【作者】 陈孝新；

【导师】 刘思峰；

【作者基本信息】 南京航空航天大学 ， 系统工程， 2009， 博士

【摘要】 灰色系统理论研究“部分信息已知、部分信息未知”的不确定性系统,把具有贫信息特征的事物作为研究对象,利用部分已知信息去发现和认识事物的发展规律。由于贫信息不确定性系统的普遍存在,决定了这一新理论具有十分广阔的发展前景。不确定灰色多属性决策是现代决策科学的一个重要领域,它在社会、经济、管理、军事和工程中具有广泛的应用。本文分别对属性值为区间灰数,或区间灰数与自然语言的灰色多属性决策问题进行了研究。本文的主要研究结果概括为以下几个方面:(1)对于属性值为区间灰数且属性权重完全已知或部分已知的不确定灰色多属性(群)决策问题,利用标准区间灰数的运算法则,求出每个方案的区间灰数型综合属性值,在决策者不能给出承担风险态度的情况下,提出了基于最小最大悔值法的灰色多属性决策方法;引入了区间灰数型正、负理想点的概念,将多属性决策的逼近理想点方法推广到灰色多属性决策情形。(2)根据规范化后的区间灰数的本质,给出了两区间灰数相离度的一个新的计算公式。提出了基于相离度的灰色区间关联系数公式和灰色区间相对关联系数公式。对属性权重部分已知的情况,提出了决策者对所有方案的偏好值为区间灰数的灰色关联决策方法;将多属性群体决策的TOPSIS方法推广到灰色多属性群体决策情形。对属性权重完全未知且决策者对方案有偏好和无偏好两种情形,分别建立了确定属性权重的非线性优化模型,给出了灰色关联决策方法;对属性权重完全未知的灰色多属性(群)决策问题,根据灰色区间关联系数的意义,提出了方案间优势度、方案间相对优势度和方案集中方案间优势比较矩阵等概念及计算公式,建立了基于灰色区间关联系数的模糊互补判断矩阵排序方法;引入了理想专家、群体关联度评分矩阵、方案间群体优势度和方案集中方案间群体优势比较矩阵等概念及计算公式,建立了基于投影的特征向量法和模糊互补判断矩阵排序方法的两种决策算法,这些方法使属性权重完全未知的决策问题摆脱了依赖权重的束缚。(3)对于属性权重完全已知的情形,针对属性值为区间灰数和自然语言的混合型灰色多属性(群)决策问题,提出了基于证据推理解析算法的决策方法;针对属性值为区间灰数和不确定自然语言的混合型灰色多属性决策问题,提出了区间灰数转换成相应的等级区间的信任度计算公式,建立了基于等级区间证据推理递归算法的决策方法。对于属性权重部分已知的情形,针对属性值为区间灰数和自然语言,或区间灰数和不确定自然语言的混合型灰色多属性决策问题,通过证据推理的解析算法或等级区间证据推理的递归算法和期望效用分别建立了非线性规划模型。提出了利用遗传算法求解的新思路,并给出了实现过程。决策者还可根据自己的风险偏好选择最优决策方案,其中风险偏好是指灰色信息的白化方法,或评价等级的效用取法。(4)研究了取折衷解的方法在混合型灰色多属性决策的应用。首次将目前应用较少的VIKOR方法拓展应用于混合型灰色多属性决策当中,分别对属性权重已知和未知的混合型多属性决策问题,利用VIKOR方法给出了决策方法。更多还原

【Abstract】 The researching objective of grey systems theory is the uncertain system whose information is partly knowable and partly unknowable. Its character is missing information. We can find its regularity using the knowable information. Due to the ubiquity of missing information uncertain systems, Grey system theories are more prosperous in the future. Furthermore, grey multiple attribute decision making is an important field in present decision sciences, and it can be applied widely to society, economics, management, military affairs and engineering. This paper is to do a research on problems of grey multiple attribute decision making with interval grey numbers, or interval grey numbers and linguistic variables, respectively. The research results are below:(1) Using the operation principle of the standard interval gery number and computing interval grey numbers of overall value of alternatives, ranking method based on the minimax regret approach is proposed for grey multiple attribute decision making problems, including grey multiple attribute group decision making problems, in which the attribute values take interval grey numbers, and the weight information is known, or known partially.Concepts of interval grey number of positive ideal point and negative ideal point are introduced and multiple attribute decision making method marching on ideal point is generalized to grey multiple attribute decision making.(2) The definition of deviation degree between two interval grey numbers is given from the essence of normalized interval grey number as well as the concept and formula. The incidence degree coefficient formula and relative incidence degree coefficient formula are constructed from an analytical technique based on deviation degree for interval grey numbers. Incidence degree decision making approach is put, in which decision-maker’preferences to alternatives are interval grey number with partial weight information.The TOPSIS method of multiple attribute group decision making is generalized to grey multiple attribute group decision making. Two nonlinear programming models and incidence degree decision making approach are established under the situations where decision maker has (or has no) preference information on alternatives for the case of the unknown attribute weight. For grey multiple attribute decision making problems without the attribute weight, according to essence of grey incidence coefficient, the concepts and formulas for predominance strength and predominance comparative matrix between alternatives are introduced and the alternative is ranked according to the priority method of fuzzy complementary judgment matrix. For grey multiple attribute group decision making problems without the attribute weight, according to essence of grey incidence degree, ideal expert, assessment matrix of group incidence degree, and formulas for group predominance strength and group predominance comparative matrix between alternatives are introduced and two methods of ranking alternatives are given by the priority method of fuzzy complementary judgment matrix and by the eigenvector algorithm based on projection.(3) For the case of the known attribute weight, the evidential reasoning approaches are proposed for hybrid grey multiple attribute (or group) decision making problems in which the attribute values are interval grey numbers and linguistic variables, respectively; the grade interval evidential reasoning approach is proposed for hybrid grey multiple attribute decision making problems in which the attribute values are interval grey numbers and uncertain linguistic variables. For hybrid grey multiple attribute decision making problems, in which the information on the attribute’s weight is known partially and the attribute values are interval grey numbers and linguistic variables, or the attribute values are interval grey numbers and uncertain linguistic variables, the approaches based on the evidential reasoning are proposed, respectively. In these approaches, through evidential reasoning algorithms, the attribute values are aggregated and two nonlinear programming models are developed. Because classic programming methods are hard to solve the nonlinear programming models, using genetic algorithms to solve the nonlinear programming models, the attribute’s weight, the maximum, minimum, and average expected values are gained. So the ranking of the alternatives can be attained. Also, selecting the risk-preferences of the decision maker is a very important, because changing the points of discontinuity in the piecewise linear utility function and choosing whitenization methods of grey information may affect the choice of the best alternative.(4) The research on the application of compromise method for hybrid grey multiple attribute decision making is given.For hybrid grey multiple attribute decision making problems, in which the information on the attribute’s weight is unknown,or known and the attribute values are interval grey numbers and linguistic variables, VIKOR method is proposed. Meanwhile, the range of VIKOR is developed.更多还原