Open Access
On admissible orders over closed subintervals of [0,1]
(Elsevier, 2020) Santana, Fagner; Bedregal, Benjamin; Viana, Petrucio; Bustince Sola, Humberto; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Estadística, Informática y Matemáticas
In this paper, we make some considerations about admissible orders on the set of closed subintervals of the unit interval I[0,1], i.e. linear orders that refine the product order on intervals. We propose a new way to generate admissible orders on I[0,1] which is more general than those we find in the current literature. Also, we deal with the possibility of an admissible order on I[0,1] to be isomorphic to the usual order on [0,1]. We prove that some orders constructed by our method are not isomorphic to the usual one and we make some considerations about the following question: is there some admissible order on I[0,1] isomorphic to the usual order on [0,1]?
Open Access
Enhancing the efficiency of the interval-valued fuzzy rule-based classifier with tuning and rule selection
(Springer, 2020) Sanz Delgado, José Antonio; Da Cruz Asmus, Tiago; Osa Hernández, Borja de la; Bustince Sola, Humberto; Institute of Smart Cities - ISC; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa, PJUPNA1926
Interval-Valued fuzzy rule-based classifier with TUning and Rule Selection, IVTURS, is a state-of-the-art fuzzy classifier. One of the key point of this method is the usage of interval-valued restricted equivalence functions because their parametrization allows one to tune them to each problem, which leads to obtaining accurate results. However, they require the application of the exponentiation several times to obtain a result, which is a time demanding operation implying an extra charge to the computational burden of the method. In this contribution, we propose to reduce the number of exponentiation operations executed by the system, so that the efficiency of the method is enhanced with no alteration of the obtained results. Moreover, the new approach also allows for a reduction on the search space of the evolutionary method carried out in IVTURS. Consequently, we also propose four different approaches to take advantage of this reduction on the search space to study if it can imply an enhancement of the accuracy of the classifier. The experimental results prove: 1) the enhancement of the efficiency of IVTURS and 2) the accuracy of IVTURS is competitive versus that of the approaches using the reduced search space.
Open Access
Comments on "Interval type-2 fuzzy sets are generalization of interval-valued fuzzy sets: towards a wider view on their relationship" [2]
(IEEE, 2016) Mendel, Jerry M.; Hagras, Hani; Bustince Sola, Humberto; Herrera, Francisco; Automática y Computación; Automatika eta Konputazioa
This letter makes some observations about “Interval type-2 fuzzy sets are generalization of interval-valued fuzzy sets: Towards a wide view on their relationship,” IEEE Trans. Fuzzy Systems that further support the distinction between an interval type-2 fuzzy set (IT2 FS) and an interval-valued fuzzy set (IV FS), points out that all operations, methods, and systems that have been developed and published about IT2 FSs are, so far, only valid in the special case when IT2 FS = IVFS, and suggests some research opportunities.
Open Access
Improving the performance of fuzzy rule-based classification systems with interval-valued fuzzy sets and genetic amplitude tuning
(Elsevier, 2010) Sanz Delgado, José Antonio; Fernández, Alberto; Bustince Sola, Humberto; Herrera, Francisco; Automática y Computación; Automatika eta Konputazioa
Among the computational intelligence techniques employed to solve classification problems, Fuzzy Rule-Based Classification Systems (FRBCSs) are a popular tool because of their interpretable models based on linguistic variables, which are easier to understand for the experts or end-users. The aim of this paper is to enhance the performance of FRBCSs by extending the Knowledge Base with the application of the concept of Interval-Valued Fuzzy Sets (IVFSs). We consider a post-processing genetic tuning step that adjusts the amplitude of the upper bound of the IVFS to contextualize the fuzzy partitions and to obtain a most accurate solution to the problem. We analyze the goodness of this approach using two basic and well-known fuzzy rule learning algorithms, the Chi et al.’s method and the fuzzy hybrid genetics-based machine learning algorithm. We show the improvement achieved by this model through an extensive empirical study with a large collection of data-sets.
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
On the influence of admissible orders in IVOVO
(Springer, 2019) Uriz Martín, Mikel Xabier; Paternain Dallo, Daniel; Bustince Sola, Humberto; Galar Idoate, Mikel; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Estadística, Informática y Matemáticas; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa, PJUPNA13
It is known that when dealing with interval-valued data, there exist problems associated with the non-existence of a total order. In this work we investigate a reformulation of an interval-valued decomposition strategy for multi-class problems called IVOVO, and we analyze the effectiveness of considering different admissible orders in the aggregation phase of IVOVO. We demonstrate that the choice of an appropriate admissible order allows the method to obtain significant differences in terms of accuracy.
Open Access
Similarity between interval-valued fuzzy sets taking into account the width of the intervals and admissible orders
(Elsevier, 2020) Bustince Sola, Humberto; Marco Detchart, Cedric; Fernández Fernández, Francisco Javier; Wagner, Christian; Garibaldi, Jonathan M.; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Estadística, Informática y Matemáticas
In this work we study a new class of similarity measures between interval-valued fuzzy sets. The novelty of our approach lays, firstly, on the fact that we develop all the notions with respect to total orders of intervals; and secondly, on that we consider the width of intervals so that the uncertainty of the output is strongly related to the uncertainty of the input. For constructing the new interval-valued similarity, interval valued aggregation functions and interval-valued restricted equivalence functions which take into account the width of the intervals are needed, so we firstly study these functions, both in line with the two above stated features. Finally, we provide an illustrative example which makes use of an interval-valued similarity measure in stereo image matching and we show that the results obtained with the proposed interval-valued similarity measures improve numerically (according to the most widely used measures in the literature) the results obtained with interval valued similarity measures which do not consider the width of the intervals.
Open Access
Medical diagnosis of cardiovascular diseases using an interval-valued fuzzy rule-based classification system
(Elsevier, 2013) Sanz Delgado, José Antonio; Galar Idoate, Mikel; Jurío Munárriz, Aránzazu; Brugos Larumbe, Antonio; Pagola Barrio, Miguel; Bustince Sola, Humberto; Automática y Computación; Automatika eta Konputazioa; Ciencias de la Salud; Osasun Zientziak; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
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.
Open Access
Orness measurements for lattice m-dimensional interval-valued OWA operators
(Elsevier, 2018) Miguel Turullols, Laura de; Paternain Dallo, Daniel; Lizasoain Iriso, María Inmaculada; Ochoa Lezaun, Gustavo; Bustince Sola, Humberto; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Institute of Smart Cities - ISC; Estadística, Informática y Matemáticas
Ordered weighted average (OWA) operators are commonly used to aggregate information in multiple situations, such as decision making problems or image processing tasks. The great variety of weights that can be chosen to determinate an OWA operator provides a broad family of aggegating functions, which obviously give diferent results in the aggregation of the same set of data. In this paper, some possible classifications of OWA operators are suggested when they are de ned on m-dimensional intervals taking values on a complete lattice satisfying certain local conditions. A first classification is obtained by means of a quantitative orness measure that gives the proximity of each OWA to the OR operator. In the case in which the lattice is finite, another classification is obtained by means of a qualitative orness measure. In the present paper, several theoretical results are obtained in order to perform this qualitative value for each OWA operator.
Open Access
Orness for real m-dimensional interval-valued OWA operators and its application to determine a good partition
(Taylor & Francis, 2019) Miguel Turullols, Laura de; Paternain Dallo, Daniel; Lizasoain Iriso, María Inmaculada; Ochoa Lezaun, Gustavo; Bustince Sola, Humberto; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y Matemáticas; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa, PJUPNA1
Ordered Weighted Averaging (OWA) operators are a profusely applied class of averaging aggregation functions, i.e. operators that always yield a value between the minimum and the maximum of the inputs. The orness measure was introduced to classify the behavior of the OWA operators depending on the weight vectors. Defining a suitable orness measure is an arduous task when we deal with OWA operators defined over more intricate spaces, such us intervals or lattices. In this work we propose a suitable definition for the orness measure to classify OWA operators defined on the set of m-dimensional intervals taking real values in [0, 1]. The orness measure is applied to decide which is the best partition of a continuous range that should be divided into four linguistic labels. This example shows the good behavior of the proposed orness measure.