Multivariate Gaussian criteria in SMAA

We consider stochastic multicriteria decision-making problems with multiple decision makers. In such problems, the uncertainty or inaccuracy of the criteria measurements and the partial or missing preference information can be represented through probability distributions. In many real-life problems the uncertainties of criteria measurements may be dependent. However, it is often difficult to quantify these dependencies. Also, most of the existing methods are unable to handle such dependency information.In this paper, we develop a method for handling dependent uncertainties in stochastic multicriteria group decision-making problems. We measure the criteria, their uncertainties and dependencies using a stochastic simulation model. The model is based on decision variables and stochastic parameters with given distributions. Based on the simulation results, we determine for the criteria measurements a joint probability distribution that quantifies the uncertainties and their dependencies. We then use the SMAA-2 stochastic multicriteria acceptability analysis method for comparing the alternatives based on the criteria distributions. We demonstrate the use of the method in the context of a strategic decision support model for a retailer operating in the liberated European electricity market.     

Extensions of the multicriteria analysis with pairwise comparison under a fuzzy environment

Multicriteria decision-making (MCDM) problems often involve a complex decision process in which multiple requirements and fuzzy conditions have to be taken into consideration simultaneously. The existing approaches for solving this problem in a fuzzy environment are complex. Combining the concepts of grey relation and pairwise comparison, a new fuzzy MCDM method is proposed. First, the fuzzy analytic hierarchy process (AHP) is used to construct fuzzy weights of all criteria. Then, linguistic terms characterized by L–R triangular fuzzy numbers are used to denote the evaluation values of all alternatives versus subjective and objective criteria. Finally, the aggregation fuzzy assessments of different alternatives are ranked to determine the best selection. Furthermore, this paper uses a numerical example of location selection to demonstrate the applicability of the proposed method. The study results show that this method is an effective means for tackling MCDM problems in a fuzzy environment.     

Multicriteria fuzzy decision-making method using entropy weights-based correlation coefficients of interval-valued intuitionistic fuzzy sets

A multicriteria fuzzy decision-making method based on weighted correlation coefficients using entropy weights is proposed under interval-valued intuitionistic fuzzy environment for the some situations where the information about criteria weights for alternatives is completely unknown. To determine the entropy weights with respect to a decision matrix provided as interval-valued intuitionistic fuzzy sets (IVIFSs), we propose two entropy measures for IVIFSs and establish an entropy weight model, which can be used to determine the criteria weights on alternatives, and then propose an evaluation formula of weighted correlation coefficient between an alternative and the ideal alternative. The alternatives can be ranked and the most desirable one(s) can be selected according to the values of the weighted correlation coefficients. Finally, two applied examples demonstrate the applicability and benefit of the proposed method: it is capable for handling the multicriteria fuzzy decision-making problems with completely unknown weights for criteria.     

Vector linear programming in zero-sum multicriteria matrix games

In this paper, a multiple-objective linear problem is derived from a zero-sum multicriteria matrix game. It is shown that the set of efficient solutions of this problem coincides with the set of Paretooptimal security strategies (POSS) for one of the players in the original game. This approach emphasizes the existing similarities between the scalar and multicriteria matrix games, because in both cases linear programming can be used to solve the problems. It also leads to different scalarizations which are alternative ways to obtain the set of all POSS. The concept of ideal strategy for a player is introduced, and it is established that a pair of Pareto saddle-point strategies exists if both players have ideal strategies. Several examples are included to illustrate the results in the paper.     

PROMETHEE-MD-2T method for project selection

Project selection is a real problem of multicriteria group decision making (MCGDM) where each decision maker expresses his/her preferences depending on the nature of the alternatives and on his/her own knowledge over them. Thus, information, as much quantitative as qualitative, coexists. The traditional methods of MCGDM developed for project selection usually discriminates in favour of quantitative information at the expense of qualitative information, and this is due to the capability to integrate this first type of information inside their procedure. In this article, two new multicriteria 2-tuple group decision methods called “Preference Ranking Organisation Method for Enrichment Evaluation Multi Decision maker 2-Tuple-I and II” (PROMETHEE-MD-2T-I and II) are presented. They are able to integrate inside their procedure both quantitative and qualitative information in an uncertain context. This has been performed by integrating a 2-tuple linguistic representation model dealing with non-homogeneous and imprecise information data made up by valued intervals, numerical and linguistic values into the aggregation operators of Promethee methods. Although they have been developed for project selection problems, these proposed methods can be applied to all kinds of decision-making problems with heterogeneous and multigranular information.     

Decision making in stock trading: An application of PROMETHEE

The key issue for decision making in stock trading is selection of the right stock at the right time. In order to select the superior stocks (alternatives) for investment, a finite number of alternatives have to be ranked considering several and sometimes conflicting criteria. Therefore, we are faced with a special multicriteria decision-making problem. The purpose of this paper is to develop a decision-making model for selecting superior stocks in stock exchange and a model is provided in order to structure this problem. The proposed model is structured around two pillars: Industry evaluation and Company evaluation. The preference ranking organization method for enrichment evaluation (PROMETHEE) has been used for solving the problem. The model has been applied at Tehran Stock Exchange (TSE) as a real case and a survey from the experts in order to determine the effective criteria for industry evaluation and company evaluation has been conducted.     

Solving Fractional Multicriteria Optimization Problems with Sum of Squares Convex Polynomial Data

This paper focuses on the study of finding efficient solutions in fractional multicriteria optimization problems with sum of squares convex polynomial data. We first relax the fractional multicriteria optimization problems to fractional scalar ones. Then, using the parametric approach, we transform the fractional scalar problems into non-fractional problems. Consequently, we prove that, under a suitable regularity condition, the optimal solution of each non-fractional scalar problem can be found by solving its associated single semidefinite programming problem. Finally, we show that finding efficient solutions in the fractional multicriteria optimization problems is tractable by employing the epsilon constraint method. In particular, if the denominators of each component of the objective functions are same, then we observe that efficient solutions in such a problem can be effectively found by using the hybrid method. Some numerical examples are given to illustrate our results.     

A polynomial algorithm for the multicriteria cent-dian location problem

Given a network with several weights per node and several lengths per edge, we address the problem of locating a facility on the network such that the convex combinations of the center and median objective functions are minimized. Since we consider several weights and several lengths, various objective functions should be minimized, and hence we have to solve a multicriteria cent-dian location problem. A polynomial algorithm to characterize the efficient location point set on the network is developed. Furthermore, this model can generalize other problems such as the multicriteria center problem and the multicriteria median problem. Computing time results on random planar networks considering different combinations of weights and lengths are reported, which strengthen the polynomial complexity of the procedure.     

A multicriteria approach to the location of public facilities

We argue that practical problems involving the location of public facilities are really multicriteria problems, and ought to be modeled as much. The general criteria are those of cost and service, but there exist several distinct criteria in each of those two categories. For the first category, fixed investment cost, fixed operating cost, variable operating cost, total operating cost, and total discounted cost are all reasonable criteria to consider. In terms of service, both demand served and response time (or distance traveled) are appropriate criteria, either agglomerated or considered on the basis of the individual clients. In this paper we treat such multicriteria questions in the framework of a model for selecting a subset of M sites at which to establish public facilities in order to serve client groups located at N distinct points. We show that for some combinations of specific criteria, parametric solutions of a generalized assignment problem (GAP) will yield all efficient solution. In most other cases the efficient solutions can be found through parametric solution of a GAP with additional constraints of a type which can be incorporated into an existing algorithm for the GAP. Rather than attempting to find all efficient solutions, however, we advocate an interactive approach to the resolution of multicriteria location problems and elaborate on a specific interactive algorithm for multicriteria optimization which for the present model solves a finite sequence of GAP's or GAP-type problems. Finally, some similar aspects of private sector location problems are discussed.     

A special class of extended multicriteria location problems

This paper is devoted to the study of extended multicriteria location problems, which are obtained from a given planar single-facility multicriteria location problem with respect to the maximum norm by adding new cost functions. By means of an appropriate decomposition approach, we develop an implementable algorithm for generating an efficient solution of such extended problems.     

军事物流中心选址评估模型

本文从影响军事物流中心的主要因素出发,建立了比较全面的评价指标体系。在进行选址评价时,针对常权综合方法难以体现决策者对决策因素惩罚或激励性的要求,提出了一种基于层次变权的模糊评价模型。并通过实例分析和计算,证明该评价模型合理、有效、可行。     

基于熵的群决策专家选择研究

群决策是研究多人如何做出统一的有效抉择.在群决策中专家决策水平直接反应到决策结论上,是影响事业的成败关键,因此专家的选择对于群决策而言是至关重要的.建立了评价群决策专家的指标集,从专家选择角度定义了理想专家,给出了专家选择的熵模型,并通过一个例子说明该模型的有效性.     

Fuzzy decision-making method based on the weighted correlation coefficient under intuitionistic fuzzy environment

A multicriteria fuzzy decision-making method based on weighted correlation coefficients using entropy weights is proposed under intuitionistic fuzzy environment for some situations where the information about criteria weights for alternatives is completely unknown. To determine the entropy weights with respect to a set of criteria represented by intuitionistic fuzzy sets (IFSs), we establish an entropy weight model, which can be used to get the criteria weights, and then propose an evaluation formula of weighted correlation coefficient between an alternative and the ideal alternative. The alternatives can be ranked and the most desirable one(s) can be selected according to the weighted correlation coefficients. Finally, two illustrative examples demonstrate the practicality and effectiveness of the proposed method.     

基于实验设计的概率语言权重信息多准则决策方法

作为模糊语言集的一种,概率语言集能够反映决策问题中评价准则权重重要程度及其概率,这在决策问题中较为实用。本文运用实验设计(Design of Experiment,DOE)的方法,对权重信息以概率语言给出的多准则决策问题进行研究:通过多次模拟权重重要程度及其概率,设计出多组实验权重,并用GRA法求得每组实验数据的得分,获得描述该决策问题准则值与评价结果相互影响关系的最适用回归方程,将决策问题的实际数据带入方程进行运算,得出方案排序结果。通过快速成型过程、柔性制造系统过程两个案例,进行对比验证。结果表明所提出的方法能较好地处理基于概率语言权重信息的多准则决策问题,计算简单且速度快,可重复性强且颇为实用。     

A group adaptive elastic-net approach for variable selection in high-dimensional linear regression

In practice, predictors possess grouping structures spontaneously. Incorporation of such useful information can improve statistical modeling and inference. In addition, the high-dimensionality often leads to the collinearity problem. The elastic net is an ideal method which is inclined to reflect a grouping effect. In this paper, we consider the problem of group selection and estimation in the sparse linear regression model in which predictors can be grouped. We investigate a group adaptive elastic-net and derive oracle inequalities and model consistency for the cases where group number is larger than the sample size. Oracle property is addressed for the case of the fixed group number. We revise the locally approximated coordinate descent algorithm to make our computation. Simulation and real data studies indicate that the group adaptive elastic-net is an alternative and competitive method for model selection of high-dimensional problems for the cases of group number being larger than the sample size.     

A new fuzzy multiple attributive group decision making methodology and its application to propulsion/manoeuvring system selection problem

In this paper, a new fuzzy multiple attribute decision-making (FMADM) method, which is suitable for multiple attributive group decision making (GDM) problems in fuzzy environment, is proposed to deal with the problem of ranking and selection of alternatives. Since the subjectivity, imprecision and vagueness in the estimates of a performance rating enter into multiple attribute decision-making (MADM) problems, fuzzy set theory provides a mathematical framework for modelling vagueness and imprecision. In the proposed approach, an attribute based aggregation technique for heterogeneous group of experts is employed and used for dealing with fuzzy opinion aggregation for the subjective attributes of the decision problem. The propulsion/manoeuvring system selection as a real case study is used to demonstrate the versatility and potential of the proposed method for solving fuzzy multiple attributive group decision-making problems. The proposed method is a generalised model, which can be applied to great variety of practical problems encountered in the naval architecture from propulsion/manoeuvring system selection to warship requirements definition.     

A multicriteria decision aid approach for energy planning problems: The case of renewable energy option

In the past, the choice among alternative energy policies at regional level was based only on cost minimization. Lately, it is widely recognized that regional energy planning forms a multi-actor and multicriteria problem. This is particularly true in the case of power generation in regions presenting high rates of increase in electricity demand, together with a significant potential of renewable energy sources, since several and often conflicting points of view must be taken into account. In this paper, the contribution of a Multicriteria Decision Aid method — namely ELECTRE III — addressing in such problems is investigated through the examination of a particular case study in a Greek island. Through the presentation of the procedure followed (identification of actors, selection of criteria, formulation of alternative strategies, application of the specific method and analysis of results and actors' reactions), an effort is made to highlight those aspects that are crucial in reaching a compromise in regional energy planning problems.     

Multitiered Supply Chain Networks: Multicriteria Decision—Making Under Uncertainty

In this paper, we present a supply chain network model with multiple tiers of decision-makers, consisting, respectively, of manufacturers, distributors, and retailers, who can compete within a tier but may cooperate between tiers. We consider multicriteria decision-making for both the manufacturers and the distributors whereas the retailers are subject to decision-making under uncertainty since the demands associated with the product are random. We derive the optimality conditions for the decision-makers, establish the equilibrium conditions, and derive the variational inequality formulation. We then utilize the variational inequality formulation to provide both qualitative properties of the equilibrium product shipment, service level, and price pattern and to propose a computational procedure, along with convergence results. This is the first supply chain network model to capture both multicriteria decision-making and decision-making under uncertainty in an integrated equilibrium framework.     

Multicriteria identification sets method

A multicriteria identification and prediction method for mathematical models of simulation type in the case of several identification criteria (error functions) is proposed. The necessity of the multicriteria formulation arises, for example, when one needs to take into account errors of completely different origins (not reducible to a single characteristic) or when there is no information on the class of noise in the data to be analyzed. An identification sets method is described based on the approximation and visualization of the multidimensional graph of the identification error function and sets of suboptimal parameters. This method allows for additional advantages of the multicriteria approach, namely, the construction and visual analysis of the frontier and the effective identification set (frontier and the Pareto set for identification criteria), various representations of the sets of Pareto effective and subeffective parameter combinations, and the corresponding predictive trajectory tubes. The approximation is based on the deep holes method, which yields metric ε-coverings with nearly optimal properties, and on multiphase approximation methods for the Edgeworth–Pareto hull. The visualization relies on the approach of interactive decision maps. With the use of the multicriteria method, multiple-choice solutions of identification and prediction problems can be produced and justified by analyzing the stability of the optimal solution not only with respect to the parameters (robustness with respect to data) but also with respect to the chosen set of identification criteria (robustness with respect to the given collection of functionals).     

基于VAGUE集多准则决策的模糊TOPSIS方法

给出了V AGUE集之间距离的新定义,在此基础上,提出一个基于V AGUE集多准则决策的模糊TOP-S IS方法,它为决策系统提供了一个有用的工具,并通过例子阐明本文方法的有效性.