Metrizable ordinal proximity measures and their aggregation

Producción CientíficaOrdered qualitative scales formed by linguistic terms are frequently used for evaluating sets of alternatives in different decision-making problems. These scales are usually implicitly considered as uniform in the sense that the psychological proximity between consecutive terms is perceived as identical. However, sometimes agents can perceive different proximities between the linguistic terms of the scale, and an appropriate method is required for aggregating these perceptions. In this paper we introduce the notion of metrizable ordinal proximity measure, discuss some aggregation procedures and propose a method based on metrics for aggregating experts’ opinions on proximities between linguistic terms on ordered qualitative scales.Ministerio de Economía, Industria y Competitividad (Project ECO2016-77900-P

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

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

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

Tratamiento ordinal de las escalas cualitativas utilizadas por el Centro de Investigaciones Sociológicas

Qualitative scales formed by linguistic terms are used by different disciplines to determine preferences and different aspects of individuals’ lives. Although it is usual to assign numbers to the response categories of scales, it is not suitable when individuals perceive different proximities between the consecutive categories of the scale, that is, when scales are not uniform. In this paper, an ordinal procedure is proposed to order a set of alternatives from the assessments given by a group of individuals through a qualitative scale not necessarily uniform. This procedure is based on ordinal proximities between the response categories of scales. The proposed procedure is illustrated with an example taken from the Barometer of the Center for Sociological Research of May 2011.Las escalas cualitativas formadas por términos lingüísticos son utilizadas por diversas disciplinas para determinar preferencias y diversos aspectos de la vida de los individuos. Aunque es habitual asignar números a las categorías de respuesta de estas escalas, no es adecuado utilizar codificaciones numéricas cuando los individuos perciben proximidades psicológicas distintas entre las categorías consecutivas de la escala, es decir, cuando las escalas cualitativas no son uniformes. En este trabajo se propone un procedimiento ordinal para jerarquizar un conjunto de alternativas a partir de las valoraciones mostradas por un grupo de individuos mediante una escala cualitativa no necesariamente uniforme. Dicho procedimiento está basado en las proximidades ordinales entre las categorías de respuesta de las escalas. El procedimiento propuesto se ilustra con un ejemplo tomado del Barómetro del Centro de Investigaciones Sociológicas (CIS) de mayo de 2011

Ordinal treatment of qualitative scales used by the Center for Sociological Research

Las escalas cualitativas formadas por términos lingüísticos son utilizadas por diversas disciplinas para determinar preferencias y diversos aspectos de la vida de los individuos. Aunque es habitual asignar números a las categorías de respuesta de estas escalas, no es adecuado utilizar codificaciones numéricas cuando los individuos perciben proximidades psicológicas distintas entre las categorías consecutivas de la escala, es decir, cuando las escalas cualitativas no son uniformes. En este trabajo se propone un procedimiento ordinal para jerarquizar un conjunto de alternativas a partir de las valoraciones mostradas por un grupo de individuos mediante una escala cualitativa no necesariamente uniforme. Dicho procedimiento está basado en las proximidades ordinales entre las categorías de respuesta de las escalas. El procedimiento propuesto se ilustra con un ejemplo tomado del Barómetro del Centro de Investigaciones Sociológicas (CIS) de mayo de 2011.Qualitative scales formed by linguistic terms are used by different disciplines to determine preferences and different aspects of individuals¿ lives. Although it is usual to assign numbers to the response categories of scales, it is not suitable when individuals perceive different proximities between the consecutive categories of the scale, that is, when scales are not uniform. In this paper, an ordinal procedure is proposed to order a set of alternatives from the assessments given by a group of individuals through a qualitative scale not necessarily uniform. This procedure is based on ordinal proximities between the response categories of scales. The proposed procedure is illustrated with an example taken from the Barometer of the Center for Sociological Research of May 2011.Universidad Pablo de Olavid

A survey of random processes with reinforcement

The models surveyed include generalized P\'{o}lya urns, reinforced random walks, interacting urn models, and continuous reinforced processes. Emphasis is on methods and results, with sketches provided of some proofs. Applications are discussed in statistics, biology, economics and a number of other areas.Comment: Published at http://dx.doi.org/10.1214/07-PS094 in the Probability Surveys (http://www.i-journals.org/ps/) by the Institute of Mathematical Statistics (http://www.imstat.org

Medidas de dispersión ordinal: aplicaciones a la medición del impacto de etiquetas lingüísticas y a problemas de decisión multicriterio con operadores OWA

Esta memoria está dedicada al análisis de la dispersión de datos de naturaleza cualitativa ordinal. En ella comenzamos haciendo una revisión profunda del estado del arte analizando y formulando rigurosamente las medidas de dispersión ordinal encontradas. A continuación estudiamos las propiedades existentes en la literatura y proponemos otras nuevas propiedades relevantes para las medidas de dispersión. Seguidamente clasificamos las medidas de dispersión ordinal en función de las propiedades que verifican. También introducimos una relación de equivalencia entre medidas de dispersión ordinal que nos permite agruparlas..

Dynamics of Macrosystems; Proceedings of a Workshop, September 3-7, 1984

There is an increasing awareness of the important and persuasive role that instability and random, chaotic motion play in the dynamics of macrosystems. Further research in the field should aim at providing useful tools, and therefore the motivation should come from important questions arising in specific macrosystems. Such systems include biochemical networks, genetic mechanisms, biological communities, neutral networks, cognitive processes and economic structures. This list may seem heterogeneous, but there are similarities between evolution in the different fields. It is not surprising that mathematical methods devised in one field can also be used to describe the dynamics of another. IIASA is attempting to make progress in this direction. With this aim in view this workshop was held at Laxenburg over the period 3-7 September 1984. These Proceedings cover a broad canvas, ranging from specific biological and economic problems to general aspects of dynamical systems and evolutionary theory

Journal of Telecommunications and Information Technology, 2011, nr 4

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