Qualitative ordinal scales: the concept of ordinal range

Many practical problems of quality control involve the use of ordinal scales. Questionnaires planned to collect judgments on qualitative or linguistic scales, whose levels are terms such as "good," "bad," "medium," etc., are extensively used both in evaluating service quality and in visual controls for manufacturing industry. In an ordinal environment, the concept of distance between two generic levels of the same scale is not defined. Therefore, a population (universe) of judgments cannot be described using "traditional" statistical distributions since they are based on the notion of distance. The concept of "distribution shape" cannot be defined as well. In this article, we introduce a new statistical entity, the so-called ordinal distribution, to describe a population of judgments expressed on an ordinal scale. We also discuss which of the traditional location and dispersion measures can be used in this context and we briefly analyze some of their properties. A new dispersion measure, the ordinal range, as an extension of the cardinal range to ordinal scales, is then proposed. A practical application in the field of quality is developed throughout the articl

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

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

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

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

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

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 new approach for evaluation of risk priorities of failure modes in FMEA

This paper presents a method for carrying out the calculus of the risk priority of failures in Failure Mode and Effect Analysis (FMEA). The novelty of the method consists of new management of data provided by the design team, normally given on qualitative scales, without necessitating an arbitrary and artificial numerical conversion. The practical effects of these issues are shown in an application example

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

Towards Validating Risk Indicators Based on Measurement Theory

Due to the lack of quantitative information and for cost-efficiency purpose, most risk assessment methods use partially ordered values (e.g. high, medium, low) as risk indicators.\ud In practice it is common to validate risk scales by asking stakeholders whether they make sense. This way of validation is subjective, thus error prone. If the metrics are wrong (not meaningful), then they may lead system owners to distribute security investments inefficiently. Therefore, when validating risk assessment methods it is important to validate the meaningfulness of the risk scales that they use. In this paper we investigate how to validate the meaningfulness of risk indicators based on measurement theory. Furthermore, to analyze the applicability of measurement theory to risk indicators, we analyze the indicators used by a particular risk assessment method specially developed for assessing confidentiality risks in networks of organizations