基于云模型与PROMETHEE方法的语言型Z-number多属性决策

针对属性权重未知,属性值为语言型Z-number的多属性决策问题,提出了一种基于云模型与丰富度评估的偏好排序组织方法（Preference ranking organization method for enrichment evaluation, PROMETHEE）的决策方法。首先,引入语言尺度函数,然后利用其建立转化模型完成语言型Z-number向云模型的转化。此外,通过定义云可能度函数,建立属性权重求解公式及构建正弦偏好函数,进而计算方案的优先指数,通过计算方案的正负方向优序级别值得到备选方案综合优序级别值,进而得到方案排序。最后通过算例及比较分析验证本方法的有效性和可行性。     

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.     

A PROMETHEE-based approach to portfolio selection problems

In this paper, we study the use of PROMETHEE outranking methods for portfolio selection problems. Starting from a new formulation of the PROMETHEE V method, we develop several alternative approaches based on the concepts of boundary portfolios and c-optimal portfolios. The proposed methods are compared in an extensive computational study. Results of these experiments show that methods based on the concept of c-optimal portfolios provide a good approximation to the (often computationally untractable) PROMETHEE ranking of all portfolios, while requiring only small computational effort even for large problems. For smaller problems, a PROMETHEE ranking of all boundary portfolios can be performed and provides a close approximation of the total ranking.     

Aspects of decision support in water management--example Berlin and Potsdam (Germany) I--spatially differentiated evaluation

Decisions about sustainable development demand spatially differentiated evaluations. As an example, we demonstrate the evaluation of water management strategies in the cities of Berlin and Potsdam (Germany) with respect to their ecological effects in 14 sections of the surface water system. Two decision support systems were compared, namely PROMETHEE, which is designed to obtain a clear decision (linear ranking), and Hasse Diagram Technique (HDT), normally providing more than one favourable solution (partial order). By PROMETHEE, the spatial differentiation had unwanted effects on the result, negating the stakeholders determined weighting of indicators. Therefore, the stakeholder can barely benefit from the convenience of obtaining a clear decision (linear ranking). In contrast, the result obtained by HDT was not influenced by spatial differentiation. Furthermore, HDT provided helpful tools to analyse the evaluation result, such as the concept of antagonistic indicators to discover conflicts in the evaluation process.     

A bi-objective mixed-model assembly line sequencing problem considering customer satisfaction and customer buying behaviour

Customer satisfaction and focusing on the most profitable customers are the key elements to achieving a sustainable competitive advantage in the current business environment. The mixed-model assembly line (MMAL) is an efficient type of manufacturing system that has been used increasingly over recent years to satisfy diverse customer demands. Product sequencing in an MMAL system has a huge effect on the performance of the firm in meeting customer demand and, therefore, on customer satisfaction. This study aims to address a sequencing problem with respect to recency, frequency and monetary factors. A two-stage framework is developed to achieve this goal. First, the prioritized orders based on the preference ranking organization method for enrichment of evaluations (PROMETHEE) are categorized into high-priority and normal-priority orders. Then, a bi-objective mathematical programming model is developed to determine the optimum sequence of products to minimize the total cost, as well as to maximize levels of customer satisfaction. After validation of the proposed model, owing to the NP-hard nature of this problem, two multi-objective metaheuristics are applied to tackle the second stage of this study. Several test problems are presented to evaluate the performance of these algorithms. The results show the superiority of one solution approach over the other.     

A multi-objective approach for multi-material topology and shape optimization

An automated multi-material approach that integrates multi-objective Topology Optimization (TO) and multi-objective shape optimization is presented. A new ant colony optimization algorithm is presented and applied to solving the TO problem, estimating a trade-off set of initial topologies or distributions of material. The solutions found usually present irregular boundaries, which are not desirable in applications. Thus, shape parameterization of the internal boundaries of the design region, and subsequent shape optimization, is performed to improve the quality of the estimated Pareto-optimal solutions. The selection of solutions for shape optimization is done by using the PROMETHEE II decision-making method. The parameterization process involves identifying the boundaries of different materials and describing these boundaries by non-uniform rational B-spline curves. The proposed approach is applied to the optimization of a C-core magnetic actuator, with two objectives: the maximization of the attractive force on the armature and the minimization of the volume of permanent magnet material.     

Optimum selection of novel developed implant material using hybrid entropy‐PROMETHEE approach

Optimum selection of appropriate biomaterial with unlike properties for the femoral head material is one of the toughest tasks. Therefore, in this article, a series of implant materials for the femoral head by vacuum casting induction furnace containing cobalt‐30chromium (Co‐30Cr) as a base material and three alloying elements (i. e. molybdenum, nickel and tungsten) were developed and evaluated for physical, mechanical and tribological properties. Density, hardness, compressive strength, coefficient of friction and volumetric wear were considered as material selection criterions. The weight of each criterion has been determined by entropy method, while the ranking of the alternatives has been carried out by the preference ranking organization method for enrichment evaluations (PROMETHEE) method. From this ranking results, it is found that the cobalt‐30chromium‐4molybdenum‐1nickel‐2tungsten (Co‐30Cr‐4Mo‐1Ni‐2W) material at given parameters is the best implant material for the femoral head component of hip joint replacement.     

基于投影寻踪模型的区间数群决策权重确定

扩展了可直接处理特征空间为区间数的PROMETHEE II多属性群决策方法,从最佳投影角度构造了专家信息前处理群决策权重确定的投影寻踪模型。考虑到传统的优化方法很难获得群决策权重的最优解,文中应用遗传算法来全局优化确定群决策权重。该方法特别适合于决策方案比较多的场合。应用实例表明了该方法具有一定的可行性、有效性和推广应用价值。     

基于 Z-numbers 模糊数的改进 PROMETHEE 法

针对评价值为模糊数的工程方案优选问题,通过 Z-numbers 模糊数方法建立模糊评价矩阵,考虑了各决策主体的可靠程度,将模糊推理引入 PROMETHE 方法,对方案进行优先排序。运用 Matlab 的模糊推理系统工具箱构建模糊规则模型,计算每两对方案的差别度,采用模糊语言评价代替优先函数的选择,得到各方案在不同属性下的优先指数,并根据综合优序级别值对各备选方案进行排序,获得最优方案。最后通过一个工程案例进行计算和分析,证明了该方法对工程方案优选问题具有良好的实践价值。