Open Access
Interval type-2 fuzzy sets are generalization of interval-valued fuzzy sets: towards a wider view on their relationship
(IEEE, 2015) Bustince Sola, Humberto; Fernández Fernández, Francisco Javier; Hagras, Hani; Herrera, Francisco; Pagola Barrio, Miguel; Barrenechea Tartas, Edurne; Automática y Computación; Automatika eta Konputazioa
In this paper, we will present a wider view on the relationship between interval-valued fuzzy sets and interval type- 2 fuzzy sets where we will show that interval-valued fuzzy sets are a particular case of the interval type-2 fuzzy sets. For this reason, both concepts should be treated in a different way. In addition, the view presented in this paper will allow a more general perspective of interval type-2 fuzzy sets which will allow representing concepts which could not be presented by intervalvalued fuzzy sets.
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
Join and meet operations for type-2 fuzzy sets with non-convex secondary memberships
(IEEE, 2016) Ruiz, Gonzalo; Hagras, Hani; Pomares, Héctor; Rojas, Ignacio; Bustince Sola, Humberto; Automática y Computación; Automatika eta Konputazioa
In this paper we will present two theorems for the join and meet operations for general type-2 fuzzy sets with arbitrary secondary memberships, which can be non-convex and/or non-normal type-1 fuzzy sets. These results will be used to derive the join and meet operations of the more general descriptions of interval type-2 fuzzy sets presented in [1], where the secondary grades can be non-convex. Hence, this work will help to explore the potential of type-2 fuzzy logic systems which use the general forms of interval type-2 fuzzy sets which are not equivalent to interval valued fuzzy sets. Several examples for both general type-2 and the more general forms of interval type-2 fuzzy sets are presented.
Open Access
On the stability of fuzzy classifiers to noise induction
(IEEE, 2023-11-09) Fumanal Idocin, Javier; Bustince Sola, Humberto; Andreu-Pérez, Javier; Hagras, Hani; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
Tabular data classification is one of the most important research problems in the artificial intelligence. One of the most important desired properties of the ideal classifier is that small changes in its input should not result in dramatic changes in its output. However, this might not be the case for many classifiers used in present day. Fuzzy classifiers should be stronger than their crisp counterparts, as they should be able to handle such changes using fuzzy sets and their membership functions. However, this hypothesis has not been empirically tested. Besides, the concept of 'small change' is somewhat imprecise and has not been quantified yet. In this work we propose to use small and progressively bigger changes in test samples to study how different crisp and fuzzy classifiers behave. We also study how to optimize classifiers to be more resistant to such kind of changes. Our results show that different fuzzy sets have different responses to this problem and have a smoother performance response compared to crisp classifiers. We also studied how to improve this and found that resistance to small changes can also result in a worse overall performance.
Open Access
A historical account of types of fuzzy sets and their relationships
(IEEE, 2016) Bustince Sola, Humberto; Barrenechea Tartas, Edurne; Pagola Barrio, Miguel; Fernández Fernández, Francisco Javier; Xu, Zeshui; Bedregal, Benjamin; Montero, Javier; Hagras, Hani; Herrera, Francisco; Baets, Bernard de; Automatika eta Konputazioa; Institute of Smart Cities - ISC; Automática y Computación
In this work we review the definition and basic properties of the different types of fuzzy sets that have appeared up to now in the literature. We also analyze the relationships between them and enumerate some of the applications in which they have been used.
Open Access
ARTxAI: explainable artificial intelligence curates deep representation learning for artistic images using fuzzy techniques
(IEEE, 2024) Fumanal Idocin, Javier; Andreu-Pérez, Javier; Cordón, Óscar; Hagras, Hani; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
Automatic art analysis employs different image processing techniques to classify and categorize works of art. When working with artistic images, we need to take into account further considerations compared to classical image processing. This is because artistic paintings change drastically depending on the author, the scene depicted, and their artistic style. This can result in features that perform very well in a given task but do not grasp the whole of the visual and symbolic information contained in a painting. In this article, we show how the features obtained from different tasks in artistic image classification are suitable to solve other ones of similar nature. We present different methods to improve the generalization capabilities and performance of artistic classification systems. Furthermore, we propose an explainable artificial intelligence method to map known visual traits of an image with the features used by the deep learning model considering fuzzy rules. These rules show the patterns and variables that are relevant to solve each task and how effective is each of the patterns found. Our results show that compared to multitask learning, our proposed context-aware features can achieve up to 19% more accurate results when using the residual network architecture and 3% when using ConvNeXt. We also show that some of the features used by these models can be more clearly correlated to visual traits in the original image than other kinds of features.
Open Access
A compact evolutionary interval-valued fuzzy rule-based classification system for the modeling and prediction of real-world financial applications with imbalanced data
(IEEE, 2014) Sanz Delgado, José Antonio; Bernardo, Darío; Herrera, Francisco; Bustince Sola, Humberto; Hagras, Hani; Automática y Computación; Automatika eta Konputazioa
The current financial crisis has stressed the need of obtaining more accurate prediction models in order to decrease the risk when investing money on economic opportunities. In addition, the transparency of the process followed to make the decisions in financial applications is becoming an important issue. Furthermore, there is a need to handle the real-world imbalanced financial data sets without using sampling techniques which might introduce noise in the used data. In this paper, we present a compact evolutionary interval-valued fuzzy rule-based classification system, which is based on IVTURSFARC-HD (Interval-Valued fuzzy rule-based classification system with TUning and Rule Selection) [22]), for the modeling and prediction of real-world financial applications. This proposed system allows obtaining good predictions accuracies using a small set of short fuzzy rules implying a high degree of interpretability of the generated linguistic model. Furthermore, the proposed system deals with the financial imbalanced datasets with no need for any preprocessing or sampling method and thus avoiding the accidental introduction of noise in the data used in the learning process. The system is also provided with a mechanism to handle examples that are not covered by any fuzzy rule in the generated rule base. To test the quality of our proposal, we will present an experimental study including eleven real-world financial datasets. We will show that the proposed system outperforms the original C4.5 decision tree, type-1 and interval-valued fuzzy counterparts which use the SMOTE sampling technique to preprocess data and the original FURIA, which is a fuzzy approximative classifier. Furthermore, the proposed method enhances the results achieved by the cost sensitive C4.5 and it gives competitive results when compared with FURIA using SMOTE, while our proposal avoids pre-processing techniques and it provides interpretable models that allow obtaining more accurate results.