Tackling an MCDM-problem with the help of some results from fuzzy set theory

The problem to be addressed and tackled in this paper arose as a byproduct from some efforts at solving problems involving multiple goals by linking linear and goal programming models. The critical issue was that some forms for interdependence among the goals could not be handled in the programming models. Here we will deal with a set of goals — with realistic counterparts in a Finnish plywood industry — in which a subset of the goals are (i) conflicting, another subset (ii) unilaterally supporting and a third subset (iii) mutually supporting. It is furthermore observed that the elements of a studied set of goals may be partly independent and partly interdependent, which makes the context a fullfledged MCDM-problem. It is tackled with a technique which is based on the theory of fuzzy sets, the conceptual framework for fuzzy decisions and the algorithms developed for fuzzy mathematical programming. The resulting fuzzy multiobjective programming model is simplified and tested with the help of a fairly complex numerical example.     

Using interdependent information on the relative importance of criteria in decision making

A multicriteria choice problem is considered. The Edgeworth-Pareto principle is established under the assumption that certain axioms hold true. Quantitative interdependent information on the relative importance of two groups of criteria is used to derive upper bounds for the unknown set of selected vectors.     

Minimum vertex cover problem for coupled interdependent networks with cascading failures

This paper defines and analyzes a generalization of the classical minimum vertex cover problem to the case of two-layer interdependent networks with cascading node failures that can be caused by two common types of interdependence. Previous studies on interdependent networks mainly addressed the issues of cascading failures from a numerical simulations perspective, whereas this paper proposes an exact optimization-based approach for identifying a minimum-cardinality set of nodes, whose deletion would effectively disable both network layers through cascading failure mechanisms. We analyze the computational complexity and linear 0–1 formulations of the defined problems, as well as prove an LP approximation ratio result that generalizes the well-known 2-approximation for the classical minimum vertex cover problem. In addition, we introduce the concept of a “depth of cascade” (i.e., the maximum possible length of a sequence of cascading failures for a given interdependent network) and show that for any problem instance this parameter can be explicitly derived via a polynomial-time procedure.     

Mutually dependent multi-criteria decision making

In this paper, a model to estimate the weights of mutually dependent criteria, based on cause-effect assessments of a group of professionals, is developed for problem of multiple criteria decision making (MCDM). Here, both DEMATEL (Decision Making Trial and Evaluation Laboratory) and TOPSIS (Technique for Order Performance by Similarity to Ideal Solution) models are combined and extended to handle fuzzy evaluations where the first is used to set the weights of the interdependent criteria and the second for drawing a decision from a group of professionals who use linguistic ratings in their evaluation. The presented model is characterized by the capability to estimate the criteria weights when the criteria are interrelated. The strict determination of the criteria weights prior to the assessment process is eliminated as they are computed by the DEMATEL part. A classical case-study of optimal sore throat treatment in primary care unit is used to demonstrate the efficiency of the proposed model.     

A choice model with imprecise ordinal evaluations

We consider multicriteria choice problems where the actions are evaluated on ordinal criteria and where they can be assessed imprecisely. In order to select the subset of best actions, the pairwise comparisons between the actions on each criterion are modeled by basic belief assignments (BBAs). Dempsterʼs rule of combination is used for the aggregation of the BBAs of each pair of alternatives in order to express a global comparison between them on all the criteria. A model inspired by ELECTRE I is also proposed and illustrated by a pedagogical example.     

Interdependent binary choices under social influence: Phase diagram for homogeneous unbiased populations

Coupled Ising models are studied in a discrete choice theory framework, where they can be understood to represent interdependent choice making processes for homogeneous populations under social influence. Two different coupling schemes are considered: the nonlocal or group interdependence model is used to study two interrelated groups making the same binary choice and the local or individual interdependence model represents a single group, where agents make two binary choices that depend on each other. For both models, phase diagrams and their implications in socioeconomic contexts are described and compared in the absence of private deterministic utilities (zero opinion fields). © 2012 Wiley Periodicals, Inc. Complexity, 2012     

Building a set of additive value functions representing a reference preorder and intensities of preference: GRIP method

We present a method called Generalized Regression with Intensities of Preference (GRIP) for ranking a finite set of actions evaluated on multiple criteria. GRIP builds a set of additive value functions compatible with preference information composed of a partial preorder and required intensities of preference on a subset of actions, called reference actions. It constructs not only the preference relation in the considered set of actions, but it also gives information about intensities of preference for pairs of actions from this set for a given decision maker (DM). Distinguishing necessary and possible consequences of preference information on the considered set of actions, GRIP answers questions of robustness analysis. The proposed methodology can be seen as an extension of the UTA method based on ordinal regression. GRIP can also be compared to the AHP method, which requires pairwise comparison of all actions and criteria, and yields a priority ranking of actions. As for the preference information being used, GRIP can be compared, moreover, to the MACBETH method which also takes into account a preference order of actions and intensity of preference for pairs of actions. The preference information used in GRIP does not need, however, to be complete: the DM is asked to provide comparisons of only those pairs of reference actions on particular criteria for which his/her judgment is sufficiently certain. This is an important advantage comparing to methods which, instead, require comparison of all possible pairs of actions on all the considered criteria. Moreover, GRIP works with a set of general additive value functions compatible with the preference information, while other methods use a single and less general value function, such as the weighted-sum.     

Multiple criteria sorting with a set of additive value functions

We present a new multiple criteria sorting method that aims at assigning actions evaluated on multiple criteria to p pre-defined and ordered classes. The preference information supplied by the decision maker (DM) is a set of assignment examples on a subset of actions relatively well known to the DM. These actions are called reference actions. Each assignment example specifies a desired assignment of a corresponding reference action to one or several contiguous classes. The set of assignment examples is used to build a preference model of the DM represented by a set of general additive value functions compatible with the assignment examples. For each action a, the method computes two kinds of assignments to classes, concordant with the DM’s preference model: the necessary assignment and the possible assignment. The necessary assignment specifies the range of classes to which the action can be assigned considering all compatible value functions simultaneously. The possible assignment specifies, in turn, the range of classes to which the action can be assigned considering any compatible value function individually. The compatible value functions and the necessary and possible assignments are computed through the resolution of linear programs.     

Geometrical representations for MCDA

In this paper geometrical representations for multicriteria decision problems are proposed. This new approach provides assistance to understand the conflictual aspects of the criteria and to tackle the problem of the weights associated to them. A generalized criterion, including a preference function, is first generated for each criterion. This allows to define unicriterion preference flows for which a geometrical representation can be obtained by using the Principal Components Analysis. The actions are represented by points and criteria by axes in the PCA plane. A decision axis taking into account the weights associated to the criteria can be defined. This technique provides the decision-maker with a considerable enrichment for the understanding of his problem: clusters of actions can be considered, the importance of the criteria can be evaluated, conflictual criteria are immediately detected, incomparability between actions is emphasized and explained, best compromise actions are easily selected, new decision-axes representing possible clusters of criteria can be considered, undesirable actions can be eliminated, … The technique consists in a powerful new qualitative decision tool. It is illustrated in the paper on some examples treated by the Promethee I and II methods. A didactic and user-friendly microcomputer code is available.     

Aspiration level approach in stochastic MCDM problems

The paper considers a discrete stochastic multiple criteria decision making problem. This problem is defined by a finite set of actions A, a set of attributes X and a set of evaluations of actions with respect to attributes E. In stochastic case the evaluation of each action with respect to each attribute takes form of a probability distribution. Thus, the comparison of two actions leads to the comparison of two vectors of probability distributions. In the paper a new procedure for solving this problem is proposed. It is based on three concepts: stochastic dominance, interactive approach, and preference threshold. The idea of the procedure comes from the interactive multiple objective goal programming approach. The set of actions is progressively reduced as the decision maker specifies additional requirements. At the beginning the decision maker is asked to define preference threshold for each attribute. Next, at each iteration the decision maker is confronted with the set of considered actions. If the decision maker is able to make a final choice then the procedure ends, otherwise he/she is asked to specify aspiration level. A didactical example is presented to illustrate the proposed technique.     

A two-phase tabu search approach to the location routing problem

In many distribution systems, the location of the distribution facilities and the routing of the vehicles from these facilities are interdependent. Although this interdependence has been recognized by academics and practitioners alike, attempts to integrate these two decisions have been limited. The location routing problem (LRP), which combines the facility location and the vehicle routing decisions, is NP-hard. Due to the problem complexity, simultaneous solution methods are limited to heuristics. This paper presents a two-phase tabu search architecture for the solution of the LRP. First introduced in this paper, the two-phase approach offers a computationally efficient strategy that integrates facility location and routing decisions. This two-phase architecture makes it possible to search the solution space efficiently, thus producing good solutions without excessive computation. An extensive computational study shows that the TS algorithm achieves significant improvement over a recent effective LRP heuristic.     

Deriving weights in multiple-criteria decision making with support vector machines

A key problem in Multiple-Criteria Decision Making is how to measure the importance of the different criteria when just a partial preference relation among actions is given. In this note we address the problem of constructing a linear score function (and thus how to associate weights of importance to the criteria) when a binary relation comparing actions and partial information (relative importance) on the criteria are given. It is shown that these tasks can be done viaSupport Vector Machines, an increasingly popular Data Mining technique, which reduces the search of the weights to the resolution of (a series of) nonlinear convex optimization problems with linear constraints. An interactive method is then presented and illustrated by solving a multiple-objective 0–1 knapsack problem. Extensions to the case in which data are imprecise (given by intervals) or intransitivities in strict preferences exist are outlined.     

Linear complementarity problems and multiple objective programming

An equivalence is demonstrated between solving a linear complementarity problem with general data and finding a certain subset of the efficient points of a multiple objective programming problem. A new multiple objective programming based approach to solving linear complementarity problems is presented. Results on existence, uniqueness and computational complexity are included.     

Fuzzy criteria for feature selection

The presence of less relevant or highly correlated features often decrease classification accuracy. Feature selection in which most informative variables are selected for model generation is an important step in data-driven modeling. In feature selection, one often tries to satisfy multiple criteria such as feature discriminating power, model performance or subset cardinality. Therefore, a multi-objective formulation of the feature selection problem is more appropriate. In this paper, we propose to use fuzzy criteria in feature selection by using a fuzzy decision making framework. This formulation allows for a more flexible definition of the goals in feature selection, and avoids the problem of weighting different goals is classical multi-objective optimization. The optimization problem is solved using an ant colony optimization algorithm proposed in our previous work. We illustrate the added value of the approach by applying our proposed fuzzy feature selection algorithm to eight benchmark problems.     

An integrated FANP–MOLP for supplier evaluation and order allocation

In the face of acute global competition, supplier management is rapidly emerging as a crucial issue to any companies striving for business success and sustainable development. To optimize competitive advantages, a company should incorporate “suppliers” as an essential part of its core competencies. Supplier evaluation, the first step in supplier management, is a complex multi-criteria decision-making (MCDM) problem, and its complexity is further aggravated if the highly important interdependence among the selection criteria is taken into consideration. The objective of this paper is to suggest a comprehensive decision method for identifying top suppliers by considering the effects of interdependence among the selection criteria, as well as to achieve optimal allocation of orders among the selected suppliers.     

考虑关联性特征匹配的城市生命线风险应对方案选择方法

针对城市生命线风险应对方案选择问题涉及的特征指标关联性和信息形式多样性,本文提出了一种考虑关联性特征匹配的混合型决策方法。首先,给出实际域、设定域和公共域的定义,并将具有区间数、语言短语等信息形式的风险事件特征指标值和应对方案特征指标值分别映射为实际域和设定域,进而通过两者的面积交织确定公共域;然后,将公理设计方法扩展到混合型决策环境,计算出反映风险事件与应对方案在各个特征指标下匹配程度的信息量,并进行应对方案的初筛;进一步地,采用2-additive Choquet积分算子将特征指标的权重、关联系数和初筛后剩余应对方案的信息量集结为反映风险事件与应对方案综合匹配程度的信息总量,并据此选择最优的应对方案。最后,通过算例分析验证了所提方法的有效性和可行性。研究结果表明,该方法能够为相关监管部门快速响应城市生命线风险、最大程度地降低风险损失和危害提供有效的决策支持。     

关于TOPSIS法应用中的逆序问题及消除的方法

在多指标决策问题中,TOPSIS法是一种常用的方法,然而传统的TOPSIS法在实际应用中容易产生逆序的现象.本文分析了逆序产生的主要原因,并提出了一种改进的方法-RTOPSIS法.应用本文的方法不仅能消除逆序的现象,而且还能正确反映指标权重对决策结果的影响.     

Comparative analysis of UTA multicriteria methods

This paper reviews the main variants of the utility additive (UTA) multicriteria method, and systematically compares their predictive performance on two sets of data. It analyses both those cases where the model provides a ranking with errors and those without errors. First, it shows that the reference projects should be chosen carefully in order to elicit as much information as possible from the decision maker: a set of projects satisfying a fractional factorial plan is recommended. Second, it discusses the use of alternative post-optimality methods for solving the problem of multiple solutions and their different predictive performances. Third, it presents the results of simulations based on utility functions involving interdependence between criteria, and shows that UTA handles this problem effectively by an adjustment of its coefficients. Finally, the influence of the model's parameters on the predictive performance is also investigated.     

Modelling and assessing ERP project risks: A Petri Net approach

Risk management of Enterprise Resource Planning (ERP) projects is largely recognized as a very complex task both by academics and practitioners. Strict interconnections among risk factors often occur so that indirect effects on the overall project performance are very likely. Unfortunately, the implications of interdependency are usually underestimated by project managers and decision makers since they are difficult to include in any risk assessment logic. This work shows how Colored Petri Nets (CPNs) can be used to model risk factors in ERP projects in order to deal with the problem of interdependence in risk assessment. The technique is presented through an application to a real case study. Findings highlight the importance of interdependence and the indirect links for an effective ranking of risks. Furthermore, results emphasize the valuable support of CPNs in risk factor modelling since they allow both a more structured and systematic risk analysis and a more accurate planning for effective risk treatment actions.     

The secretary problem with multiple job vacancies and batch candidate arrivals

We extend the secretary problem with multiple vacancies to allow batch arrival of candidates. We establish structural properties of the optimal policies. We show that the optimal reward is convex and submodular in the values of candidates, which means that there is benefit for having a candidate pool with more variable or less interdependent values. Similar properties continue to hold when there are multiple classes of vacancies. Our model is applicable to recruitment, dynamic auctions and sequential investment.