几类模糊多属性决策方法研究
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摘要
多属性决策是现代决策科学的重要分支,其理论与方法在经济、管理、工程和军事等诸多领域都有着广泛的应用。在理论研究方面,多属性决策自从其诞生以来就一直是学术界关注的研究课题。由于客观事物的复杂性、不确定性以及人类思维的模糊性,当专家受一些主、客观因素制约时,属性值往往以区间数、三角模糊数、语言变量、不确定语言变量或直觉模糊信息等不同形式的模糊决策信息给出。多属性决策问题很多是定性问题,模糊性就更显著,这使得模糊多属性决策问题引起了学术界极大的关注。因此研究模糊多属性决策问题具有重要的理论意义和较高的实际应用价值。本文研究了基于模糊信息的几类多属性决策问题,主要包括以下几个方面：
1.研究了区间数多属性决策的灰色关联分析方法和基于三参数区间数据的调和集结算子。首先针对属性权重信息不完全的区间数的多属性决策问题,给出了解决该问题的灰色关联分析方法；其次针对对方案有偏好的区间数多属性决策问题,给出了区间数多属性决策问题的灰色关联分析方法；最后基于连续区间数有序加权调和平均(C-OWHA)算子,提出了CP-OWHA算子、WHCP-OWHA算子、OWHCP-OWHA算子和CCP-OWHA算子,并提出了一种三参数区间数的多属性群决策方法。
2.研究了基于三角模糊环境的调和集结算子和决策方法。首先提出了模糊有序加权调和平均(FOWHA)算子,并分析了该算子的性质,进而给出了一种基于FOWHA算子多属性决策方法；其次提出了模糊加权调和平均(FWHA)算子和模糊的诱导有序加权调和平均(FIOWHA)算子,提出了一种多属性群决策方法。
3.研究了二元语义的多属性决策方法。首先依据传统的灰色关联分析方法,提出一种二元语义群决策方法；其次提出了二元语义加权调和平均(T-WHA)算子、二元语义有序加权调和平均(T-OWHA)算子和二元语义组合加权调和平均T-CWHA)算子,并提出了一种基于T-WHA和T-CWHA算子的二元语义多属性群决策方法；然后针对属性值和权重值均为语言评价信息的多属性群决策问题,提出了扩展的二元语义加权几何(ET-WG)算子和扩展的二元语义有序加权几何(ET-OWG)算子,并分析了这些算子的一些性质,然后提出了一种群决策方法。最后提出了扩展的二元语义加权调和平均(ET-WHA)算子和扩展的二元语义有序加权调和平均(ET-OWHA)算子,分析了这些算子的一些性质,并提出了一种基于ET-WHA算子和ET-OWHA算子的群决策方法。
4.研究了不确定语言多属性决策方法。首先提出了不确定语言混合几何平均(ULHGM)算子,证明了ULWGM算子和ULOWG算子均为ULHGM算子的特例,同时提出了一种不确定语言多属性群决策方法；其次针对属性权重完全未知的不确定语言多属性决策问题,给出了一个求解权重的组合方法;针对属性权重完全未知,且对方案有偏好的不确定语言多属性决策问题,给出了求解权重的方法,进而对决策方案进行排序和择优。
5.研究了直觉模糊多属性决策方法。首先针对属性权重完全未知或属性权重不完全的直觉模糊多属性决策问题,给出了求解权重的最大偏差的目标规划模型。其次将上述方法推广到区间直觉模糊多属性决策问题;最后提出了动态直觉模糊加权几何(DIFWG)算子和不确定动态直觉模糊加权几何(UDIFWG)算子,并给出了相应的动态直觉模糊多属性决策方法。
Multiple attribute decision making (MADM) is an important branch of modern decision sciences. Its theory and method are widely applied to many areas, such as economics, management, engineering, military affairs, and so forth. In the fundamental research, the MADM have been always the research topics which the academic circles pay attention since its birth. However, in many situations, the input arguments take the form of fuzzy information such as interval numbers, triangular fuzzy number, linguistic variables, uncertain linguistic variables or intuitionistic fuzzy information because of complexity and uncertainty of object, lack of knowledge and people's limited expertise related with problem domain. The MADM problems are often qualitative problems, and their fuzziness is more remarkable. So, the fuzzy MADM problems arouse the academic circles enormous interest. Therefore, the research on fuzzy MADM has important theoretic significance and higher practical application. Thus, the purpose of this paper is to do a deep research on the fuzzy MADM problems under some situations. The detailed arrangement of this paper stands out as follows:
1. Study on the MADM problems with interval data. (1) a modified grey relational analysis (GRA) method is proposed to solve the interval MADM problems with incomplete weight information; (2) a modified grey relational analysis (GRA) method is proposed to solve the interval MADM problems with preference information on alternatives; (3) Based on the C-OWHA operator, the continuous three parameters interval argument OWHA (CP-OWHA) operator are proposed and a method based on the WHCP-OWHA and CCP-OWHA operators is developed to solve three parameters interval MAGDM problems.
2. Study on the MADM problems with triangular fuzzy number. (1) A fuzzy ordered weighted harmonic averaging (FOWHA) operator is proposed and a new decision making method based on the FOWHA operator is proposed; (2) fuzzy weighted harmonic averaging (FWHA) operator and fuzzy induced ordered weighted harmonic averaging (FIOWHA) operator are proposed to solve fuzzy MAGDM.
3. Study on the MADM problems with 2-tuple linguistic information. (1) a modified grey relational analysis (GRA) method is proposed to solve the 2-tuple linguistic MAGDM problems; (2) the 2-tuple linguistic weighted harmonic averaging (T-WHA),2-tuple linguistic ordered weighted harmonic averaging (T-OWHA) and 2-tuple linguistic combined weighted harmonic averaging (T-CWHA) operator are proposed and properties of the operators are analyzed. Then, a method based on the T-WHA and T-CWHA operators for MAGDM is presented. (3) the extended 2-tuple linguistic weighted geometric (ET-WG) and the extended 2-tuple linguistic ordered weighted geometric (ET-OWG) operator are proposed to solve MAGDM with 2-tuple linguistic information; (4) the extended 2-tuple linguistic weighted harmonic averaging (ET-WHA) and the extended 2-tuple linguistic ordered weighted harmonic averaging (ET-OWHA) operator are proposed to solve MAGDM with 2-tuple linguistic information.
4. Study on the MADM problems with uncertain linguistic information. (1) An uncertain linguistic hybrid geometric mean (ULHGM) operator is proposed. An approach to MAGDM with uncertain linguistic information is developed based on the ULWGM and the ULHGM operators. (2) A combined method is used to solve uncertain linguistic MADM problems with completely unknown weight information; (3) a combined method is used to solve uncertain linguistic MADM problems with preference information on alternatives.
5. Study on the MADM problems with intuitionistic fuzzy information. (1) two optimization models based on the maximizing deviation method are develop to solve MADM problems with intuitionistic fuzzy information; (2) two optimization models based on the maximizing deviation method are extended to the interval-valued intuitionistic fuzzy setting; (3) the dynamic intuitionistic fuzzy weighted geometric (DIFWG) operator and uncertain dynamic intuitionistic fuzzy weighted geometric (UDIFWG) operator are proposed to solve dynamic intuitionistic fuzzy MADM problems.
1.研究了区间数多属性决策的灰色关联分析方法和基于三参数区间数据的调和集结算子。首先针对属性权重信息不完全的区间数的多属性决策问题,给出了解决该问题的灰色关联分析方法；其次针对对方案有偏好的区间数多属性决策问题,给出了区间数多属性决策问题的灰色关联分析方法；最后基于连续区间数有序加权调和平均(C-OWHA)算子,提出了CP-OWHA算子、WHCP-OWHA算子、OWHCP-OWHA算子和CCP-OWHA算子,并提出了一种三参数区间数的多属性群决策方法。
2.研究了基于三角模糊环境的调和集结算子和决策方法。首先提出了模糊有序加权调和平均(FOWHA)算子,并分析了该算子的性质,进而给出了一种基于FOWHA算子多属性决策方法；其次提出了模糊加权调和平均(FWHA)算子和模糊的诱导有序加权调和平均(FIOWHA)算子,提出了一种多属性群决策方法。
3.研究了二元语义的多属性决策方法。首先依据传统的灰色关联分析方法,提出一种二元语义群决策方法；其次提出了二元语义加权调和平均(T-WHA)算子、二元语义有序加权调和平均(T-OWHA)算子和二元语义组合加权调和平均T-CWHA)算子,并提出了一种基于T-WHA和T-CWHA算子的二元语义多属性群决策方法；然后针对属性值和权重值均为语言评价信息的多属性群决策问题,提出了扩展的二元语义加权几何(ET-WG)算子和扩展的二元语义有序加权几何(ET-OWG)算子,并分析了这些算子的一些性质,然后提出了一种群决策方法。最后提出了扩展的二元语义加权调和平均(ET-WHA)算子和扩展的二元语义有序加权调和平均(ET-OWHA)算子,分析了这些算子的一些性质,并提出了一种基于ET-WHA算子和ET-OWHA算子的群决策方法。
4.研究了不确定语言多属性决策方法。首先提出了不确定语言混合几何平均(ULHGM)算子,证明了ULWGM算子和ULOWG算子均为ULHGM算子的特例,同时提出了一种不确定语言多属性群决策方法；其次针对属性权重完全未知的不确定语言多属性决策问题,给出了一个求解权重的组合方法;针对属性权重完全未知,且对方案有偏好的不确定语言多属性决策问题,给出了求解权重的方法,进而对决策方案进行排序和择优。
5.研究了直觉模糊多属性决策方法。首先针对属性权重完全未知或属性权重不完全的直觉模糊多属性决策问题,给出了求解权重的最大偏差的目标规划模型。其次将上述方法推广到区间直觉模糊多属性决策问题;最后提出了动态直觉模糊加权几何(DIFWG)算子和不确定动态直觉模糊加权几何(UDIFWG)算子,并给出了相应的动态直觉模糊多属性决策方法。
Multiple attribute decision making (MADM) is an important branch of modern decision sciences. Its theory and method are widely applied to many areas, such as economics, management, engineering, military affairs, and so forth. In the fundamental research, the MADM have been always the research topics which the academic circles pay attention since its birth. However, in many situations, the input arguments take the form of fuzzy information such as interval numbers, triangular fuzzy number, linguistic variables, uncertain linguistic variables or intuitionistic fuzzy information because of complexity and uncertainty of object, lack of knowledge and people's limited expertise related with problem domain. The MADM problems are often qualitative problems, and their fuzziness is more remarkable. So, the fuzzy MADM problems arouse the academic circles enormous interest. Therefore, the research on fuzzy MADM has important theoretic significance and higher practical application. Thus, the purpose of this paper is to do a deep research on the fuzzy MADM problems under some situations. The detailed arrangement of this paper stands out as follows:
1. Study on the MADM problems with interval data. (1) a modified grey relational analysis (GRA) method is proposed to solve the interval MADM problems with incomplete weight information; (2) a modified grey relational analysis (GRA) method is proposed to solve the interval MADM problems with preference information on alternatives; (3) Based on the C-OWHA operator, the continuous three parameters interval argument OWHA (CP-OWHA) operator are proposed and a method based on the WHCP-OWHA and CCP-OWHA operators is developed to solve three parameters interval MAGDM problems.
2. Study on the MADM problems with triangular fuzzy number. (1) A fuzzy ordered weighted harmonic averaging (FOWHA) operator is proposed and a new decision making method based on the FOWHA operator is proposed; (2) fuzzy weighted harmonic averaging (FWHA) operator and fuzzy induced ordered weighted harmonic averaging (FIOWHA) operator are proposed to solve fuzzy MAGDM.
3. Study on the MADM problems with 2-tuple linguistic information. (1) a modified grey relational analysis (GRA) method is proposed to solve the 2-tuple linguistic MAGDM problems; (2) the 2-tuple linguistic weighted harmonic averaging (T-WHA),2-tuple linguistic ordered weighted harmonic averaging (T-OWHA) and 2-tuple linguistic combined weighted harmonic averaging (T-CWHA) operator are proposed and properties of the operators are analyzed. Then, a method based on the T-WHA and T-CWHA operators for MAGDM is presented. (3) the extended 2-tuple linguistic weighted geometric (ET-WG) and the extended 2-tuple linguistic ordered weighted geometric (ET-OWG) operator are proposed to solve MAGDM with 2-tuple linguistic information; (4) the extended 2-tuple linguistic weighted harmonic averaging (ET-WHA) and the extended 2-tuple linguistic ordered weighted harmonic averaging (ET-OWHA) operator are proposed to solve MAGDM with 2-tuple linguistic information.
4. Study on the MADM problems with uncertain linguistic information. (1) An uncertain linguistic hybrid geometric mean (ULHGM) operator is proposed. An approach to MAGDM with uncertain linguistic information is developed based on the ULWGM and the ULHGM operators. (2) A combined method is used to solve uncertain linguistic MADM problems with completely unknown weight information; (3) a combined method is used to solve uncertain linguistic MADM problems with preference information on alternatives.
5. Study on the MADM problems with intuitionistic fuzzy information. (1) two optimization models based on the maximizing deviation method are develop to solve MADM problems with intuitionistic fuzzy information; (2) two optimization models based on the maximizing deviation method are extended to the interval-valued intuitionistic fuzzy setting; (3) the dynamic intuitionistic fuzzy weighted geometric (DIFWG) operator and uncertain dynamic intuitionistic fuzzy weighted geometric (UDIFWG) operator are proposed to solve dynamic intuitionistic fuzzy MADM problems.
引文
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