Bipolar aggregation method for fuzzy nominal classification using Weighted Cardinal Fuzzy Measure (WCFM)

The issue of designing a procedure to assign objects (candidates, projects, decisions, options, etc.) characterized by multiple attributes or criteria to predefined classes characterized by fuzzyly defined multiple features, conditions or constraints, is considered in this paper. Such assignment problems are known in the literature as nominal or non ordered classification problems as opposed to ordinal classification in which case classes are ordered according to some desires of decision maker(s). Because of the importance of these problems in many domains such as social, economics, medical, engineering, mangement etc., there is a need to design sound and appropriate evaluation algorithms and methods to deal with them. In this paper we will consider an approach based on an evaluation strategy that consists in aggregating separately elements that act in the same sens (either contributing to the exlusion of a class from assignment or its consideration for inclusion given an object) that we refer to as bipolar analysis. Then, relying on the fact that elements to aggregate have synergetic relationships (they are complementary), we propose to use Choquet integral as the appropriate aggregation operator with a proposed fuzzy measure or capacity known as weighted cardinal fuzzy measure (WCFM) which tractability permits to overcome dificulties that dissuade the use of Choquet integral in practices. Furthermore, bipolar property results in evaluation by two degrees: classifiability measure that measures to what extent an object can be considered for inclusion in a class and rejectability measure, a degree that measures the extent to which one must avoid including an object to a class rendering final choice flexible as many classes may be qualified for inclusion of an object. Application of this approach to a real world problem in the domain of banking has shown a real potentiality

Solving unstructured classification problems with multicriteria decision aiding

Tese de mestrado integrado. Engenharia Electrotécnica e de Computadores (Automação). Universidade do Porto. Faculdade de Engenharia. 201

Using ELECTRE TRI outranking method to sort MOMILP nondominated solutions

Several interactive methods exist to identify nondominated solutions in a Multiple Objective Mixed Integer Linear Program. But what if the Decision Maker is also interested in sorting those solutions (assigning them to pre-established ordinal categories)? We propose an interactive "branch-and-bound like" technique to progressively build the nondominated set, combined with ELECTRE TRI method (Pessimistic procedure) to sort identified nondominated solutions. A disaggregation approach is considered in order to avoid direct definition of all ELECTRE TRI preference parameters. Weight-importance coefficients are inferred and category reference profiles are determined based on assignment examples provided by the Decision Maker. A computation tool was developed with a twofold purpose: support the Decision Maker involved in a decision process and provide a test bed for research purposes.http://www.sciencedirect.com/science/article/B6VCT-48GF3RT-B/1/55841cf788557c60dac156a4e7b1890

Synthesis of main criteria, methods and issues of multicriteria supplier selection

O objetivo do presente artigo é identificar na literatura quais são os principais critérios considerados no processo de decisão, os principais métodos individuais e combinados e os subproblemas da seleção de fornecedores no contexto multicritério. Cabe ressaltar que as tarefas de avaliar e identificar os melhores fornecedores para um novo produto ou serviço são essenciais ao gerenciamento da cadeia de suprimentos (GCS). Para executá-las apropriadamente, considerando-se a natureza multicritério da seleção de fornecedores, torna-se necessária a inclusão de uma abordagem de agregação dos critérios, cuja escolha depende basicamente dos objetivos da decisão, tipos de critérios a serem utilizados e racionalidade do decisor. Para atingir o objetivo proposto, optou-se por utilizar o procedimento da revisão sistemática da literatura que segue o protocolo proposto por Cronin, Ryan e Coughlan (2008), abrangendo artigos publicados nas bases ISI Web of Knowledge e Scopus, no período de 2001 a 2012. Além de sintetizar o conhecimento acerca do tema, o artigo ressalta os principais critérios, métodos e subproblemas da seleção de fornecedores, com isso, contribui ao identificar os aspectos que devem ser desenvolvidos em estudos futuros e ao apresentar aos gestores abordagens existentes para a tomada de decisões relativa à seleção de fornecedores de forma sistematizada.The purpose of this paper is to identify the main criteria considered in supplier selection, the main methods used and sub-problems in a multicriteria context. The tasks of identifying the best suppliers of new products or services or even for evaluating the performance of an existing supplier is essential to supply chain management (SCM). In order to perform these tasks properly, and considering the multicriteria nature of supplier selection, it is necessary to include an approach using aggregation of criteria, primarily chosen depending on the objectives of the decision, types of criteria to be used and the rationality of the decision maker. In order to achieve this objective this research used a systematic literature review of articles published in ISI Web of Knowledge and Scopus for the period 2001-2012 following the protocol proposed by Cronin, Ryan and Coughlan (2008). In addition to synthesizing knowledge about the subject, the article highlights the key criteria, methods and sub-problems of selection of suppliers, contributing by identifying the aspects that should be developed in future studies. It also provides managers with existing approaches to making decisions about supplier selection in a systematic way

Fuzzy nominal classification using bipolar analysis

The process of assigning objects (candidates, projects, decisions, options, etc.) characterized by multiple attributes or criteria to predefined classes characterized by entrance conditions or constraints constitutes a subclass of multi-criteria decision making problems known as nominal or non-ordered classification problems as opposed to ordinal classification. In practice, class entrance conditions are not perfectly defined; they are rather fuzzily defined so that classification procedures must be design up to some uncertainty degree (doubt, indecision, imprecision, etc.). The purpose of this chapter is to expose recent advances related to this issue with particular highlights on bipolar analysis that consists in considering for a couple of object and class, two measures: classifiability measure that measures to what extent the former object can be considered for inclusion in the later class and rejectability measure, a degree that measures the extent to which one should avoid including this object into that class rendering final choice flexible and robust as many classes may be qualified for inclusion of an object. This apparent theoretical subject finds applications in almost any socio-economic domain and particularly in digital marketing. An application to supply chain management, where a certain number of potential suppliers of a company are to be classified in a number of classes in order to apply the appropriate strategic treatment to them, will be considered for illustration purpose

Bipolar fuzzy nominal classification (BFNC) framework

Nominal classification (NC) is a subfield of multi-criteria decision making where an object (in a broad sense) characterized by some attributes (with their valuation belonging to an ordered set, numeric in general) must be assigned to one of pre-defined classes or categories; these classes are characterized by some numerical valued features. This is also known as supervised classification as opposed to unsupervised classification in machine learning literature. In many applications such as that of risk analysis, characterization of classes by features may not be precisely defined; they will be rather fuzzily expressed using linguistic appreciation such as high is better, low is more appreciated, medium range is better, etc. leading to what is referred to as fuzzy nominal classification (FNC). On other hand bipolar reasoning is pervasive in classification in the sense that given a couple (feature, class), there will be some values of the feature that lead to automatically assigning (respect. automatically excluding to assign) the considered object into that class leading to what we name bipolar fuzzy nominal classification or BFNC for short; the main purpose of this paper is to develop this BFNC framework with risk analysis as an illustrative application domain. The stepping stones of this framework are two indexes for each couple (class, object) known as classifiability index (that measures the extent to which the considered object can be included into that class) and the rejectability index measuring the extent to which one should avoid including this object into that class. By using two indexes for classification, many classes can be qualified for inclusion of a given object rendering this framework flexible. Analyzing risks for large-scale complex systems requires identifying, assessing, and prioritizing different risk scenarios for their appropriate treatment such as resources allocation for risk mitigation, risk prevention, risk sharing, etc. To this end and given scarcity of resources in general, one must consider first prioritizing, filtering, or scoring risks that return to assigning them to pre-defined classes or categories; that is nominally classifying them. The developed BFNC framework applied to a real world application in the domain of countries’ risk classification shows its practical potentialities

Une méthode multicritère de tri en utilisant plusieurs actions caractéristiques de référence pour définir chaque catégorie : la méthode Electre Tri-nC

International audienceThis 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.Dans cet article, une nouvelle méthode de tri, qui généralise la méthode Electre Tri-C, est proposée. On appelle cette méthode Electre Tri-nC. Cette méthode de tri est appropriée à des contextes d’aide à la décision où les catégories sont complètement ordonnées et chacune d’elles étant définie par plusieurs actions caractéristiques de référence au lieu d’une seule par catégorie. Electre Tri-nC a également été connue pour vérifier un ensemble d’exigences structurelles naturelles (la conformité, l’homogénéité, la monotonie et la stabilité), qui peuvent être considérées comme ses propriétés fondamentales. Cette méthode est constituée de deux règles couplées, appelées la règle descendante et la règle ascendante, qui doivent être utilisées conjointement (et pas séparément). Chacune de ces deux règles fait intervenir une fonction de sélection, qui est utilisée pour choisir une catégorie parmi deux catégories consécutives pour l’affectation possible d’une action. Le processus de co-construction entre l’analyste et le décideur peut être amélioré en ajoutant une nouvelle action caractéristique de référence. Cela implique la modification de la définition d’une catégorie et, par conséquent, à des impacts sur les résultats d’affectation, après cette modification. Dans cet article ce type de phénomènes est analysé de façon précise. Un exemple numérique est aussi présenté afin d’illustrer les résultats théoriques majeurs fournis par la méthode Electre Tri-nC. Une comparaison avec certaines méthodes de tri, qui partagent quelques éléments clés avec cette nouvelle méthode de tri, notamment en utilisant plusieurs actions caractéristique de référence pour définir chacune des catégories, permet de conclure que la méthode Electre Tri-nC est appropriée pour être appliquée aux problèmes de tri