查、专家对绩效评价指标的比较等进行处理,得出中小板上市公司的绩效评价指标体系,根据该指标体系可以实现对上市公司运营情况的衡量,方便企业本身、股东和投资者了解中小板上市公司的绩效,进行有效决策。
通过对理论研究的运用,印证二元语义表示模型表示模糊语言偏好的方便性。同时,在中小板上市公司的绩效评价指标构建中,运用基于二元语义的决策支持系统进行非财务指标权重的群体决策评价,系统输入简单,处理结果可靠。同时,由于系统提供了初始化设置模块,扩展系统的应用范围。
With the development of science and technology, and with the rapid increasing of knowledge and information, the decision-making problem becomes more and more complicate, a decision-maker can not resolve it because of his/her limited experience and wisdom. The decision-maker need consult with other decision-makers to seek more knowledge and information to deal with the complicated situations. Group decision-making basically solicits opinions from experts and combines these judgments into a coherent group decision.
Group decision making is still the hot research issues in psychology and management research field that attracts scholars to study, because there are some contradictories in group decision-making, such as contradiction between individual rationality and group rationality, comparison between individual performance functions, the dilemma between effectiveness and unbiased regulation in conflicting group decision-making. There are still some questions in group decision-making need further theory study and case study.
Meanwhile, it is difficult for decision-makers to express their intuitionistic preferences using accurate numbers, it is easier for decision-maker to use fuzzy numbers to express. And the decision-makers can express their preferences more accurately with the fuzzy linguistic preferences. All in all, due to uncertainty information, the understanding problem and the limited knowledge of decision-makers, there exists fuzziness in decision-making.
There are many representation approaches for fuzzy linguistic preference, for example, interval-valued fuzzy number, triangular fuzzy number, trapezoidal fuzzy number, linguistic label and 2-tuple linguistic representation model. Fuzzy group decision-making using different fuzzy linguistic preference representation method and aggregating method gets different decision results. There is not a perfect system for fuzzy group decision-making.
Therefore, "Research on Group Decision Making Method under Fuzzy Linguistic Preference represented by 2-tuple Linguistic Representation model" was selected as the title of the dissertation. Researches on fuzzy group decision-making method were in progress to further study. The study will improve the effectiveness and rationality of fuzzy group decision-making, and will enrich the group decision-making theory and expand the method database for group decision-making. And the 2-tuple linguistic representation group decision-making system based on the theory research will simplify the application fuzzy group decision-making.
The paper mainly studied the following problems such as the representation method of fuzzy linguistic preference, the consistency of fuzzy judgment matrix, the decision-making method under incomplete information, and the group decision-making method. The research mainly focused on the following four points.
(1) Based on the criteria such as representation accuracy, information loss in processing, and operating research, different kinds of fuzzy representation methods and the confusion methods for different fuzzy linguistic preference representation were studied. And the suitable fuzzy linguistic preference representation method was selected, which set the foundation of the paper.
(2) The study on judging the accuracy of a fuzzy judgment matrix was undergone to improve the effectiveness of the decision-making. The paper investigated the judgment of ordinal consistency of a fuzzy judgment matrix and the revising approach for a fuzzy judgment matrix without ordinal consistency. It also researched the threshold of consistency index according to different matrix cardinality to reveal whether the threshold was the same regardless of matrix cardinality.
(3) Researches on decision-making under incomplete linguistic 2-tuple judgment matrix were carried out to enrich the method database for incomplete decision-making. When a decision-maker is not confident about some judgment or do not want to express their opinions, the decision-maker will give an incomplete fuzzy judgment matrix to show their preference.
(4) Key points of group decision-making such as decision power designating, the process of group thinking, and the measurement of consensus were analyzed. The decision power designating method and aggregating approaches were investigated for group decision-making using 2-tuple linguistic representation model to improve the rationality of fuzzy group decision-making.
Methods such as literature analysis, analytic hierarchy process, computer simulation, statistical analysis, analogous analysis, entropy method, questionnaire investigation, case study, object-oriented programming method and so on, were used in the research of the paper. Quantitative method and qualitative method was combined to deal with the study. And theories were applied to practical applications in the research.
After designing the study plan for the research content, the research was deeply carried out with the aid of the above method. The main new ideas of the paper are as follows:
(1) Based on the literature analysis on ordinal consistency and transitiveness theory of a binary relation, the paper proposed a new method to judge the ordinal consistency of a fuzzy judgment matrix. And a revising method was put forward, which was based on the concepts of non-transitive router number and non-transitive router contributing number. The new method will enrich the method database for ordinal consistency judgment and revising, and help the expert to improve his/her revising effectiveness.
(2) The paper simulated 10000 3×3, 4×4, 5×5, 6×6 ordinal consistent fuzzy judgment matrices. The average and the standard deviation of its consistency index were calculated. The conclusion was that the threshold of consistency index should be different with different confidence degree and matrix cardinality, which solved the judging problem for consistency of fuzzy judgment matrix.
(3) The properties of linguistic 2-tuple judgment matrix with additive consistency were studied based on the analysis of properties of fuzzy complementary judgment matrix and 2-tuple linguistic judgment matrix. The transitivity property of additive consistency was used to compute the indirect valued of an element. An estimating method was put forward to estimate the missing values in an incomplete linguistic 2-tuple judgment matrix, which provided a new solution for incomplete decision-making.
(4) A new method was used to designate the decision power of each decision maker under group decision-making using linguistic 2-tuple representation. The basic idea of the decision power designating was that the consistency of each element was not the same, thus the decision power of the decision-maker should not be given the same priority. The responding individual aggregating method, the measurement for contribution degree of the decision-makers and consensus were proposed. And the group decision-making support system under 2-tuple linguistic representation model was designed based on the researched theory.
In acquiring the performance framework for small and medium entrepreneur board listed companies, linguistic 2-tuple representation model was used to analyze the questionnaire about satisfied degree of the evaluation attributes and the linguistic 2-tuple matrices which were given by experts from different company. Thus the performance evaluation framework was build for small and medium entrepreneur board listed company.
The application of the theory indicated that the 2-tuple linguistic representation model was suitable for representing fuzzy linguistic preference. Meanwhile, during the building of company performance evaluation indicators, the group decision-making system based on 2-tuple linguistic representation model was used to manipulate the evaluation given by experts for non-financial indicators. The input of the system is simple and the processing result is reliable. The system has the initialization modular, which will expand the application range.
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