Learning aggregation weights from 3-tuple comparison sets

An important task in multiple-criteria decision making is how to learn the weights and parameters of an aggregation function from empirical data. We consider this in the context of quantifying ecological diversity, where such data is to be obtained as a set of pairwise comparisons specifying that one community should be considered more diverse than another. A problem that arises is how to collect a sufficient amount of data for reliable model determination without overloading individuals with the number of comparisons they need to make. After providing an algorithm for determining criteria weights and an overall ranking from such information, we then investigate the improvement in accuracy if ranked 3-tuples are supplied instead of pairs. We found that aggregation models could be determined accurately from significantly fewer 3-tuple comparisons than pairs. © 2013 IEEE

The Gini index,the dual decomposition of aggregation functions, and the consistent measurement of inequality

In several economic fields, such as those related to health, education or poverty, the individuals’ characteristics are measured by bounded variables. Accordingly, these characteristics may be indistinctly represented by achievements or shortfalls. A difficulty arises when inequality needs to be assessed. One may focus either on achievements or on shortfalls but the respective inequality rankings may lead to contradictory results. Specifically, this paper concentrates on the poverty measure proposed by Sen. According to this measure the inequality among the poor is captured by the Gini index. However, the rankings obtained by the Gini index applied to either the achievements or the shortfalls do not coincide in general. To overcome this drawback, we show that an OWA operator is underlying in the definition of the Sen measure. The dual decomposition of the OWA operators into a self-dual core and anti-self-dual remainder allows us to propose an inequality component which measures consistently the achievement and shortfall inequality among the poor.Aggregation functions, dual decomposition, OWA operators, Gini index, consistent measures of achievement/shortfall inequality, Sen index, poverty measures.

Transitive matrices, strict preference and intensity operators

Let X be a set of alternatives and a_{ij} a positive number expressing how much the alternative x_{i} is preferred to the alternative x_{j}. Under suitable hypothesis of no indifference and transitivity over the pairwise comparison matrix A= (a_{ij}), the alternatives can be ordered as a chain . Then a coherent priority vector is a vector giving a weighted ranking agreeing with the obtained chain and an intensity vector is a coherent priority vector encoding information about the intensities of the preferences. In the paper we look for operators F that, acting on the row vectors translate the matrix A in an intensity vector

OWA-Based Multi-Criteria Decision Making based on Fuzzy Methods

One of the most important challenges in Multi-Attribute Decision Making (MADM) problem is "How can the optimal weights of the criteria be determined properly by the decision maker?". In the relevant research literature, various methods based on the requirements and assumptions of the problem were introduced to determine the weights of the criteria. In this regard, in particular, the Yager's OWA operator is one of the most significant and widely used approaches to evaluate the weight of criteria. But there is a drawback, which is that the results of Yager's OWA operator depend only on the level and size of decision-maker's risk and the dimension of the criteria. Therefore, in this paper, using a multi-objective decision making approach, we try to express this MADM challenge in the form of a generalization of the Yager's OWA operators and Ahn's method. One of the advantages of this generalization is that the proposed method uses all the information in the decision matrix compared to the methods proposed by Yager's OWA operators and the Ahn's method. The proposed approach is also able to enter the types of preferences considered by the decision maker for the criteria calculations as crisp or fuzzy quantities. Numerical examples and real dataset analysis based on a survey of students' opinions on teaching activities are provided

Strategic weight manipulation in multiple attribute decision making

In some real-world multiple attribute decision making (MADM) problems, a decision maker can strategically set attribute weights to obtain her/his desired ranking of alternatives, which is called the strategic weight manipulation of the MADM. In this paper, we define the concept of the ranking range of an alternative in the MADM, and propose a series of mixed 0-1 linear programming models (MLPMs) to show the process of designing a strategic attribute weight vector. Then, we reveal the conditions to manipulate a strategic attribute weight based on the ranking range and the proposed MLPMs. Finally, a numerical example with real background is used to demonstrate the validity of our models, and simulation experiments are presented to show the better performance of the ordered weighted averaging operator than the weighted averaging operator in defending against the strategic weight manipulation of the MADM problems

Modelling cyber-security experts' decision making processes using aggregation operators

An important role carried out by cyber-security experts is the assessment of proposed computer systems, during their design stage. This task is fraught with difficulties and uncertainty, making the knowledge provided by human experts essential for successful assessment. Today, the increasing number of progressively complex systems has led to an urgent need to produce tools that support the expert-led process of system-security assessment. In this research, we use Weighted Averages (WAs) and Ordered Weighted Averages (OWAs) with Evolutionary Algorithms (EAs) to create aggregation operators that model parts of the assessment process. We show how individual overall ratings for security components can be produced from ratings of their characteristics, and how these individual overall ratings can be aggregated to produce overall rankings of potential attacks on a system. As well as the identification of salient attacks and weak points in a prospective system, the proposed method also highlights which factors and security components contribute most to a component's difficulty and attack ranking respectively. A real world scenario is used in which experts were asked to rank a set of technical attacks, and to answer a series of questions about the security components that are the subject of the attacks. The work shows how finding good aggregation operators, and identifying important components and factors of a cyber-security problem can be automated. The resulting operators have the potential for use as decision aids for systems designers and cyber-security experts, increasing the amount of assessment that can be achieved with the limited resources available

Enhancing the ELECTRE decision support method with semantic data

Prendre una decisió quan les opcions es defineixen mitjançant un conjunt divers de criteris no és fàcil. Aqueta tesi es centra en ampliar la metodologia ELECTRE, que és el mètode del tipus "outranking" més utilitzat. En aquesta tesi ens centrem en problemes de decisió que involucren informació no numèrica, tal com els criteris semàntics multivaluats, que poden prendre com a valors els conceptes d'una ontologia de domini determinada. Primer proposo una nova manera de manipular els criteris semàntics per evitar l'agregació de les puntuacions numèriques abans del procediment de classificació. Aquest mètode, anomenat ELECTRE-SEM, segueix els mateixos principis que el clàssic ELECTRE però, en aquest cas, els índexs de concordança i discordança es defineixen en termes de la comparació per parelles de les puntuacions que indiquen l'interès de l'usuari sobre diferents conceptes de l'ontologia. En segon lloc, proposo crear un perfil d'usuari semàntic mitjançant el emmagatzemant de puntuacions de preferències a l'ontologia. Es vincula una puntuació d'interès numèrica als conceptes més específics, això permet distingir millor les preferències de l'usuari, i també s'incorpora un procediment d'agregació per inferir les preferències de l'usuari considerant les relacions taxonòmiques entre conceptes. La metodologia proposada s'ha aplicat en dos casos d’estudi: l'avaluació de plantes de generació d'energia i la recomanació d'activitats turístiques a Tarragona.Tomar una decisión cuando las opciones se definen sobre un conjunto diverso de criterios no es fácil. Esta tesis se centra en ampliar la metodología ELECTRE, que es el método del tipo "outranking" más utilizado. En esta tesis nos centramos en problemas de decisión que involucren información no numérica, tal como los criterios semánticos multi-valuados, que pueden tomar como valores los conceptos de una ontología de dominio determinada. Primero propongo una nueva forma de manejar los criterios semánticos para evitar la agregación de puntuaciones numéricas antes del procedimiento de clasificación. Este método, llamado ELECTRE-SEM, sigue los mismos principios que el clásico ELECTRE, pero en este caso los índices de concordancia y discordancia se definen en términos de la comparación por pares de unas puntuaciones que indican el interés del usuario sobre distintos conceptos de la ontología. En segundo lugar, propongo crear un perfil de usuario semántico mediante el almacenamiento de puntuaciones de preferencias en la ontología. Se asocian puntuaciones numéricas a los conceptos más específicos, lo cual permite distinguir mejor las preferencias del usuario, y se incorpora un proceso de agregación para inferir las preferencias del usuario mediante las relaciones taxonómicas entre conceptos. La metodología propuesta ha sido aplicada en dos casos de estudio: la evaluación de las plantas de generación de energía y la recomendación de actividades turísticas en Tarragona.Reach a decision when options are defined on a set of diverse criteria is not easy. This thesis is focused on improving the methodology ELECTRE, which is the most used outranking-based method. In this dissertation, we focus on decision problems involving non-numerical information, such as multi-valued semantic criteria, which may take as values the concepts of a given domain ontology. First, I propose a new way of handling semantic criteria to avoid the aggregation of the numerical scores before the ranking procedure. This method, called ELECTRE-SEM, follows the same principles than the classic ELECTRE but in this case the concordance and discordance indices are defined in terms of the pairwise comparison of the interest scores. Second, I also propose to create a semantic user profile by storing preference scores into the ontology. The numerical interest score attached to the most specific concepts permits to distinguish better the preferences of the user, improving the quality of the decision by the incorporation of an aggregation methodology to infer the user's preferences by considering taxonomic relations between concepts. The proposed methodology has been applied in two case studies: the assessment of power generation plants and the recommendation of touristic activities in Tarragona

Multiple Attribute Strategic Weight Manipulation With Minimum Cost in a Group Decision Making Context With Interval Attribute Weights Information

Abstract—In multiple attribute decision making (MADM), strategic weight manipulation is understood as a deliberate manipulation of attribute weight setting to achieve a desired ranking of alternatives. In this paper, we study the strategic weight manipulation in a group decision making (GDM) context with interval attribute weight information. In GDM, the revision of the decision makers’ original attribute weight information implies a cost. Driven by a desire to minimize the cost, we propose the minimum cost strategic weight manipulation model, which is achieved via optimization approach, with the mixed 0-1 linear programming model being proved appropriate in this context. Meanwhile, some desired properties to manipulate a strategic attribute weight based on the ranking range under interval attribute weight information are proposed. Finally, numerical analysis and simulation experiments are provided with a twofold aim: 1) to verify the validity of the proposed models and 2) to show the effects of interval attribute weights information and the unit cost, respectively, on the cost to manipulate strategic weights in the MADM in a group decision context.This work was supported in part by National Science Foundation of China under Grant 71571124, Grant 71871149, and Grant 71601133; in part by Sichuan University under Grant sksyl201705 and Grant 2018hhs-58; and in part by FEDER Funds under Grant TIN2016- 75850-R