Group decision making procedure considering preference strength under incomplete information

This article deals with the multiple criteria decision making problem with incomplete information when multiple decision makers (Multiple Criteria Group Decision Making: MCGDM) are involved. Usually decision makers (DMs) are willing or able to provide only incomplete information, because of time pressure, lack of knowledge or data, and their limited expertise related to the problem domain. There have only been a few studies considering incomplete information in group settings. We also consider the case where importance weights are given incompletely. This article suggests the possibility that individually optimized results can be used to build group consensus. Individual optimization results by pairwise dominance, contain useful information in forming consensus, such as, ordinal rankings or preference intensity of an alternative over the others. Rather than using ordinal rankings for aggregation which do not consider preference strength, we suggest a procedure that takes account of individual DMs' preference strength.     

非完备决策信息系统中的不确定性度量

针对粗糙集数据分析中的不确定性度量问题。本文首先构造一种新型的考虑条件属性缺失度的目标概念条件熵和决策知识条件熵。在此基础上,提出基于条件熵的属性权重确定技术和最小条件熵非完备属性取值补充方法,用以解决属性权重完全未知的非完备多属性决策问题。应用实例分析表明:该方法能有效结合粗粒度的初步分级信息,客观地确定决策因素取值,具有很强的解释意义,得到的决策结果更为合理有效。     

一类基于优势关系的不完全信息多属性决策方法

针对属性权重和属性值信息均不完全,且含有非线性形式的多属性决策问题,提出一种基于优势关系实现方案择优与排序的决策方法.首先定义方案优势、弱优势和潜在优关系,构建等价的非线性规划模型,确定优势和潜在优方案;然后揭示、论证了非劣集与潜在优集的关系,提出了方案优势度指标,并据此给出了方案择优与排序的实现步骤;最后,提出采用变量替换法求解非线性决策模型.实例计算结果表明,所提出的方法是可行且有效的.     

信息不完全下多属性群决策的证据合成方法

针对不完全信息下多属性群决策问题,分析决策者判断信息的可靠性对群决策结果的影响,提出一种基于相对可靠度的证据合成方法。首先对定量和定性属性值进行归一化处理;然后分析决策者判断信息的相对可靠度,运用Dempster合成法则对所有焦元的基本概率分配值进行计算与合成,并给出证据推理方法的主要步骤;最后给出了一个算例。     

混合值不完备决策信息系统的粗糙分类方法

针对混合值不完备决策信息系统,提出一种将邻域联系度粗糙集与贝叶斯理论相结合的分类方法。定义了一种新的属性辨识矩阵——同异反辨识矩阵,给出了基于同异反辨识矩阵的t分配约简算法,以及对约简后的决策信息系统建立基于邻域联系度粗糙集的最小错误率贝叶斯决策准则,用于对含有混合属性值以及不完备数据的对象进行分类。实验表明所提出的方法是客观有效的。     

基于信任机制的不完全信息大群体决策方法

针对不完全偏好信息大群体决策问题, 引入访问控制中的信任机制, 建立直接信任度与推荐信任度, 提出一种基于信任机制的补值方法; 分析了基于距离相似度存在的问题, 定义了一种新的距离相似度, 并与余弦相似度结合, 构建了决策偏好二元相似度的相聚模型; 利用聚类方法求解决策成员的权重, 并与补值后的完整偏好矩阵进行合成, 求得决策方案排序. 最后, 利用一个现有的文献案例验证了所提出方法的有效性和优越性.

     

A data envelopment analysis approach to multicriteria decision problems with incomplete information

As a decision aid for discrete multicriteria decision problems, this paper proposes a multilevel graph of alternatives to represent the ranking, to the extent that this is possible when incomplete information on weights is available under the assumption of the additive value function. To construct it, the nested decomposition of the set of alternatives is established along the lines of data envelopment analysis (DEA). A numerical example is given to illustrate a multilevel graph based on the nested decomposition and compare it with the hierarchical dominance graph based on dominance relations proposed by Park and Kim.     

On a decision procedure for quantified linear programs

Quantified linear programming is the problem of checking whether a polyhedron specified by a linear system of inequalities is non-empty, with respect to a specified quantifier string. Quantified linear programming subsumes traditional linear programming, since in traditional linear programming, all the program variables are existentially quantified (implicitly), whereas, in quantified linear programming, a program variable may be existentially quantified or universally quantified over a continuous range. In this paper, the term linear programming is used to describe the problem of checking whether a system of linear inequalities has a feasible solution. On account of the alternation of quantifiers in the specification of a quantified linear program (QLP), this problem is non-trivial. QLPs represent a class of declarative constraint logic programs (CLPs) that are extremely rich in their expressive power. The complexity of quantified linear programming for arbitrary constraint matrices is unknown. In this paper, we show that polynomial time decision procedures exist for the case in which the constraint matrix satisfies certain structural properties. We also provide a taxonomy of quantified linear programs, based on the structure of the quantifier string and discuss the computational complexities of the constituent classes. This research has been supported in part by the Air Force Office of Scientific Research under contract FA9550-06-1-0050.     

Hidden Markov model-based asynchronous exponential stabilization for stochastic Markovian jump systems with incomplete controller mode information

In this paper, the exponential stability of a kind of It $\widehat{\mathrm{o}}$ Markovian jump system is studied. Specifically, the exponential stability is ensured by designing an asynchronous delayed-feedback controller, whose modes are inconsistent with those of the original system. We have built the necessary new relationship between controller modes and system modes, which can facilitate the stability analysis and also make the famous existing ones special cases of the proposed one. Moreover, practically ubiquitous controller delays, which occur between the sensors and controllers, to the detriment of the system stability, are taken into account, and their maximum values are provided in a theoretic way. In this way, the exponential stability can be well ensured against controller delays. With an eye to practical applications, the transition rates of the considered system and the designed asynchronous controller are assumed to be uncertain, and they can be well dealt with by using a new approach with lower conservatism. Furthermore, a practical example and some comparative examples are given to demonstrate the effectiveness and superiorities of the obtained conclusion.     

A novel fuzzy multi-criteria decision framework for sustainable supplier selection with incomplete information

Both academic and corporate interest in sustainable supply chains has increased in recent years. Supplier selection process is one of the key operational tasks for sustainable supply chain management. This paper examines the problem of identifying an effective model based on sustainability principles for supplier selection operations in supply chains. Due to its multi-criteria nature, the sustainable supplier evaluation process requires an appropriate multi-criteria analysis and solution approach. The approach should also consider that decision makers might face situations such as time pressure, lack of expertise in related issue, etc., during the evaluation process. The paper develops a novel approach based on fuzzy analytic network process within multi-person decision-making schema under incomplete preference relations. The method not only makes sufficient evaluations using the provided preference information, but also maintains the consistency level of the evaluations. Finally, the paper analyzes the sustainability of a number of suppliers in a real-life problem to demonstrate the validity of the proposed evaluation model.     

Maximizing deviation method for neutrosophic multiple attribute decision making with incomplete weight information

This paper develops a method for solving the multiple attribute decision-making problems with the single-valued neutrosophic information or interval neutrosophic information. We first propose two discrimination functions referred to as score function and accuracy function for ranking the neutrosophic numbers. An optimization model to determine the attribute weights that are partly known is established based on the maximizing deviation method. For the special situations where the information about attribute weights is completely unknown, we propose another optimization model. A practical and useful formula which can be used to determine the attribute weights is obtained by solving a proposed nonlinear optimization problem. To aggregate the neutrosophic information corresponding to each alternative, we utilize the neutrosophic weighted averaging operators which are the single-valued neutrosophic weighted averaging operator and the interval neutrosophic weighted averaging operator. Thus, we can determine the order of alternatives and choose the most desirable one(s) based on the score function and accuracy function. Finally, some illustrative examples are presented to verify the proposed approach and to present its effectiveness and practicality.     

On the stability of price-adjusting oligopolies with incomplete information

A general linear price-adjusting scheme is examined in non-linear Bertrand oligopolies that contains the models of Negishi and Jin as special cases among others. The existence of a unique equilibrium of the dynamic process is first proved, and then under realistic conditions, the global asymptotic stability of the equilibrium is verified. Particular cases illustrate the general results.     

Bargaining with incomplete information

This paper analyses the process and outcomes of competitive bilateral negotiation for a model based on negotiation decision functions. Each agent has time constraints in the form of a deadline and a discounting factor. The importance of information possessed by participants is highlighted by exploring all possible incomplete information scenarios – both symmetric and asymmetric. In particular, we examine a range of negotiation scenarios in which the amount of information that agents have about their opponent’s parameters is systematically varied. For each scenario, we determine the equilibrium solution and study its properties. The main results of our study are as follows. Firstly, in some scenarios agreement takes place at the earlier deadline, while in others it takes place near the beginning of negotiation. Secondly, in some scenarios the price surplus is split equally between the agents while in others the entire price surplus goes to a single agent. Thirdly, for each possible scenario, the equilibrium outcome possesses the properties of uniqueness and symmetry – although it is not always Pareto optimal. Finally, we also show the relative impacts of the opponent’s parameters on the bargaining outcome.     

On group decision making with four formats of incomplete preference relations

In this paper, a new approach is proposed to solve group decision making (GDM) problems where the preference information on alternatives provided by decision makers (DMs) is represented in four formats of incomplete preference relations, i.e., incomplete multiplicative preference relations, incomplete fuzzy preference relations, incomplete additive linguistic preference relations, incomplete multiplicative linguistic preference relations. In order to make the collective opinion close each decision maker’s opinion as near as possible, an optimization model is constructed to integrate the four different formats of incomplete preference relations and to compute the collective ranking values of the alternatives. The ranking of alternatives or selection of the most desirable alternative(s) is directly obtained from the derived collective ranking values. A numerical example is also used to illustrate the applicability of the proposed approach.     

基于正态分布区间数的信息不完全的群决策方法

针对属性值为正态分布区间数而属件权重信息不完全的多属性群决策问题,定义了一些新的集成算子,即正态分布区间数的加权算术平均(NDINWAA)算子、正态分布区间数的有序加权平均(NDINOWA)算子和正态分布区间数的混合加权平均(NDINHA)算子,进而提出一种幕于正态分布区间数的信息不完全的多属性群决策方法.该方法利用NDINWAA算了和NDINHA算子对正态分布区间数属性值进行集成,利用正态分布区间数属性值的方差,通过建立优化模型确定最优属性权重,利用期望-方差准则对方案进行排序并择优.实例分析表明了该方法的可行性和有效性.     

A method for multiple attribute decision making with incomplete weight information in linguistic setting

The aim of this paper is to investigate the multiple attribute decision making problems with linguistic information, in which the information about attribute weights is incompletely known, and the attribute values take the form of linguistic variables. We first introduce some approaches to obtaining the weight information of attributes, and then establish an optimization model based on the ideal point of attribute values, by which the attribute weights can be determined. For the special situations where the information about attribute weights is completely unknown, we establish another optimization model. By solving this model, we get a simple and exact formula, which can be used to determine the attribute weights. We utilize the numerical weighting linguistic average (NWLA) operator to aggregate the linguistic variables corresponding to each alternative, and then rank the alternatives by means of the aggregated linguistic information. Finally, the developed method is applied to the ranking and selection of propulsion/manoeuvring system of a double-ended passenger ferry.     

信息量不完备决策表属性约简的一种新算法

目前,基于不完备决策表的属性约简研究较少。基于信息量的不完备决策表属性约简是一种新的属性约简。由于在该属性约简中,计算相容关系是最主要的计算,也比计算等价关系要难得多。基于信息量的不完备决策表的属性约简算法的时间复杂度一般为O（|C|²|U|²）。为降低其时间复杂度,首先分析了老算法的不足,然后给出了一个效率较好的计算相容类的算法。最后设计了一个新的基于信息量的不完备决策表的属性约简算法,其时间复杂度为O（|C|²|U|²）。     

Modeling a Markovian decision process by neural network

One of the difficulties in generating an optimal policy for systems planning and control by the Markov decision process is that the state transition probabilities must be known a priori. A usual approach to estimate the state transition probabilities is by using historical data. However, if the process is not completely stationary, it may be more convenient to obtain estimates of the transition probabilities by using another approach, namely, parameter adaptation by neural networks.

A significant advantage of neural network modeling of the Markovian decision problem is that the temporal nonstationary state transition probabilities can be revised by a parameter learning paradigm. The objective of this paper is to present this approach and demonstrate its applicability by modeling a finite-stage decision problem.     

GRA method for multiple attribute decision making with incomplete weight information in intuitionistic fuzzy setting

The aim of this paper is to investigate the multiple attribute decision-making problems with intuitionistic fuzzy information, in which the information about attribute weights is incompletely known, and the attribute values take the form of intuitionistic fuzzy numbers. In order to get the weight vector of the attribute, we establish an optimization model based on the basic ideal of traditional grey relational analysis (GRA) method, by which the attribute weights can be determined. Then, based on the traditional GRA method, calculation steps for solving intuitionistic fuzzy multiple attribute decision-making problems with incompletely known weight information are given. The degree of grey relation between every alternative and positive-ideal solution and negative-ideal solution are calculated. Then, a relative relational degree is defined to determine the ranking order of all alternatives by calculating the degree of grey relation to both the positive-ideal solution (PIS) and negative-ideal solution (NIS) simultaneously. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.