Clustering U.S. 2016 presidential candidates through linguistic appraisals

Producción CientíficaThe main purpose of this paper is to cluster the United States (U.S.) 2016 presidential candidates taking the linguistic appraisals made by a random representative sample of adults living in the U.S. as our starting point. To do this, we have used the concept of ordinal proximity measure (see García-Lapresta and Pérez-Román), which allows to determine the degree of consensus in a group of agents when a set of alternatives is evaluated through non-necessarily qualitative scales.Ministerio de Economía, Industria y Competitividad (project ECO2016-77900-P

Aggregating opinions in non-uniform ordered qualitative scales

Producción CientíficaThis paper introduces a new voting system in the setting of ordered qualitative scales. The process is conducted in a purely ordinal way by considering an ordinal proximity measure that assigns an ordinal degree of proximity to each pair of linguistic terms of the qualitative scale. Once the agents assess the alternatives through the qualitative scale, the alternatives are ranked according to the medians of the ordinal degrees of proximity between the obtained individual assessments and the highest linguistic term of the scale. Since some alternatives may share the same median, an appropriate tie-breaking procedure is introduced. Some properties of the proposed voting system have been provided.Ministerio de Economía, Industria y Competitividad (Project ECO2016-77900-P

Measuring dispersion in the context of ordered qualitative scales

Producción CientíficaThe main purpose of this contribution is to measure the dispersion associated with the different results of a variable when they form a set of linguistic terms obtained after examining different qualities of people, services, etc, ordered, but with a non-homogeneous and non-quantifiable distance between the linguistic terms.Ministerio de Economía, Industria y Competitividad (project ECO2016-77900-P

Decision-making in semi-democratic contexts

Producción CientíficaA general problem, which may concern practical contexts of different nature, is to aggregate multi-experts rankings on a set of alternatives into a single fused ranking. Aggregation should also take into account the experts’ importance, which may not necessarily be the same for all of them. We synthetically define this context as semi-democratic. The main aim of the paper is the analysis of the possible semi-democratic paradigms that can be conceived when the experts’ importance is not the same: (i) the importance is described by means of a weighting vector; (ii) the importance is expressed by a weak order on the set of experts; (iii) the importance is described by a weak order on the set of experts with additional information on the ordinal proximities among them. The three paradigms can be applied in different decision-making situations, where some experts perform multiple assignments. In this paper various situations are discussed and analyzed in detail. A series of examples, in the field of interior design of a new car, will complement the description.Ministerio de Economía, Industria y Competitividad (Project ECO2016-77900-P)European Regional Development Fund (ERDF

Positional voting rules generated by aggregation functions and the role of duplication

Producción CientíficaIn this paper, we consider a typical voting situation where a group of agents show their preferences over a set of alternatives. Under our approach, such preferences are codied into individual positional values which can be aggregated in several ways through particular functions, yielding positional voting rules and providing a social result in each case. We show that scoring rules belong to such class of positional voting rules. But if we focus our interest on OWA operators as aggregation functions, other well-known voting systems naturally appear. In particular, we determine those ones verifying duplication (i.e., clone irrelevance) and present a proposal of an overall social result provided by them.Ministerio de Economía, Industria y Competitividad (ECO2012-32178)Junta de Castilla y León (programa de apoyo a proyectos de investigación – Ref. VA066U13

Two characterizations of the dense rank

Producción CientíficaIn this paper, we have considered the dense rank for assigning positions to alternatives in weak orders. If we arrange the alternatives in tiers (i.e., indifference classes), the dense rank assigns position 1 to all the alternatives in the top tier, 2 to all the alternatives in the second tier, and so on. We have proposed a formal framework to analyze the dense rank when compared to other well-known position operators, such as the standard, modified and fractional ranks. As the main results, we have provided two different axiomatic characterizations which determine the dense rank by considering position invariance conditions along horizontal extensions (duplication), as well as through vertical reductions and movements (truncation, and upward or downward independency).PROYECTO PID2021-122506NB-I00. Toma de decisiones basadas en valoraciones cualitativas y ordinales. FONDOS FEDER, MICINN. MINISTERIO DE CIENCIA E INNOVACIÓN, AGENCIA ESTATAL DE INVESTIGACIÓN, UNION EUROPE

An ordinal multi-criteria decision-making procedure in the context of uniform qualitative scales

Producción CientíficaIn this contribution, we propose a multi-criteria decision-making procedure that has been devised in a purely ordinal way. Agents evaluate the alternatives regarding several criteria by assigning one or two consecutive terms of a uniform ordered qualitative scale to each alternative in each criterion. Weights assigned to criteria are managed through replications of the corresponding ratings, and alternatives are ranked according to the medians of their ratings after the replications

A consensus reaching process in the context of non-uniform ordered qualitative scales

Producción CientíficaIn this paper, we consider that a group of agents judge a set of alternatives by means of an ordered qualitative scale. The scale is not assumed to be uniform, i.e., the psychological distance between adjacent linguistic terms is not necessarily always the same. In this setting, we propose how to measure the consensus in each subset of at least two agents over each subset of alternatives. We introduce a consensus reaching process where some agents may be invited to change their assessments over some alternatives in order to increase the consensus. All the steps are managed in a purely ordinal way through ordinal proximity measures.Ministerio de Economía, Industria y Competitividad (ECO2012-32178)Junta de Castilla y León (programa de apoyo a proyectos de investigación – Ref. VA066U13

Ordinal proximity measures in the context of unbalanced qualitativescales and some applications to consensus and clustering

Producción CientíficaIn this paper, we introduce ordinal proximity measures in the setting of unbalanced qualitative scales by comparing the proximities between linguistic terms without numbers, in a purely ordinal approach. With this new tool, we propose how to measure the consensus in a set of agents when they assess a set of alternatives through an unbalanced qualitative scale. We also introduce an agglomerative hierarchical clustering procedure based on these consensus measures.Ministerio de Economía, Industria y Competitividad (ECO2012-32178)Junta de Castilla y León (programa de apoyo a proyectos de investigación – Ref. VA066U13

Consensus-based clustering under hesitant qualitative assessments

Producción CientíficaIn this paper, we consider that agents judge the feasible alternatives through linguistic terms – when they are confident in their opinions – or linguistic expressions formed by several consecutive linguistic terms – when they hesitate. In this context, we propose an agglomerative hierarchical clustering process where the clusters of agents are generated by using a distance-based consensus measure.Ministerio de Economía, Industria y Competitividad (ECO2012-32178)Junta de Castilla y León (programa de apoyo a proyectos de investigación – Ref. VA066U13