基于近似随进占优的概率区间数信息多属性决策方法

针对传统区间数包含信息量太少,导致决策结果具有很大不确定性的问题,提出了基于VIKOR的概率区间数多属性决策方法。该方法首先将概率信息引入区间数,定义概率区间数的运算规则和集结算子。接着基于近似随机占优理念,定义了一种新的主客观结合的占优度,在此基础上确立了概率区间数的比较规则。最后将专家给出的概率区间数决策矩阵转化为占优度矩阵,并利用 VIKOR 方法对其求解。算例分析表明,该方法对概率分布的缓急变化具有很好的稳定性,而对于概率分布的偏态趋势变化具有敏感性。得到的决策结果在与传统方法一致的基础上更为准确。     

多方参与决策且指标集有差异的方案排序方法

针对多方参与决策且指标集有差异的群体决策问题,提出一种基于模糊软集理论的方案排序方法.依据各方决策者所考虑的指标参数和打分值信息给出多方决策信息的模糊软集表示方法,并利用模糊软集的且运算得到综合各方决策者所考虑指标参数的新模糊软集及其隶属度矩阵;然后在考虑指标权重的前提下构建关于方案的加权比较矩阵,进而通过计算得出的各方案优势度确定方案的排序结果;最后,通过一个算例表明了所提出方法的可行性和有效性.     

指标期望为随机变量情形的多指标决策方法

针对指标期望为随机变量情形的多指标决策问题, 提出一种决策分析方法. 该方法首先通过计算指标值相对于指标期望的损益值, 将决策矩阵转化为关于指标期望的损益矩阵; 然后运用随机占优准则, 通过判断针对每个指标两两方案之间的随机占优关系, 进而构建两两方案的随机占优关系矩阵, 并使用PROMETHEE II 方法对方案进行排序; 最后以某研究所移动硬盘采购问题为例, 对所提出方法的实用性进行说明.

     

一种基于前景随机占优准则的随机多属性决策方法

针对属性值为随机变量的随机多属性决策问题,提出一种决策分析方法.该方法将决策者的行为因素引入随机多属性决策,将具有随机变量的决策矩阵转化为关于参考点的收益和损失矩阵,依据前景随机占优准则判断并确定两两方案之间比较所具有的占优关系,并构建相应的前景随机占优关系矩阵.在此基础上,运用PROMETHEE Ⅱ方法得到了方案的排序结果.通过一个算例验证了所提出方法的可行性和有效性.     

A decision framework for cultural and creative products based on IF-TODIM method and group consensus reaching model

Along with increasing the emphasis on cultural attributes, product design is not only satisfied with the realization of function and appearance, but also considers the embodiment of human emotion and social style. As a result, the number of creative product based on cultural style is increasing. However, existing product decision studies do not consider this style-oriented product- ranking problem, ignore the influence of cultural style and fuzzy decision-making environment on the limited psychological behavior of decision makers (DMs). Decision is a worthwhile research topic in order to facilitate ranking for cultural and creative products (CCPs). Therefore, this paper provides a decision framework based on intuitionistic fuzzy TODIM (IF-TODIM) method and group consensus reaching (GCR) model to fill this gap. Benefit from the theory of intuitionistic fuzzy set, IF-TODIM method can deal with the limited psychological behavior of DMs and the fuzziness of decision environment. This method bases on CCPs characteristics and cultural hierarchy theory (CHT) to select the decision criteria, and applies IF-TODIM method to quantify the relationship of DMs’ preferences and establish the dominance matrix for the alternatives. Furthermore, the GCP model is introduced to improve the group consensus of DMs, and the modified overall dominance matrixes are adopted to determine the alternatives scores and ranking results. The new Chinese style decorations are used as a case study to demonstrate the practicality and feasibility of the proposed method. Moreover, comparing with IF-TOPSIS method are further to verify its effectiveness and superiority.     

三角模糊数在多属性决策中的建模

为了获得三角模糊数的多属性决策数学模型,将语言变量和三角模糊数引入到多属性决策中,用语言变量或三角模糊数表示多属性决策中的属性值和各属性的权重,采用加权和法求得每个备选方案的三角模糊数最终评价值,并应用三角模糊数的减法运算定义任意两个三角模糊数的优越度,在方案两两对比求得优越度后建立方案的互补判断矩阵,采用最小平方法求得方案排序向量,根据排序向量元素的大小进行方案排序。     

A family of dominance rules for multiattribute decision making under uncertainty

Multiattribute decision-making involves choosing from a set of alternatives each of which is evaluated along multiple criteria that reflect the dimensions of interest to the goals and values of the decision-maker. Dominance-based decision-making narrows down the focus of the decision to the Pareto optimal set. The elimination of dominated alternatives is a compelling principle of rationality since each dominated alternative is logically inferior to its dominating alternative, given the criteria of evaluation. One kind of uncertainty in multiattribute decision making arises out of noisy or inaccurate criteria evaluations. The application of the principle of dominance is not quite rational if the criteria evaluations are known to be noisy. In this paper, we see how dominance-based decision-making can be applied to multiattribute decision-making problems with uncertainty due to noisy criteria values. In particular it will be shown that, for bounded uncertainty it is possible to produce the smallest sufficient subset that is guaranteed to contain all of the nondominated alternatives, and the largest necessary subset that contains only nondominated alternatives. For unbounded uncertainty, we will see how these notions of sufficiency and necessity can be adapted to varying degrees of probabilistic assurances desired by the decision-maker, and that the varying degrees of user assurance map naturally to a family of dominance rules.     

基于前景随机占优的多属性多标度大群体决策方法

针对具有属性期望的多属性多标度大群体决策问题,在考虑参与决策人心理行为的情境下,将每个参与决策人给出的属性期望视为其参照点,并构建群体感知的收益-损失的概率分布;然后,基于前景随机占优准则建立方案比较的前景随机占优关系矩阵,并通过计算方案比较的前景随机优势度来得到方案的排序.算例分析表明了所提出方法的可行性和有效性.     

Stochastic Dominance for Measure Based Uncertain Decision Making

Our interest is in the problem of comparing alternatives with uncertain payoffs when the uncertainty is represented using a measure. We first describe various aspects of the use of a measure to represent uncertainty. We recall that probability is a special well‐understood example of measure‐based uncertainty. We note that stochastic dominance provides a well‐established method for comparing alternatives in the case of probabilistic uncertainty. Inspired by this we develop an extension of the use of stochastic dominance for comparing uncertainty profiles to the case where the uncertainty is represented by a measure. We refer to this as measure based stochastic dominance. Do to the fact that in most cases a stochastic dominance relationship does not exist between alternatives this requires us to consider the use of surrogates for measure based stochastic dominance to compare alternatives. Here we investigate a class of surrogates for measure based stochastic dominance that we call Measure Weighted Means (MWM). As we see these MWM are numeric values consistent with measure based stochastic dominance.     

Transformation of Shaped Nested Graphs and Diagrams

This paper describes a new computational model for rule-based programming with graphs and diagrams. Using existing nesting concepts for graphs, this model defines an intuitive way of nested graph transformation that is based on variable matching. Shape rules are introduced for specifying structural consistency conditions on nested graphs. Shape rules set up a decidable type discipline for a refined model of shapely nested graph transformation. Since the refined model is compatible with the diagram editor DiaGen, it can be extended by customizable diagram interfaces so that it specifies rule-based diagram transformation.     

A generic multi-attribute analysis system

This paper describes a generic decision support system based on an additive multiattribute utility model that is intended to allay many of the operational difficulties involved in the multicriteria decision-making process. The system accounts for uncertainty about the alternative consequences and admits incomplete information about the decision-makers’ preferences, which leads to classes of utility functions and weight intervals. The additive model is used to assess, on the one hand, average overall utilities, on which the ranking of alternatives is based and, on the other, minimum and maximum overall utilities, which give further insight into the robustness of this ranking. When the information obtained is not meaningful enough so as to definitively recommend an alternative, an iteration process can be carried out by tightening the imprecise parameters and assessing the non-dominated and potentially optimal alternatives or using Monte Carlo simulation techniques to determine useful information about dominance among the alternatives.     

Optimal expansion of competence sets with multilevel skills

The purpose of competence set expansion is to find an optimal expansion process at the minimal cost and then obtain the required competence set from the acquired competence set to solve a problem. Several models have been proposed to address the competence set expansion problem of only a single decision maker or multiple decision makers without considering multilevel skills. However, a practical competence set expansion model should involve multiple decision makers and multilevel skills. This study discusses an optimal expansion model of incorporating competence sets of group decision makers with multilevel skills. The proposed method not only obtains the optimal competence set expansion of all decision makers with the maximal total benefit but finds all optimal alternatives of the competence set expansion model. A cooperative alliance problem is solved to illustrate the usefulness of the proposed method.     

A method for large group decision-making based on evaluation information provided by participators from multiple groups

Large group decision-making (LGDM) is a special group decision-making (GDM) problem, in which a large number of persons take part in decision process, while research concerning this issue is still relatively scarce. The objective of this paper is to develop a method to solve the LGDM problem, in which a large number of persons from multiple groups take part in the decision process and express their personal evaluations on the alternatives according to the pre-established identifier set. In the method, the percentage distribution on evaluations of each group concerning each alternative is determined. The decision weight of each group concerning each alternative is obtained by aggregating the subjective weight, which is provided by the organizer, and the objective weight, determined according to the level of consensus among participators' evaluations. According to the percentage distributions and decision weights, the dominance degrees on pairwise comparisons of alternatives are calculated, and a ranking of alternatives can be determined using the PROMETHEE II method. Finally, an example is given to illustrate the use of the proposed method.     

Extending Malakooti's model for ranking multicriteria alternatives with preference strength and partial information

The paper deals with a multiple attribute decision making methodology when a decision maker (DM) specifies his/her preferences in imprecise ways, which is basically an extended version of Malakooti's prior work. Usually, it is said that the DM is willing, or able, to provide partial information, because of time pressure, lack of domain knowledge, or data and the like. In this paper, we consider two categories of partial preference information. First, partial information is related to holistic preference judgments about some pair of alternatives. Second, in a situation where the characteristics of some attributes considered are abstract, or noncommensurate, it is sometimes difficult to make an exact performance evaluation of alternatives with respect to those attributes. To circumvent this difficulty, we allow the DM to specify partial information on performance evaluations, which is similar to the types of preference judgments on some pairs of alternatives. Prioritizing multiple attribute alternatives under two categories of partial information causes an intractable nonlinear program, which is the first issue we try to resolve in the paper. We further propose a measure of preference strength as a decision rule. With partial information, often the use of strict dominance rule yields a larger number of nondominated candidates than the DM wants. The paper assumes a situation where the DM is not willing to provide additional information to reduce the number of nondominated candidates, but he/she wants to have a single optimal candidate or rank ordering of alternatives. It is then necessary to develop a method like one we propose as a preference strength measure.     

A multiple attributes decision making method using individual and collaborative attribute data in a fuzzy environment

Although multiple attribute decision making (MADM) problems with both individual attribute data of a single alternative and collaborative attribute data of pairwise alternatives exist in the real world, they have seldom been a focus of research. This paper proposes a MADM method using individual and collaborative attribute data in a fuzzy environment, in which experts use linguistic variables to express their opinions. In the method, first, the evaluation matrix of individual attributes date and the judgment matrix of collaborative attributes data are constructed. Then, the central dominance of one alternative outranking other all alternatives is defined for aggregating the collaborative data. From this, an integrated decision matrix incorporating individual and collaborative attribute data is constructed. Further, based on an extended TOPSIS, the fuzzy positive-ideal solution (FPIS) and the fuzzy negative-ideal solution (FNIS) are determined, and the relative closeness of each alternative to the FPIS and FNIS is calculated to determine the ranking order of all alternatives. Finally, two examples are used to illustrate the applicability of the proposed method.     

A method for stochastic multiple criteria decision making based on dominance degrees

This paper proposes a method for solving the stochastic multiple criteria decision making (SMCDM) problem, where consequences of alternatives with respect to criteria are represented by random variables with probability distributions. Firstly, definitions and related analysis of dominance degree of one probability distribution over another are given. Then, by calculating the dominance degrees, the dominance degree matrix of alternative pairwise comparisons with respect to each criterion is built. Further, using PROMETHEE II method, an overall dominance degree matrix of alternative pairwise comparisons is constructed, and a net flow of each alternative is calculated. Based on the obtained net flows, a ranking of alternatives is determined. Finally, numerical examples for the three cases are given to illustrate the use of the proposed method.     

基于广义Choquet积分的Pythagorean不确定语言TODIM方法及其应用

针对评价信息为Pythagorean不确定语言变量且指标具有关联性的多指标决策问题,考虑到决策者的参照依赖和损失规避等有限理性行为,提出一种基于广义Choquet积分的Pythagorean不确定语言TODIM方法.首先,给出Pythagorean 不确定语言变量的定义及其相关理论;其次,考虑决策者的参照依赖行为,计算各方案相对于其他方案关于各指标的收益或损失值;再次,考虑决策者的损失规避行为,集成指标关联情形下方案的收益或损失值,得到每个方案相对于其他各个方案的个体感知优势度;最后,计算各方案的总体感知优势度,并依据总体感知优势度进行方案排序.一个雾霾污染治理的算例验证了所提出方法的实用性和有效性.     

Establishing dominance and potential optimality in multi-criteria analysis with imprecise weight and value

The model presented in this paper does not require exact estimations of decision parameters such as attribute weights and values that may often be considerable cognitive burden of human decision makers. Information on the decision parameters is only assumed to be in the form of arbitrary linear inequalities which form constraints in the model. We consider two criteria, dominance and potential optimality, to check whether or not each alternative is outperform for a fixed feasible region denoted by the constraints. In particular, we develop a method to identify potential optimality of alternatives when all (or subsets) of the attribute values as well as weights are imprecisely know. This formulation becomes a nonlinear programming problem hard to be solved generally so that we provide in this paper how this problem is transformed into a linear programming equivalent.Scope and purposeMost managerial decisions involve choosing an optimal alternative from a number of available alternatives. Researchers have proposed a lot of methods to assist decision makers in choice making with a set of, usually conflicting, criteria or attributes. Many of these approaches require exact (or precise) information about either or both attribute values and/or trade-off weights. In some practice, however, it is not easy for decision makers to provide such exact data because, for example, intangible attributes to reflect social and environmental impacts may be included. To cope with such problem, a mathematical programming model-based approach to multi-criteria decision analysis is presented in this paper when both attribute weights and marginal values are imprecisely identified. A weighted additive rule is used to evaluate the performance of alternatives. We then show how to obtain non-dominated and potentially optimal alternatives in order to support choice making.     

CP-nets的定性偏好决策及一致性推理

CPnets是一种简单而又直观的图形化偏好表示工具,特别适合描述不完全信息下的具有依赖关系的多属性 定性偏好决策。首先通过构造CP-net s导出图及对其性质的研究,得出强占优测试本质上是导出图上顶点之间的可 达性问题,从而利用图的深度优先通历算法实现了二值网的强占优测试;然后分别从无环图、有环图的角度给出CP- nets一致性的相关定理和性质,提出了判断一致性的3种方法,使得CP-nets的一致性问题得到解决;强化和扩充了 I3outilier所提出的一些概念,深化了CP-net s的基础理论研究。