Francisco Javier Ruiz

Multi-Classification by Using Tri-Class SVM

The standard form for dealing with multi-class classification problems when bi-classifiers are used is to consider a two-phase (decomposition, reconstruction) training scheme. The most popular decomposition procedures are pairwise coupling (one versus one, 1-v-1), which considers a learning machine for each Pair of classes, and the one-versus-all scheme (one versus all, 1-v-r), which takes into consideration each class versus the remaining classes. In this article a 1-v-1 tri-class Support Vector Machine (SVM) is presented. The expansion of the architecture of this machine into three categories specifically addresses the decomposition problem of how to prevent the loss of information which occurs in the usual 1-v-1 training procedure. The proposed machine, by means of a third class, allows all the information to be incorporated into the remaining training patterns when a multi-class problem is considered in the form of a 1-v-1 decomposition. Three general structures are presented where each improves some features from the precedent structure. In order to deal with multi-classification problems, it is demonstrated that the final machine proposed allows ordinal regression as a form of decomposition procedure. Examples and experimental results are presented which illustrate the performance of the new tri-class SV machine.

IDD: A Supervised Interval Distance-Based Method for Discretization

This article introduces a new method for supervised discretization based on interval distances by using a novel concept of neighbourhood in the targets space. The method proposed takes into consideration the order of the class attribute, when this exists, so that it can be used with ordinal discrete classes as well as continuous classes, in the case of regression problems. The method has proved to be very efficient in terms of accuracy and faster than the most commonly supervised discretization methods used in the literature. It is illustrated through several examples and a comparison with other standard discretization methods is performed for three public data sets by using two different learning tasks: a decision tree algorithm and SVM for regression.

Modeling group assessments by means of hesitant fuzzy linguistic term sets

Hesitant linguistic term sets have been introduced to capture the human way of reasoning using linguistic expressions involving different levels of precision. In this paper, a lattice structure is provided to the set of hesitant fuzzy linguistic term sets by means of the operations intersection and connected union. In addition, in a group decision making framework, hesitant fuzzy linguistic descriptions are defined to manage situations in which decision makers are assessing different alternatives by means of hesitant fuzzy linguistic term sets. Based on the introduced lattice structure, two distances between hesitant fuzzy linguistic descriptions are defined. These metric structures allow distances between decision makers to be computed. A centroid of the decision making group is proposed for each distance to model group representatives in the considered group decision making framework.

Understanding the impact of brand colour on brand image

A new preference disaggregation method is proposed.The method is able to handle non-monotonic preferences.The role of brand colour in brand image is studied by applying the method on a real dataset.Results show that colour plays an important role in almost all of the brand image attributes.Results show that colour hue has less impact on brand perception, compared to colour saturation and value. What is the role that colour plays in perception of a brand by customers? How can we explore the cognitive role that colour plays in determining brand perception? To answer these questions we propose a preference disaggregation method based on multi-criteria decision aid. We identify the criteria aggregation model that underlies the global preference of a brand with respect to each brand image attribute. The proposed method is inspired by the well-known UTASTAR algorithm, but unlike the original formulation, it represents preferences by means of non-monotonic value functions. The method is applied to a database of brands ranked on each brand image attribute. For each brand image attribute, non-monotonic marginal value functions from each component of the brand colour are obtained separately. These functions contain the fitness between each colour component and each brand image attribute, in an understandable manner.

Consensus, dissension and precision in group decision making by means of an algebraic extension of hesitant fuzzy linguistic term sets

Abstract Present measures of the degree of agreement in group decision-making using hesitant fuzzy linguistic term sets allow consensus or agreement measurement when decision makers’ assessments involve hesitance. Yet they do not discriminate with different degrees of consensus among situations with discordant or polarized assessments. The visualization of differences among groups for which there is no agreement but different possible levels of disagreement is an important issue in collective decision-making situations. In this paper, we propose new collective and individual consensus measures that explicitly consider the hesitance of the decision makers’ hesitance in giving an opinion and also the gap between non-overlapping assessments, thus allowing the measurement of the polarization present within the group’s opinions. In addition, an expert’s profile is defined by considering the expert’s behavior in previous assessments in group decision-making processes in terms of precision and dissension.

A linear programming approach for learning non-monotonic additive value functions in multiple criteria decision aiding

A new framework for preference disaggregation in multiple criteria decision aiding is introduced. The proposed approach aims to infer non-monotonic additive preference models from a set of indirect pairwise comparisons. The preference model is presented as a set of marginal value functions and the discriminatory power of the inferred preference model is maximized against its complexity. To infer a value function that is compatible with the supplied preference information, the proposed methodology leads to a linear programming optimization problem that is easy to solve. The applicability and effectiveness of the new methodology is demonstrated in a thorough experimental analysis covering a broad range of decision problems.

Gait identification by using spectrum analysis on state space reconstruction

This paper describes a method for identifying a person while walking by means of a triaxial accelerometer attached to the waist. Human gait is considered as a dynamical system whose attractor is reconstructed by time delay vectors. A Spectral Analysis on the state space reconstruction is used to characterize the attractor. Parameters involved in the reconstruction and characterization process are evaluated to examine the effect in gait identification. The method is tested in five volunteers, obtaining an overall accuracy of 92%.

A passivity framework for fuzzy control system stability: case of two-input-single output fuzzy-controllers

The paper presents a passivity framework to analyse the asymptotic stability of zero-steady-state error solutions of fuzzy control systems. Typical two-input-single-output fuzzy, controllers (FC) are considered for which we propose a continuous-time single input nonlinear dynamic representation based on a pseudo-derivative of the error. The nonlinear part is a two-input mapping with a set of properties arising from the mini or product-inference rule, as well as properties of the input and output fuzzy sets used. The stability analysis is performed for the class of linear time invariant plant models with PI-like FC, it is based on general results coming from positive real and passive systems, leading to two graphical tests. Hints are given to deal with the case of PD-like FC.

A consensus degree for hesitant fuzzy linguistic decision making

This paper proposes a measure of consensus for group decision making in the hesitant fuzzy linguistic term sets framework. An extension of the set of hesitant fuzzy linguistic term sets is considered to capture differences among discordant assessments. The difference between a pair of disjoint assessments is given by a measure that takes into account the gap between them. The proposed measure of consensus is defined using this extension, and, as a result, we obtain more accurate values, i.e., the new measure is able to distinguish among group consensus levels that were indistinguishable according to existing measures of consensus. An illustrative example is provided to show the potential of the proposed consensus degree, the process of its computation and a comparison with an existing approach based on a similarity among decision makers.

A Representative in Group Decision by Means of the Extended Set of Hesitant Fuzzy Linguistic Term Sets

Hesitant fuzzy linguistic term sets were introduced to grasp the uncertainty existing in human reasoning when expressing preferences. In this paper, an extension of the set of hesitant fuzzy linguistic term sets is presented to capture differences between non-compatible preferences. In addition, an order relation and two closed operation over this set are also introduced to provide a lattice structure to the extended set of hesitant fuzzy linguistic term sets. Based on this lattice structure a distance between hesitant fuzzy linguistic descriptions is defined. This distance enables differences between decision makers to be quantified. Finally, a representative of a decision making group is presented as the centroid of the group based on the introduced distance.