基于直觉语言信息的多准则决策方法研究
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摘要
在社会经济生活中,存在大量直觉模糊和语言多准则决策问题。直觉模糊数只能粗略表示准则或方案隶属或非隶属于某一个特定模糊概念的程度,语言评价不能刻画非隶属度和决策者的犹豫程度,为此本文定义了直觉语言数。
在直觉语言数多准则问题中,由于大量决策问题自身的模糊性和不确定性会导致方案的准则权重等参数不能完全确定,在群决策过程中也可能会碰到语言评价集不一致的难题,因此对直觉语言多准则的相关理论和方法进行研究具有重要理论和实践意义。论文的主要工作和成果如下：
(1)定义了直觉语言数,根据直觉数的相关概念分别给出了直觉语言数的期望值公式和四则运算法则,定义了直觉语言数的得分函数、精确函数、Hamming距离和集结算子。同时,建立了直觉语言集结算子和直觉语言VIKOR的多准则决策模型。
(2)定义了直觉语言数的模糊熵和相似度,建立了三种信息不完全的直觉语言多准则模型。在直觉语言规划模型中,建立直觉语言模糊熵的优化模型,求解模型可得准则权重系数,再进一步集成方案准则值实现方案集的排序。在对方案有偏好的直觉语言多准则模型中通过建立规划模型来实现主观偏好和客观偏好总偏差的最小化,求解线性规划得到各准则的最优权系数,进而得到各方案综合期望值,通过比较综合期望值的大小得到整个方案集的一个排序。最后给出了直觉语言多准则的SIR模型,建立模型可求得整个方案的优势度和劣势度的范围,通过比较区间数可得方案排序。
(3)定义了直觉二元语义及其距离,建立了多粒度直觉语言多准则模型。针对语言评价集有多个粒度的直觉语言多准则问题给出了两种解决模型,第一种模型定义了多粒度语言的一致化转化函数,通过相关算子集成群决策信息得到方案排序。在基于多粒度直觉二元语义的多准则模型中,首先对多个语言评价集给出了一种基于二元语义距离和期望的转化方法,再进一步求解出方案相对于正理想方案或负理想方案的隶属度,比较隶属度大小得到方案集排序。
In the social life and economic activities, there are a large number of intuitionistic fuzzy and linguistic multi-criteria Multi-criteria Decision-making problems. Intuitionistic fuzzy numbers can only be a rough description to which the criteria or program attached to a certain vague concept, and linguistic evaluation can not portray the non-attachment degree and hesitation degree of decision-makers. In this respect, intuitionistic linguistic numbers is defined in this paper.
Further, in the multi-criteria problems based on intuitionistic linguistic numbers, the weight parameters for programs can not be fully identified as a result of ambiguity and uncertainty of many decision-making problems, and in the group decision-making process, problems of inconsistence of evaluation linguistic term sets may also be encountered, therefore it is theoretical and practical significant to do some research on the theory and methods of the intuitionistic linguistic multi-criteria problems. The main work and achievements are as follows:
(1) The intuitionistic linguistic fuzzy numbers is defined, the expectation formula and four algorithms of intuitionistic linguistic number are given according to related concepts of intuitionistic fuzzy numbers. The definition of scoring function, precise function, Hamming distance and settlement sub-set of intuitionistic linguistic fuzzy numbers are defined. At the same time, multi-criteria decision making model respectively based on intuitionistic linguistic set and intuitionistic linguistic VIKOR model in which the criteria value are intuitionistic linguistic fuzzy numbers are established.
(2) Fuzzy entropy and similarity of intuitionistic linguistic fuzzy numbers are defined, three intuitionistic linguistic multi-criteria models with incomplete information are established. In intuitionistic linguistic programming models, this paper establishes an optimization model based on the intuitionistic linguistic fuzzy entropy, criteria weight parameters can be available via solving the model, further the ranking of the whole alternative set can be achieved by integrating criteria values of alternatives. In the model of intuitionistic linguistic multi-criteria decision-making with preference information on alternatives, the minimization of whole deviation between objective and subjective preferences can be achieved through the establishment of programming model, by solving linear programming, the optimized criteria weight coefficients are attained, Then, the alternatives'integrated expected values are attained. The ranking can be obtained by comparing the alternatives'integrated expected values. Finally, the SIR model of intuitionistic linguistic multi-criteria is given. The range of superiority index and inferiority index of each alternative are obtained through establishing model, and the ranking for alternatives are obtained through comparison of interval numbers.
(3) Intuitionistic two-tuple linguistic numbers and its Hamming distance are defined, the multi-granularity intuitionistic linguistic multi-criteria model is established. In which linguistic term sets have multi-granularity and criteria information is intuitionistic linguistic fuzzy set, twe moldels are proposed. In the first model, a new transformation function is given to uniform the multi-granular linguistic sets. Then, by aggregating evaluation matrices from experts and criteria information based on operator, integrated intuitionistic linguistic fuzzy information of alternatives are attained and the ranking of the whole alternative set can be obtained. In the Intuitionistic two-tuple linguistic model, the multi-granular linguistic sets are uniformed based on distance and expectation of two-tuple linguistic.The membership degree to the ideal solution of alternative is attained for every evaluation matrix and integrated membership degree is attained through calculating and by comparing the integrated membership degree, alternatives are ranked.
在直觉语言数多准则问题中,由于大量决策问题自身的模糊性和不确定性会导致方案的准则权重等参数不能完全确定,在群决策过程中也可能会碰到语言评价集不一致的难题,因此对直觉语言多准则的相关理论和方法进行研究具有重要理论和实践意义。论文的主要工作和成果如下：
(1)定义了直觉语言数,根据直觉数的相关概念分别给出了直觉语言数的期望值公式和四则运算法则,定义了直觉语言数的得分函数、精确函数、Hamming距离和集结算子。同时,建立了直觉语言集结算子和直觉语言VIKOR的多准则决策模型。
(2)定义了直觉语言数的模糊熵和相似度,建立了三种信息不完全的直觉语言多准则模型。在直觉语言规划模型中,建立直觉语言模糊熵的优化模型,求解模型可得准则权重系数,再进一步集成方案准则值实现方案集的排序。在对方案有偏好的直觉语言多准则模型中通过建立规划模型来实现主观偏好和客观偏好总偏差的最小化,求解线性规划得到各准则的最优权系数,进而得到各方案综合期望值,通过比较综合期望值的大小得到整个方案集的一个排序。最后给出了直觉语言多准则的SIR模型,建立模型可求得整个方案的优势度和劣势度的范围,通过比较区间数可得方案排序。
(3)定义了直觉二元语义及其距离,建立了多粒度直觉语言多准则模型。针对语言评价集有多个粒度的直觉语言多准则问题给出了两种解决模型,第一种模型定义了多粒度语言的一致化转化函数,通过相关算子集成群决策信息得到方案排序。在基于多粒度直觉二元语义的多准则模型中,首先对多个语言评价集给出了一种基于二元语义距离和期望的转化方法,再进一步求解出方案相对于正理想方案或负理想方案的隶属度,比较隶属度大小得到方案集排序。
In the social life and economic activities, there are a large number of intuitionistic fuzzy and linguistic multi-criteria Multi-criteria Decision-making problems. Intuitionistic fuzzy numbers can only be a rough description to which the criteria or program attached to a certain vague concept, and linguistic evaluation can not portray the non-attachment degree and hesitation degree of decision-makers. In this respect, intuitionistic linguistic numbers is defined in this paper.
Further, in the multi-criteria problems based on intuitionistic linguistic numbers, the weight parameters for programs can not be fully identified as a result of ambiguity and uncertainty of many decision-making problems, and in the group decision-making process, problems of inconsistence of evaluation linguistic term sets may also be encountered, therefore it is theoretical and practical significant to do some research on the theory and methods of the intuitionistic linguistic multi-criteria problems. The main work and achievements are as follows:
(1) The intuitionistic linguistic fuzzy numbers is defined, the expectation formula and four algorithms of intuitionistic linguistic number are given according to related concepts of intuitionistic fuzzy numbers. The definition of scoring function, precise function, Hamming distance and settlement sub-set of intuitionistic linguistic fuzzy numbers are defined. At the same time, multi-criteria decision making model respectively based on intuitionistic linguistic set and intuitionistic linguistic VIKOR model in which the criteria value are intuitionistic linguistic fuzzy numbers are established.
(2) Fuzzy entropy and similarity of intuitionistic linguistic fuzzy numbers are defined, three intuitionistic linguistic multi-criteria models with incomplete information are established. In intuitionistic linguistic programming models, this paper establishes an optimization model based on the intuitionistic linguistic fuzzy entropy, criteria weight parameters can be available via solving the model, further the ranking of the whole alternative set can be achieved by integrating criteria values of alternatives. In the model of intuitionistic linguistic multi-criteria decision-making with preference information on alternatives, the minimization of whole deviation between objective and subjective preferences can be achieved through the establishment of programming model, by solving linear programming, the optimized criteria weight coefficients are attained, Then, the alternatives'integrated expected values are attained. The ranking can be obtained by comparing the alternatives'integrated expected values. Finally, the SIR model of intuitionistic linguistic multi-criteria is given. The range of superiority index and inferiority index of each alternative are obtained through establishing model, and the ranking for alternatives are obtained through comparison of interval numbers.
(3) Intuitionistic two-tuple linguistic numbers and its Hamming distance are defined, the multi-granularity intuitionistic linguistic multi-criteria model is established. In which linguistic term sets have multi-granularity and criteria information is intuitionistic linguistic fuzzy set, twe moldels are proposed. In the first model, a new transformation function is given to uniform the multi-granular linguistic sets. Then, by aggregating evaluation matrices from experts and criteria information based on operator, integrated intuitionistic linguistic fuzzy information of alternatives are attained and the ranking of the whole alternative set can be obtained. In the Intuitionistic two-tuple linguistic model, the multi-granular linguistic sets are uniformed based on distance and expectation of two-tuple linguistic.The membership degree to the ideal solution of alternative is attained for every evaluation matrix and integrated membership degree is attained through calculating and by comparing the integrated membership degree, alternatives are ranked.
引文
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