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

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

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

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

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

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

Managing the Smiley Face Scale Used by Booking.com in an Ordinal Way

Producción CientíficaUser reviews are a new source of information in the hospitality and tourism sector. Usually, these reviews contain comments of users and assessments expressed through ordered qualitative scales. The website Booking.com uses a smiley face scale to ask users the degree of satisfaction regarding several aspects of accommodations. The scoring system of the website assigns numerical values to each item of the smiley face scale. However, when users perceive different proximities between pairs of items of an ordered qualitative scale, these numerical codifications are because they may misrepresent the original ordinal information. In this paper, we analyze the drawbacks and limitations of the scoring system of Booking.com and we manage its smiley face scale through a purely ordinal procedure. This procedure avoids assigning numerical codifications to items of scales and it takes into account how users perceive the proximities between pairs of items. The findings show the importance of considering how users understand qualitative scales when they face subjective assessments through ordered qualitative scales

The dual decomposition of aggregation functions and its application in welfare economics

Producción CientíficaIn this paper, we review the role of self-duality in the theory of aggregation functions, the dual decomposition of aggregation functions into a self-dual core and an anti-self-dual remainder, and some applications to welfare, inequality, and poverty measures.Ministerio de Economía, Industria y Competitividad (ECO2012-32178)Junta de Castilla y León (programa de apoyo a proyectos de investigación – Ref. VA066U13

An ordinal multi-criteria decision-making procedure under imprecise linguistic assessments

Producción CientíficaMany decision-making problems such as quality control analysis, market surveys or sensory analysis require ordered qualitative scales, rather than numerical ones. It is very common to assign some cardinal mathematical objects, such as numerical values, intervals of real numbers or fuzzy numbers, to the linguistic terms of ordered qualitative scales. However, when agents perceive that the psychological proximity between each pair of consecutive terms of the scale is not identical, these conversions are meaningless and an ordinal approach to deal with these non-uniform ordered qualitative scales is more appropriate. The aim of this paper is to introduce an ordinal multi-criteria decision-making procedure for ranking alternatives in the setting of ordered qualitative scales that are nonnecessarily uniform. The possibility of doubt is also considered, by allowing agents to assign two consecutive terms of the scale when they hesitate. The proposed procedure is applied to a real case study in which nine experts assessed eight wines regarding different criteria.Ministerio de Economía, Industria y Competitividad (project ECO2016-77900-P )European Regional Development Fund (ERDF