An extension of the FlowSort sorting method to deal with imprecision

We propose an extension of the FlowSort sorting method to the case when there is imprecision on the input data. Within multicriteria decision aid, a lot of attention has been paid to sorting problems where a set of actions has to be assigned to completely ordered categories. However, few methods suit when the data or the parameters of the model are not precisely defined. In this paper, instead of reducing the imprecise data to single values, we consider that the sorting parameters or the data are defined by intervals. We analyse the properties usually required for a sorting method and illustrate this extension on a practical example.     

MPOC: an agglomerative algorithm for multicriteria partially ordered clustering

In the field of multicriteria decision aid, considerable attention has been paid to supervised classification problems where the purpose is to assign alternatives into predefined ordered classes. In these approaches, often referred to as sorting methods, it is usually assumed that classes are either known a priori or can be identified by the decision maker. On the other hand, when the objective is to identify groups (clusters) of alternatives sharing similar characteristics, the problem is known as a clustering problem, also called an unsupervised learning problem. This paper proposes an agglomerative clustering method based on a crisp outranking relation. The method regroups alternatives into partially ordered classes, based on a quality of partition measure which reflects the percentage of pairs of alternatives that are compatible with a decision-maker’s multicriteria preference model.     

An algorithm for ordinal sorting based on ELECTRE with categories defined by examples

This work proposes a Progressive Assisted Sorting Algorithm (PASA) based on a multicriteria evaluation ELECTRE-type method. The purpose of the PASA is to aid a decision maker to progressively sort a set of alternatives into a set of categories, which we considered are ordered (ordinal sorting), following a consistency principle. We consider the principle that if an alternative outranks (is as good as) a second one, then it must belong to the same category or to a better category. The set of alternatives already sorted by the decision maker will implicitly define the categories, and will constrain the range of categories where other alternatives may be sorted. We show how the same idea may be used in an aggregation/disaggregation approach, considering some parameters of ELECTRE are not fixed a priori, but are constrained only by the examples provided. In this context, we establish a “convex-shape property” stating that the range of possible categories for an alternative is always an interval of categories. A discussion contrasting this approach with ELECTRE TRI is included in the conclusions.     

Multicriteria sorting using a valued indifference relation under a preference disaggregation paradigm

Most multicriteria decision methods need the definition of a significant amount of preferential information from a decision agent. The preference disaggregation analysis paradigm infers the model’s parameter values from holistic judgments provided by a decision agent. Here, a new method for inferring the parameters of a fuzzy outranking model for multicriteria sorting is proposed. This approach allows us to use most of the preferential information contained in a reference set. The central idea is to characterize the quality of the model by measuring discrepancies and concordances amongst (i) the preference relations derived from the outranking model, and (ii) the preferential information contained in the reference set. The model’s parameters are inferred from a multiobjective optimization problem, according to some additional preferential information from a decision agent. Once the model has been fitted, sorting decisions about new objects are performed by using a fuzzy indifference relation. This proposal performs very well in some examples.     

A stochastic method for robustness analysis in sorting problems

ELECTRE TRI is a multiple criteria decision aiding sorting method with a history of successful real-life applications. In ELECTRE TRI, values for certain parameters have to be provided. We propose a new method, SMAA-TRI, that is based on stochastic multicriteria acceptability analysis (SMAA), for analyzing the stability of such parameters. The stability analysis can be used for deriving robust conclusions. SMAA-TRI allows ELECTRE TRI to be used with uncertain, arbitrarily distributed values for weights, the lambda cutting level, and profiles. The method consists of analyzing finite spaces of arbitrarily distributed parameter values. Monte Carlo simulation is applied in this in order to describe for each alternative the share of parameter values that have it assigned to different categories. We show the real-life applicability by re-analyzing a case study in the field of risk assessment.     

A multicriteria assignment procedure for a nominal sorting problematic

This paper addresses the problem of the assignment of an action in the particular case where the categories defined a priori are not ordered. In multicriteria literature, it is the nominal sorting problematic. We propose a simple and easy method to understand the procedure of assignment to tackle this problematic. Afterwards, we shall illustrate the proposed method by using an example that is inspired by a research carried out the construction sector of the work accident prevention field.     

Multicriteria sorting using a valued preference closeness relation

To define a metric or a similarity relation with good properties is a crucial issue in most analogy and rule induction oriented methods for multicriteria sorting. Here, we propose a valued indifference (closeness) relation which is inspired on concordance and discordance measures. The criterion “weights” are obtained from the preferential information embedded in a reference set. This proposal performs very well in several practical problems.     

Eliciting Electre Tri category limits for a group of decision makers

Multiple criteria sorting aims at assigning alternatives evaluated on several criteria to predefined ordered categories. In this paper, we consider a well known multiple criteria sorting method, Electre Tri, which involves three types of preference parameters: (1) category limits defining the frontiers between consecutive categories, (2) weights and majority level specifying which coalitions form a majority, and (3) veto thresholds characterizing discordance effects. We propose an elicitation procedure to infer category limits from assignment examples provided by multiple decision makers. The procedure computes a set of category limits and vetoes common to all decision makers, with variable weights for each decision maker. Hence, the method helps reaching a consensus among decision makers on the category limits and veto thresholds, whereas finding a consensus on weights is left aside. The inference procedure is based on mixed integer linear programming and performs well even for datasets corresponding to real-world decision problems. We provide an illustrative example of the use of the method and analyze the performance of the proposed algorithms.     

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).     

A multicriteria model for risk sorting of natural gas pipelines based on ELECTRE TRI integrating Utility Theory

This paper proposes a multicriteria model for assessing risk in natural gas pipelines, and for classifying sections of pipeline into risk categories. The model integrates Utility Theory and the ELECTRE TRI method. It aims to help transmission and distribution companies, when engaged in risk management and decision-making, to consider the multiple dimensions of risk that may arise from pipeline accidents. Pipeline hazard scenarios are presented, and it is argued that the assessment of risk in natural gas pipelines should not be based solely on probabilities of human fatalities, but should involve a wider perspective that simultaneously takes into consideration the human, environmental and financial dimensions of impacts of pipeline accidents. Finally, in order to verify the effectiveness of the model set out, a numerical application based on a real case study is presented.     

A new approach to multi-criteria sorting based on fuzzy outranking relations: The THESEUS method

In this paper, we propose the THESEUS method, a new approach based on fuzzy outranking relations to multi-criteria sorting problems. Compared with other outranking-based methods, THESEUS is inspired by another view of multi-criteria classification problems. It utilizes a new way of evaluating the assignment of an object to an element of the set of ordered categories that were previously defined. This way is based on comparing every possible assignment with the information from various preference relations that are derived from a fuzzy outranking relation defined on the universe of objects. The appropriate assignment is determined by solving a simple selection problem.The capacity of a reference set for making appropriate assignments is related to a good characterization of the categories. A single reference action characterizing a category may be insufficient to achieve well-determined assignments. In this paper, the reference set capacity to perform appropriate assignments is characterized by some new concepts. This capacity may be increased when more objects are added to the reference set. THESEUS is a method for handling the preference information contained in such larger reference sets.     

Using expert’s rules as background knowledge in the ClusDM methodology

In complex domains it is usually quite difficult to introduce context information. However, sometimes that information should be taken into account to make decisions, because it provides some relevant knowledge that cannot be expressed using an attribute-value representation. This is the case of the determination of risk of contamination of soils. In this paper, we propose to use conjunctive rules to introduce additional background knowledge to a MCDM sorting method called ClusDM. ClusDM is based on the aggregation of the data with unsupervised clustering techniques. The paper presents a new algorithm to incorporate rules to guide the clustering process in a semi-supervised way. The paper also describes how it works in the case sorting a set of possible contaminated soils, and compares the results obtained by ClusDM when rules are used or not.     

Ranking multicriteria alternatives: The method ZAPROS III

The new version of the method for the construction of partial order on the set of multicriteria alternatives is presented. This method belongs to the family of verbal decision analysis (VDA) methods and gives a more efficient means of problem solution. The method is based on psychologically valid operations for information elicitation from a decision maker: comparisons of two distances between the evaluations on the ordinal scales of two criteria. The information received from a decision maker is used for the construction of a binary relation between a pair of alternatives which yields preference, indifference and incomparability relations. The method allows construction of a partial order on the set of given alternatives as well as on the set of all possible alternatives. The illustrative example is given.     

CL.E.KMODES: a modified <Emphasis Type="Italic">k</Emphasis>-modes clustering algorithm

In this paper we present a new method for clustering categorical data sets named CL.E.KMODES. The proposed method is a modified k-modes algorithm that incorporates a new four-step dissimilarity measure, which is based on elements of the methodological framework of the ELECTRE I multicriteria method. The four-step dissimilarity measure introduces an alternative and more accurate way of assigning objects to clusters. In particular, it compares each object with each mode, for every attribute that they have in common, and then chooses the most appropriate mode and its corresponding cluster for that object. Seven widely used data sets are tested to verify the robustness of the proposed method in six clustering evaluation measures.     

Axiomatizations of the Euclidean compromise solution

A multicriteria optimization problem is one of choosing an alternative that optimizes several—possibly conflicting—objective functions simultaneously. The utopia point of a multicriteria optimization problem is the vector that specifies for each objective function the most favorable feasible value. The Euclidean compromise solution in multicriteria optimization is a solution that selects from a feasible set the alternative such that its vector of criteria values has minimal Euclidean distance to the utopia point. This paper provides several axiomatic characterizations of the Euclidean compromise solution that are based on consistency properties.     

Rough sets theory for multicriteria decision analysis

The original rough set approach proved to be very useful in dealing with inconsistency problems following from information granulation. It operates on a data table composed of a set U of objects (actions) described by a set Q of attributes. Its basic notions are: indiscernibility relation on U, lower and upper approximation of either a subset or a partition of U, dependence and reduction of attributes from Q, and decision rules derived from lower approximations and boundaries of subsets identified with decision classes. The original rough set idea is failing, however, when preference-orders of attribute domains (criteria) are to be taken into account. Precisely, it cannot handle inconsistencies following from violation of the dominance principle. This inconsistency is characteristic for preferential information used in multicriteria decision analysis (MCDA) problems, like sorting, choice or ranking. In order to deal with this kind of inconsistency a number of methodological changes to the original rough sets theory is necessary. The main change is the substitution of the indiscernibility relation by a dominance relation, which permits approximation of ordered sets in multicriteria sorting. To approximate preference relations in multicriteria choice and ranking problems, another change is necessary: substitution of the data table by a pairwise comparison table, where each row corresponds to a pair of objects described by binary relations on particular criteria. In all those MCDA problems, the new rough set approach ends with a set of decision rules playing the role of a comprehensive preference model. It is more general than the classical functional or relational model and it is more understandable for the users because of its natural syntax. In order to workout a recommendation in one of the MCDA problems, we propose exploitation procedures of the set of decision rules. Finally, some other recently obtained results are given: rough approximations by means of similarity relations, rough set handling of missing data, comparison of the rough set model with Sugeno and Choquet integrals, and results on equivalence of a decision rule preference model and a conjoint measurement model which is neither additive nor transitive.     

Multicriteria classification and sorting methods: A literature review

The assignment of alternatives (observations/objects) into predefined homogenous groups is a problem of major practical and research interest. This type of problem is referred to as classification or sorting, depending on whether the groups are nominal or ordinal. Methodologies for addressing classification and sorting problems have been developed from a variety of research disciplines, including statistics/econometrics, artificial intelligent and operations research. The objective of this paper is to review the research conducted on the framework of the multicriteria decision aiding (MCDA). The review covers different forms of MCDA classification/sorting models, different aspects of the model development process, as well as real-world applications of MCDA classification/sorting techniques and their software implementations.     

A multicriteria accreditation system for information technology skills and qualifications

Employees must acquire new competences and qualifications throughout their lives, in order to be able to deal with the multiple changes in the labour market. The specific knowledge and competences, acquired either formally or non-formally, must be recognized so that they can be transferred and utilized. The existing titles of studies and accreditation mechanisms do not generally cover this need. This paper aims to propose an integrated approach for the evaluation of information technology knowledge and skills, regardless of where and how they have been acquired, so as to apply a continuous education and training policy. The proposed multicriteria methodology for the evaluation of qualifications and skills concerns candidates wishing to be accredited in an information technology specialization or profession. The methodology refers to the evaluation of the professional experience, studies and vocational training of the candidates for accreditation. It contains the analysis and modelling of the qualitative criteria as well as the implementation of multicriteria aggregation–disaggregation techniques attributing value to each criterion. Then, the candidates are classified in categories of professionals using the Electre Tri method, accepting as input data the multicriteria assessments on each criterion. The proposed evaluation approach has been adapted to the Greek educational system and is applied to a specific example of candidate.     

On Optimization over the Efficient Set in Linear Multicriteria Programming

The efficient set of a linear multicriteria programming problem can be represented by a reverse convex constraint of the form g(z)≤0, where g is a concave function. Consequently, the problem of optimizing some real function over the efficient set belongs to an important problem class of global optimization called reverse convex programming. Since the concave function used in the literature is only defined on some set containing the feasible set of the underlying multicriteria programming problem, most global optimization techniques for handling this kind of reverse convex constraint cannot be applied. The main purpose of our article is to present a method for overcoming this disadvantage. We construct a concave function which is finitely defined on the whole space and can be considered as an extension of the existing function. Different forms of the linear multicriteria programming problem are discussed, including the minimum maximal flow problem as an example. The research was partly done while the third author was visiting the Department of Mathematics, University of Trier with the support by the Alexander von Humboldt Foundation. He thanks the university as well as the foundation.     

A multiple criteria sorting method where each category is characterized by several reference actions: The Electre Tri-nC method

This paper presents Electre Tri-nC, a new sorting method which takes into account several reference actions for characterizing each category. This new method gives a particular freedom to the decision maker in the co-construction decision aiding process with the analyst to characterize the set of categories, while there is no constraint for introducing only one reference action as typical of each category like in Electre Tri-C (Almeida-Dias et al., 2010). As in such a sorting method, this new sorting method is composed of two joint rules. Electre Tri-nC also fulfills a certain number of natural requirements. Additional results on the behavior of the new method are also provided in this paper, namely the ones with respect to the addition or removal of the reference actions used for characterizing a certain category. A numerical example illustrates the manner in which Electre Tri-nC can be used by a decision maker. A comparison with some related sorting procedures is presented and it allows to conclude that the new method is appropriate to deal with sorting problems.