Inferring social network user profiles using a partial social graph

Classification problems refer to the assignment of alternatives to predefined categories. In this work we focus on ordered classification, called sorting, in which the predefined categories indicate several degrees of interest or suitability of alternatives for a certain user. The assignment of alternatives is based on multiple conflicting criteria. This multi-criteria sorting approach is specially interesting for recommender systems aimed at finding the most suitable alternatives for each user. First, we study the ELECTRE-TRI-B sorting method, which follows the outranking approach based on comparing the evaluations of alternatives with the profile limits separating the categories. The complexity of some recommenders systems requires the extension of the classical ELECTRE-TRI-B method to manage a taxonomical organization of the set of criteria. In this paper we consider a set of criteria in the form of a hierarchy. The intermediate criteria in such a hierarchy correspond to different aspects of the recommendation procedure, such as content, context or cost. At each of these criteria, a sorting problem must be solved. Therefore, we propose extending ELECTRE-TRI-B to handle assignments of alternatives on several levels of the hierarchy. A hierarchical procedure for sorting is proposed, called ELECTRE-TRI-B-H. Secondly, the paper explains the integration of ELECTRE-TRI-B-H into a recommender system of touristic activities related to wine, called GoEno-Tur. This system is developed for the region of Tarragona, Catalonia (Spain), which is a well-recognized area of wine and cava production.     

MOEA/D with uniform decomposition measurement for many-objective problems

Many-objective problems (MAPs) have put forward a number of challenges to classical Pareto-dominance based multi-objective evolutionary algorithms (MOEAs) for the past few years. Recently, researchers have suggested that MOEA/D (multi-objective evolutionary algorithm based on decomposition) can work for MAPs. However, there exist two difficulties in applying MOEA/D to solve MAPs directly. One is that the number of constructed weight vectors is not arbitrary and the weight vectors are mainly distributed on the boundary of weight space for MAPs. The other is that the relationship between the optimal solution of subproblem and its weight vector is nonlinear for the Tchebycheff decomposition approach used by MOEA/D. To deal with these two difficulties, we propose an improved MOEA/D with uniform decomposition measurement and the modified Tchebycheff decomposition approach (MOEA/D-UDM) in this paper. Firstly, a novel weight vectors initialization method based on the uniform decomposition measurement is introduced to obtain uniform weight vectors in any amount, which is one of great merits to use our proposed algorithm. The modified Tchebycheff decomposition approach, instead of the Tchebycheff decomposition approach, is used in MOEA/D-UDM to alleviate the inconsistency between the weight vector of subproblem and the direction of its optimal solution in the Tchebycheff decomposition approach. The proposed MOEA/D-UDM is compared with two state-of-the-art MOEAs, namely MOEA/D and UMOEA/D on a number of MAPs. Experimental results suggest that the proposed MOEA/D-UDM outperforms or performs similarly to the other compared algorithms in terms of hypervolume and inverted generational distance metrics on different types of problems. The effects of uniform weight vector initializing method and the modified Tchebycheff decomposition are also studied separately.     

Ranking alternatives in a preferential voting system using fuzzy concepts and data envelopment analysis

In this paper, a new method for aggregating the opinions of experts in a preferential voting system is proposed. The method, which uses fuzzy concept in handling crisp data, is computationally efficient and is able to completely rank the alternatives. Through this method, the number of votes for certain rank position that each alternative receives are first grouped together to form fuzzy numbers. The nearest point to a fuzzy number concept is then used to introduce an artificial ideal alternative. Data envelopment analysis is next used to find the efficiency scores of the alternatives in a pair-wise comparison with the artificial ideal alternative. Alternatives are rank based on these efficiency scores. If the alternatives are not completely ranked, a weight restriction method also based on fuzzy concept is used on the un-discriminated alternatives until they are completely ranked. Two examples are given for illustration of the method.     

Ranking alternatives in a preferential voting system using fuzzy concepts and data envelopment analysis

In this paper, a new method for aggregating the opinions of experts in a preferential voting system is proposed. The method, which uses fuzzy concept in handling crisp data, is computationally efficient and is able to completely rank the alternatives. Through this method, the number of votes for certain rank position that each alternative receives are first grouped together to form fuzzy numbers. The nearest point to a fuzzy number concept is then used to introduce an artificial ideal alternative. Data envelopment analysis is next used to find the efficiency scores of the alternatives in a pair-wise comparison with the artificial ideal alternative. Alternatives are rank based on these efficiency scores. If the alternatives are not completely ranked, a weight restriction method also based on fuzzy concept is used on the un-discriminated alternatives until they are completely ranked. Two examples are given for illustration of the method.     

基于前景理论和统计推断的区间数多准则决策方法

针对准则权重不完全确定且准则值为区间数的多准则群决策问题,提出一种基于前景理论的多准则决策方法。基于统计推断原理,以各准则下的方案值为样本推断其发生的概率,进而确定期望值参考点。基于区间数可能度确定价值函数,以方案区分度最大为目标构建非线性优化模型并确定方案排序。最后,通过实例分析表明了所提出方法的有效性和可行性。     

基于扩展原理的混合型证据推理不确定决策方法

提出一种基于扩展原理的混合证据推理不确定决策模型.通过α截集将同一决策问题中各属性使用的精确数、区间数和模糊数等异构评估信度统一分解为区间结构,采用区间证据推理方法求解各隶属度下的效用区间,并按隶属度次序重组方案效用;化简模糊数质心公式,并用于模糊定量评估的信度计算和方案模糊效用的排序;最后,通过具体实例验证了所提出方法的有效性和可行性.将该方法在算例中的适用情况进行比较和分析,结果表明所提出的方法具有良好的适应性.     

Extremist vs. centrist decision behavior: quasi-convex utility functions for interactive multi-objective linear programming problems

This paper presents the fundamental theory and algorithms for identifying the most preferred alternative for a decision maker (DM) having a non-centrist (or extremist) preferential behavior. The DM is requested to respond to a set of questions in the form of paired comparison of alternatives. The approach is different than other methods that consider the centrist preferential behavior.In this paper, an interactive approach is presented to solve the multiple objective linear programming (MOLP) problem. The DM's underlying preferential function is represented by a quasi-convex value (utility) function, which is to be maximized. The method presented in this paper solves MOLP problems with quasi-convex value (utility) functions by using paired comparison of alternatives in the objective space. From the mathematical point of view, maximizing a quasi-convex (or a convex) function over a convex set is considered a difficult problem to solve, while solutions for quasi-concave (or concave) functions are currently available. We prove that our proposed approach converges to the most preferred alternative.We demonstrate that the most preferred alternative is an extreme point of the MOLP problem, and we develop an interactive method that guarantees obtaining the global most preferred alternative for the MOLP problem. This method requires only a finite number of pivoting operations using a simplex-based method, and it asks only a limited number of paired comparison questions of alternatives in the objective space. We develop a branch and bound algorithm that extends a tree of solutions at each iteration until the MOLP problem is solved. At each iteration, the decision maker has to identify the most preferred alternatives from a given subset of efficient alternatives that are adjacent extreme points to the current basis. Through the branch and bound algorithm, without asking many questions from the decision maker, all branches of the tree are implicitly enumerated until the most preferred alternative is obtained. An example is provided to show the details of the algorithm. Some computational experiments are also presented.Scope and purposeThis paper presents the fundamental theory, algorithm, and examples for identifying the most preferred alternative (solution) for a decision maker (DM) having a non-centrist (or extremist) preferential behavior for Multiple Objective Linear Programming (MOLP) problems. The DM is requested to respond to a set of questions in the form of paired comparison of alternatives.Although widely applied, Linear Programming is limited to a single objective function. In many real world situations, DMs are faced with multiple objective problems in that several competing and conflicting objectives have to be considered. For these problems, there exist many alternatives that are feasible and acceptable. However, the DM is interested in finding “the most preferred alternative”. In the past three decades, many methods have been developed for solving MOLP problems.One class of these methods is called “interactive”, in which the DM responds to a set of questions interactively so that his/her most preferred alternative can be obtained. In most of these methods, the value (utility) function (that presents the DM's preference) is assumed to be linear or additive, concave, pseudo-concave, or quasi-concave. However, for MOLP problems, there has not been any effort to recognize and solve the quasi-convex utility functions, which are among the most difficult class of problems to solve. The quasi-convex class of utility functions represents an extremist preferential behavior, while the other aforementioned methods (such as quasi-concave) represent a conservative behavioral preference. It is shown that the method converges to the optimal (the most preferred) alternative. The approach is computationally feasible for moderately sized problems.     

Improved method of multicriteria fuzzy decision-making based on vague sets

An improved method is presented, which provides improved score functions to measure the degree of suitability of each of a set of alternatives, with respect to a set of criteria presented with vague values. The improved algorithm for score functions is introduced by taking into account the effect of an unknown degree (hesitancy degree) of the vague values on the degree of suitability to which each alternative satisfies the decision-maker’s requirement. The meaning of the proposed function is more transparent than that of other existing functions, which are not reasonable in some cases. The proposed function illustrates that it has stronger discrimination in comparison with previous functions. The applicability of this improved multicriteria fuzzy decision-making approach is also demonstrated by means of examples. The improved method can be used to rank the decision alternatives according to the decision criteria. The functions proposed in this paper can provide a more useful technique than previous functions, in order to efficiently help the decision-maker.     

An interval difference based evidential reasoning approach with unknown attribute weights and utilities of assessment grades

In this paper, the concept of interval difference is firstly defined. Then, an interval difference based evidential reasoning approach is proposed to analyze multiple attribute decision making problems in three situations, including (1) unknown attribute weights and utilities of assessment grades, (2) unknown attribute weights, and (3) unknown utilities of assessment grades. Three optimization models are constructed to identify potentially optimal alternatives in the three situations. For each potentially optimal alternative, three pairs of optimization problems are constructed to generate the optimized intervals of attribute weights and utilities of assessment grades or one of them. By using the optimized intervals, the interval difference of potentially optimal alternatives is calculated and used to generate their rank-order. This process is repeated until all alternatives are identified as potentially optimal alternatives. A complete rank-order of all alternatives is then generated. The performance of six executive cars is assessed using the proposed approach to demonstrate its applicability and validity.     

基于空间网格划分的多目标进化算法

为了有效求解多目标优化问题,找到分布宽广、均匀的Pareto解集,提出了一个基于空间网格划分的进化算法。将目标空间网格化,利用网格的位置,删除大量被支配个体。在杂交算子中利用了单个目标最优的个体信息,以增加非劣解的宽广性。利用一种新设计的基于最大距离排序的方法删除非劣解集中多余个体。数值实验表明提出的算法是可行有效的。     

A stochastic multicriteria acceptability analysis–evidential reasoning method for uncertain multiattribute decision‐making problems

Evidential reasoning (ER) is an effective approach for assessing alternatives with uncertain attribute values in the context of decision making. For the ER approach to be able to handle variations in the weights of uncertain attributes in an appropriate manner, this paper proposes a method to solve problems of uncertain multiattribute decision making that involve both uncertain attribute values and uncertain attribute weights, which this method does by combining the ER approach and stochastic multicriteria acceptability analysis‐2 (SMAA‐2). First, the uncertainty in attribute values is described by using a belief decision matrix as in the ER approach. The analytical ER algorithm is then used to create the utility function in the SMAA‐2 model, and that function is used to calculate the probability of different sorting positions of the decision units under weight‐related restrictions. Finally, the results of ranking are obtained by combining the sorting weights. An example is provided to verify the effectiveness of the proposed method.     

A hybrid approach using two-level SOM and combined AHP rating and AHP/DEA-AR method for selecting optimal promising emerging technology

Emerging technologies are playing an important role in establishing competitive advantage for technology based companies. Selecting an efficient and important emerging technology to invest in is significant to the companies also. In this study, we propose a method for selecting optimal emerging technology which is efficient, important and the most suitable to a company’s actual levels of input resource among various emerging technology alternatives. In order to select optimal emerging technology, the proposed method uses two-level-SOM to cluster the emerging technology alternatives based on alternatives’ required levels of input resource. For selecting efficient and important promising emerging technology, the proposed method calculates emerging technology alternatives’ efficiency score by using AHP/DEA-AR and their importance score by using AHP rating method in each technology cluster generated by two-level-SOM. Finally, the proposed method selects optimal promising emerging technology according to a company’s actual levels of input resource and each emerging technology alternative’s combined scores which is calculated by adding its efficiency score and importance score. A Korean company’s case of selecting optimal promising nanotechnology is employed to illustrate the proposed method. The result shows that the proposed method can provide an effective and reasonable selection of optimal promising emerging technology.     

MOTGA: A multiobjective Tchebycheff based genetic algorithm for the multidimensional knapsack problem

This paper presents a new multiobjective genetic algorithm based on the Tchebycheff scalarizing function, which aims to generate a good approximation of the nondominated solution set of the multiobjective problem. The algorithm performs several stages, each one intended for searching potentially nondominated solutions in a different part of the Pareto front. Pre-defined weight vectors act as pivots to define the weighted-Tchebycheff scalarizing functions used in each stage. Therefore, each stage focuses the search on a specific region, leading to an iterative approximation of the entire nondominated set.     

基于证据推理和第3 代前景理论的不确定性多属性决策方法

针对多状态不确定性多属性决策问题, 建立基于证据推理和第3 代前景理论的决策方法. 首先, 给出不确定性知识表示方法—– 确定因子结构及其构造方法; 然后, 将第3 代前景理论构造价值函数和确定权重函数引入决策方法中, 得到每个方案在各属性下的前景价值; 进一步, 根据证据推理方法对前景价值进行信息融合得到各方案的合成前景价值, 并依据合成前景价值对方案进行排序; 最后, 通过算例验证了所提出方法的可行性和有效性.

     

三参数区间灰数信息下风险型多准则决策方法

针对概率和准则值均为三参数区间灰数的多准则决 策问题,本文提出了一种基于前景理论的决策方法. 该方法首先定义了三参数区间灰数的距离和精确记分函数,并通 过讨论其性质给出了比较大小的方法; 其次,通过给出三参数区间灰数前景价值和概率权重函 数的定义,以多参考点为思路,构建前景决策矩阵, 并通过提出参考点集结算子,集结出综合前景决策矩阵. 进而,由优化模型求得的最优准则权系数加权得出方案的综合前景值及排序; 最后,通过算例对比说明了该方法的合理性和可靠性.     

Aggregating preference ranking with fuzzy Data Envelopment Analysis

Selecting the best alternative in a group decision making is a subject of many recent studies. The most popular method proposed for ranking the alternatives is based on the distance of each alternative to the ideal alternative. The ideal alternative may never exist; hence the ranking results are biased to the ideal point. The main aim in this study is to calculate a fuzzy ideal point that is more realistic to the crisp ideal point. On the other hand, recently Data Envelopment Analysis (DEA) is used to find the optimum weights for ranking the alternatives. This paper proposes a four stage approach based on DEA in the Fuzzy environment to aggregate preference rankings. An application of preferential voting system shows how the new model can be applied to rank a set of alternatives. Other two examples indicate the priority of the proposed method compared to the some other suggested methods.     

An approach to multiattribute decision making with interval-valued intuitionistic fuzzy assessments and incomplete weights

This article proposes an approach to multiattribute decision making with incomplete attribute weight information where individual assessments are provided as interval-valued intuitionistic fuzzy numbers (IVIFNs). By employing a series of optimization models, the proposed approach derives a linear program for determining attribute weights. The weights are subsequently used to synthesize individual IVIFN assessments into an aggregated IVIFN value for each alternative. In order to rank alternatives based on their aggregated IVIFN values, a novel method is developed for comparing two IVIFNs by introducing two new functions: the membership uncertainty index and the hesitation uncertainty index. An illustrative investment decision problem is employed to demonstrate how to apply the proposed procedure and comparative studies are conducted to show its overall consistency with existing approaches.     

Fuzzy multicriteria decision making method based on the improved accuracy function for interval-valued intuitionistic fuzzy sets

A new accuracy function for the theory of interval-valued intuitionistic fuzzy set, which overcomes some difficulties arising in the existing methods for determining rank of interval-valued intuitionistic fuzzy numbers, is proposed by taking into account the hesitancy degree of interval-valued intuitionistic fuzzy sets. By comparing it with several proposed accuracy functions, the necessity and efficiency of our accuracy function are provided by giving related examples. A fuzzy multicriteria decision making method is established to select the best alternative in multicriteria decision making process which is taken as interval-valued intuitionistic fuzzy set of criterion values for alternatives. While aggregating the interval-valued intuitionistic fuzzy information corresponding to each alternative, we utilize the interval-valued intuitionistic fuzzy weighted aggregation operators. Then the accuracy degree of the aggregated interval-valued intuitionistic fuzzy information is computed via the new proposed accuracy function. Thus, we can rank all the alternatives according to the accuracy function and choose the optimal one(s). Finally, an illustrative example is given to demonstrate the practicality and effectiveness of the proposed approach.     

Product concept generation and selection using sorting technique and fuzzy c-means algorithm

Product conceptualization is regarded as a key activity in new product development (NPD). In this stage, product concept generation and selection plays a crucial role. This paper presents a product concept generation and selection (PCGS) approach, which was proposed to assist product designers in generating and selecting design alternatives during the product conceptualization stage. In the PCGS, general sorting was adapted for initial requirements acquisition and platform definition; while a fuzzy c-means (FCM) algorithm was integrated with a design alternatives generation strategy for clustering design options and selecting preferred product concepts. The PCGS deliberates and embeds a psychology-originated method, i.e., sorting technique, to widen domain coverage and improve the effectiveness in initial platform formation. Furthermore, it successfully improves the FCM algorithm in such a way that more accurate clustering results can be obtained. A case study on a wood golf club design was used for illustrating the proposed approach. The results were promising and revealed the potential of the PCGS method.     

考虑偏好反转的区间不确定多属性决策方法

针对实际决策中的不确定性和偏好反转问题, 提出一种区间不确定多属性决策方法. 该方法先用证据推理方法集结区间不确定评估信息, 采用累积前景理论代替主观期望效用理论以构建方案的综合前景价值, 从而应对不确定环境下可能的决策偏好反转, 最后区间可能度用于方案综合前景价值排序. 介绍了决策过程, 给出求解方案综合前景价值的非线性规划模型, 并通过实例验证了方法的可行性、合理性和有效性.