Open Access
A first study on the use of interval-valued fuzzy sets with genetic tuning for classification with imbalanced data sets
(Springer, 2009) Sanz Delgado, José Antonio; Fernández, Alberto; Bustince Sola, Humberto; Herrera, Francisco; Automática y Computación; Automatika eta Konputazioa
Classification with imbalanced data-sets is one of the recent challenging problems in Data Mining. In this framework, the class dis- tribution is not uniform and the separability between the classes is often difficult. From the available techniques in the Machine Learning field, we focus on the use of Fuzzy Rule Based Classification Systems, as they provide an interpretable model for the end user by means of linguistic variables. The aim of this work is to increase the performance of fuzzy modeling by adding a higher degree of knowledge by means of the use of Interval- valued Fuzzy Sets. Furthermore, we will contextualize the Interval-valued Fuzzy Sets with a post-processing genetic tuning of the amplitude of their upper bounds in order to enhance the global behaviour of this methodology.
Open Access
A method for inference in approximate reasoning based on normal intuitionistic fuzzy sets
(Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, 1995) Bustince Sola, Humberto; Burillo López, Pedro; Mohedano Salillas, Victoria; Automática y Computación; Automatika eta Konputazioa
This paper introduces a method of approximate inference which operates with nornal intuitionistic fuzzy. We give a definition of degree of compatibility between intuitionistic fuzzy sets and we present a method for the construction of these sets. Lastly we present the method of inference in approximate reasoning with normal intuitionistic fuzzy sets and we study its most immediate properties.
Open Access
Intuitionistic fuzzy relations (Part I)
(Universitat Politècnica de Catalunya, 1995) Burillo López, Pedro; Bustince Sola, Humberto; Automática y Computación; Automatika eta Konputazioa
This paper introduces the concept of intuitionistic fuzzy relation. We also study the choice of t-norms and t-conorms which must be done in order that the composition of intuitionistic fuzzy relations fulfills the largest number of properties. On the other hand, we also analyse the intuitionistic fuzzy relations in a set and their properties. Besides, we also study the properties of the intuitionistic fuzzy relations in a set and the properties of the composition with different t-norms and t-conorms.
Open Access
On the intuitionistic fuzzy relations
(Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, 1995) Burillo López, Pedro; Bustince Sola, Humberto; Atanassov, Krassimir; Automática y Computación; Automatika eta Konputazioa
Intuitionistic fuzzy relations which generalize the already existing relations are introduced and their basic properties are shown.
Open Access
Orderings in the referential set induced by intuitionistic fuzzy relation
(Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, 1995) Burillo López, Pedro; Bustince Sola, Humberto; Automática y Computación; Automatika eta Konputazioa
In this paper we present different orderings in the referential set induced by intuitionistic fuzzy relations of ordering. We can see how these induced orders justify the definition given of intuitionistic fuzzy antisymmetry and the definition of partial enclosure.
Open Access
Intuitionistic fuzzy relations (Part II). Effect of Atanassov's operators on the properties of the intuitionistic fuzzy relations
(Universitat Politècnica de Catalunya, 1995) Burillo López, Pedro; Bustince Sola, Humberto; Automática y Computación; Automatika eta Konputazioa
In this paper we study the effect of Atanassov's operator on the properties of properties reflexive, symmetric, antisymmetric, perfect antisymmetric and transitive intuitionistic fuzzy relations. We finish the paper analysing the partial enclosure of the intuitionistic fuzzy relations and its effect on the conservation of the transitive property through Atanassov's operator.
Open Access
About the intuitionistic fuzzy set generators
(Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, 1997) Bustince Sola, Humberto; Mohedano Salillas, Victoria; Automática y Computación; Automatika eta Konputazioa
In this paper form the definition of intuitionistic fuzzy sets we analyze the intuitionistic fuzzy generators and the complementation in these sets. We start by defining the intuitionistic fuzzy generators in order to then study the particular cases for which this definition coincides with the fuzzy complementation. Afterwards we analyze the existence of equilibrium points, dual points and we present characterization theorems of intuitionistic fuzzy generators. Lastly, we study a manner of constructing intuitionistic fuzzy sets and analyse the structure of the complementary of intuitionistic fuzzy sets built.
Open Access
Handling multicriteria fuzzy decision-making problems based on intuitionistic fuzzy sets
(Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, 1995) Bustince Sola, Humberto; Automática y Computación; Automatika eta Konputazioa
In this paper we present a new technique for handling multicriteria decision making problems based on intuitionistic fuzzy sets. In this new technique we use the degree of reliability and of non-reliability of each criterion in relation to a set of alternatives. We also present a new score function in order to evaluate the degree of suitability of the choice of a certain alternative.
Open Access
A theorem for constructing interval-valued intuitionistic fuzzy sets from intuitionistic fuzzy sets
(Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, 1995) Bustince Sola, Humberto; Burillo López, Pedro; Automática y Computación; Automatika eta Konputazioa
In this paper we present a theorem that allows us to construct interval-valued intuitionistic fuzzy sets from intuitionistic fuzzy sets. We also study the way of recovering intuitionistic fuzzy sets used in the construction of the interval-valued intuitionistic fuzzy set from different operators. We analise the numerical measures of information of the internal-valued intuitionistic fuzzy set constructed in function with the numerical measures of information of the intuitionistic fuzzy sets used in its construction. We review the most important properties of intuitionistic fuzzy sets and of internal-valued intuitionistic fuzzy sets and we analise three operators among these sets along with their properties.