NUEVO MODELO DE REPRESENTACION Y AGREGACION DE LA INFORMACION UTILIZANDO LAS EXTENSIONES DE LOS CONJUNTOS DIFUSOS. APLICACIONES

TIN2010-15055

Nombre agencia financiadora Ministerio de Ciencia e Innovación
Acrónimo agencia financiadora MICINN
Programa Programa Nacional de Investigación Fundamental
Subprograma Investigación fundamental no-orientada
Convocatoria Investigación fundamental no-orientada
Año convocatoria 2010
Unidad de gestión Subdirección General de Proyectos de Investigación
Centro beneficiario UNIVERSIDAD PÚBLICA DE NAVARRA (UPNA)
Centro realización UNIVERSIDAD PÚBLICA DE NAVARRA (UPNA)
Identificador persistente http://dx.doi.org/10.13039/501100004837

Publicaciones

Found(s) 5 result(s)
Found(s) 1 page(s)

IIVFDT: ignorance functions based interval-valued fuzzy decision tree with genetic tuning

Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
  • 0000-0002-1427-9909
  • Fernández, Alberto
  • 0000-0002-1279-6195
  • Herrera, Francisco
Electronic version of an article published as International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems Vol. 20, Suppl. 2 (October 2012) 1–30 DOI: 10.1142/S0218488512400132 © World Scientific Publishing Company http://www.worldscientific.com/worldscinet/ijufks, The choice of membership functions plays an essential role in the success of fuzzy systems. This is a complex problem due to the possible lack of knowledge when assigning punctual values as membership degrees. To face this handicap, we propose a methodology called Ignorance functions based Interval-Valued Fuzzy Decision Tree with genetic tuning, IIVFDT for short, which allows to improve the performance of fuzzy decision trees by taking into account the ignorance degree. This ignorance degree is the result of a weak ignorance function applied to the punctual value set as membership degree.

Our IIVFDT proposal is composed of four steps: (1) the base fuzzy decision tree is generated using the fuzzy ID3 algorithm; (2) the linguistic labels are modeled with Interval-Valued Fuzzy Sets. To do so, a new parametrized construction method of Interval-Valued Fuzzy Sets is defined, whose length represents such ignorance degree; (3) the fuzzy reasoning method is extended to work with this representation of the linguistic terms; (4) an evolutionary tuning step is applied for computing the optimal ignorance degree for each Interval-Valued Fuzzy Set.

The experimental study shows that the IIVFDT method allows the results provided by the initial fuzzy ID3 with and without Interval-Valued Fuzzy Sets to be outperformed. The suitability of the proposed methodology is shown with respect to both several state-of-the-art fuzzy decision trees and C4.5. Furthermore, we analyze the quality of our approach versus two methods that learn the fuzzy decision tree using genetic algorithms. Finally, we show that a superior performance can be achieved by means of the positive synergy obtained when applying the well known genetic tuning of the lateral position after the application of the IIVFDT method.
The choice of membership functions plays an essential role in the success of fuzzy systems. This is a complex problem due to the possible lack of knowledge when assigning punctual values as membership degrees. To face this handicap, we propose a methodology called Ignorance functions based Interval-Valued Fuzzy Decision Tree with genetic tuning, IIVFDT for short, which allows to improve the performance of fuzzy decision trees by taking into account the ignorance degree. This ignorance degree is the result of a weak ignorance function applied to the punctual value set as membership degree. Our IIVFDT proposal is composed of four steps: (1) the base fuzzy decision tree is generated using the fuzzy ID3 algorithm; (2) the linguistic labels are modeled with Interval-Valued Fuzzy Sets. To do so, a new parametrized construction method of Interval-Valued Fuzzy Sets is defined, whose length represents such ignorance degree; (3) the fuzzy reasoning method is extended to work with this representation of the linguistic terms; (4) an evolutionary tuning step is applied for computing the optimal ignorance degree for each Interval-Valued Fuzzy Set. The experimental study shows that the IIVFDT method allows the results provided by the initial fuzzy ID3 with and without Interval-Valued Fuzzy Sets to be outperformed. The suitability of the proposed methodology is shown with respect to both several state-of-the-art fuzzy decision trees and C4.5. Furthermore, we analyze the quality of our approach versus two methods that learn the fuzzy decision tree using genetic algorithms. Finally, we show that a superior performance can be achieved by means of the positive synergy obtained when applying the well known genetic tuning of the lateral position after the application of the IIVFDT method., This work was supported in part by the Spanish Ministry of Science and Technology
under projects TIN2011-28488 and TIN2010-15055.




IVTURS: A linguistic fuzzy rule-based classification system based on a new interval-valued fuzzy reasoning method with tuning and rule selection

Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
  • 0000-0002-1427-9909
  • Fernández, Alberto
  • 0000-0002-1279-6195
  • Herrera, Francisco
Interval-valued fuzzy sets have been shown to be a useful tool for dealing with the ignorance related to the definition of the linguistic labels. Specifically, they have been successfully applied to solve classification problems, performing simple modifications on the fuzzy reasoning method to work with this representation and making the classification based on a single number. In this paper we present IVTURS, a new linguistic fuzzy rule-based classification method based on a new completely interval-valued fuzzy reasoning method. This inference process uses interval-valued restricted equivalence functions to increase the relevance of the rules in which the equivalence of the interval membership degrees of the patterns and the ideal membership degrees is greater, which is a desirable behaviour. Furthermore, their parametrized construction allows the computation of the optimal function for each variable to be performed, which could involve a potential improvement in the system’s behaviour. Additionally, we combine this tuning of the equivalence with rule selection in order to decrease the complexity of the system. In this paper we name our method IVTURS-FARC, since we use the FARC-HD method to accomplish the fuzzy rule learning process. The experimental study is developed in three steps in order to ascertain the quality of our new proposal. First, we determine both the essential role that interval-valued fuzzy sets play in the method and the need for the rule selection process. Next, we show the improvements achieved by IVTURS-FARC with respect to the tuning of the degree of ignorance when it is applied in both an isolated way and when combined with the tuning of the equivalence. Finally, the significance of IVTURS-FARC is further depicted by means of a comparison by which it is proved to outperform the results of FARC-HD and FURIA, which are two high performing fuzzy classification algorithms., This work was supported in part by the Spanish Ministry of Science and Technology under projects TIN2011-28488 and TIN2010-15055 and the Andalusian Research Plan P10-TIC-6858 and P11-TIC-7765.




Using the Choquet integral in the fuzzy reasoning method of fuzzy rule-based classification systems

Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
  • 0000-0001-6657-948X
  • 0000-0002-1279-6195
  • 0000-0003-4427-3935
  • 0000-0002-5845-887X
  • 0000-0002-1427-9909
In this paper we present a new fuzzy reasoning method in which the Choquet
integral is used as aggregation function. In this manner, we can take into account the
interaction among the rules of the system. For this reason, we consider several fuzzy
measures, since it is a key point on the subsequent success of the Choquet integral, and
we apply the new method with the same fuzzy measure for all the classes. However, the
relationship among the set of rules of each class can be different and therefore the best
fuzzy measure can change depending on the class. Consequently, we propose a learning
method by means of a genetic algorithm in which the most suitable fuzzy measure for
each class is computed. From the obtained results it is shown that our new proposal
allows the performance of the classical fuzzy reasoning methods of the winning rule and
additive combination to be enhanced whenever the fuzzy measure is appropriate for the
tackled problem., This work was partially supported by the Spanish Ministry of Science and Technology under projects
TIN2010-15055 and TIN2011-29520.




Medical diagnosis of cardiovascular diseases using an interval-valued fuzzy rule-based classification system

Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
  • 0000-0002-1427-9909
  • 0000-0003-2865-6549
  • 0000-0002-4087-586X
  • 0000-0001-6951-6396
  • 0000-0003-4764-5298
  • 0000-0002-1279-6195
Objective: To develop a classifier that tackles the problem of determining the risk of a patient of suffering from a cardiovascular disease within the next ten years. The system has to provide both a diagnosis and an interpretable model explaining the decision. In this way, doctors are able to analyse the usefulness of the information given by the system. Methods: Linguistic fuzzy rule-based classification systems are used, since they provide a good classification rate and a highly interpretable model. More specifically, a new methodology to combine fuzzy rule-based classification systems with interval-valued fuzzy sets is proposed, which is composed of three steps: 1) the modelling of the linguistic labels of the classifier using interval-valued fuzzy sets; 2) the use of the Kα operator in the inference process and 3) the application of a genetic tuning to find the best ignorance degree that each interval-valued fuzzy set represents as well as the best value for the parameter α of the Kα operator in each rule. Results: The suitability of the new proposal to deal with this medical diagnosis classification problem is shown by comparing its performance with respect to the one provided by two classical fuzzy classifiers and a previous interval-valued fuzzy rule-based classification system. The performance of the new method is statistically better than the ones obtained with the methods considered in the comparison. The new proposal enhances both the total number of correctly diagnosed patients, around 3% with respect the classical fuzzy classifiers and around 1% versus the previous interval-valued fuzzy classifier, and the classifier ability to correctly differentiate patients of the different risk categories. Conclusion: The proposed methodology is a suitable tool to face the medical diagnosis of cardiovascular diseases, since it obtains a good classification rate and it also provides an interpretable model that can be easily understood by the doctors., This work was partially supported by the Spanish Ministry of Science and Technology under project TIN2010-15055 and the Research Services of the Universidad Pública de Navarra.




Pre-aggregation functions: construction and an application

Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
  • Lucca, Giancarlo
  • 0000-0002-1427-9909
  • 0000-0001-6986-9888
  • 0000-0002-6757-7934
  • Mesiar, Radko
  • Kolesárová, Anna
  • 0000-0002-1279-6195
In this work we introduce the notion of preaggregation
function. Such a function satisfies the same boundary
conditions as an aggregation function, but, instead of requiring
monotonicity, only monotonicity along some fixed direction (directional
monotonicity) is required. We present some examples
of such functions. We propose three different methods to build
pre-aggregation functions. We experimentally show that in fuzzy
rule-based classification systems, when we use one of these
methods, namely, the one based on the use of the Choquet
integral replacing the product by other aggregation functions,
if we consider the minimum or the Hamacher product t-norms
for such construction, we improve the results obtained when
applying the fuzzy reasoning methods obtained using two classical
averaging operators like the maximum and the Choquet integral., This work was supported in part by the Spanish Ministry of Science
and Technology under projects TIN2008-06681-C06-01, TIN2010-
15055, TIN2013-40765-P, TIN2011-29520.