March 2021
Journal paper accepted
24/03/21/08:55 Filed in: Journal paper
N. Madrid, C. López-Molina and P. Hurtik. Non-linear scale-space based on fuzzy contrast enhancement: Theoretical results. Fuzzy Sets and Systems 421:133-157, 2021.
ABSTRACT This work presents a contrast enhancement operator based on a fuzzy-numerical description of images at the pixel level; this operator is further used to construct a scale-space, whose theoretical and practical properties are reviewed. A very remarkable feature of our scale-space is that, in contrast to many other scale-spaces, it converges to non-trivial stages. Within the study of our scale-space, we present a series of theoretical results that show that the convergence of the scale-space is closely related to the signal's convexity. Specifically, we prove formally that the intensities in convex signals tend to converge to the minimum intensity. As a result, our scale-space increases the contrast in the image and homogenizes images. In addition to theoretical results, we illustrate the scale-space's behaviour in ad-hoc 1D signals and in greyscale images. Finally, to validate the potential application of this theoretical approach, we show that the proposal can be used as a preprocessing that performed before a neural network technique, increasing the accuracy in a classification task.
ABSTRACT This work presents a contrast enhancement operator based on a fuzzy-numerical description of images at the pixel level; this operator is further used to construct a scale-space, whose theoretical and practical properties are reviewed. A very remarkable feature of our scale-space is that, in contrast to many other scale-spaces, it converges to non-trivial stages. Within the study of our scale-space, we present a series of theoretical results that show that the convergence of the scale-space is closely related to the signal's convexity. Specifically, we prove formally that the intensities in convex signals tend to converge to the minimum intensity. As a result, our scale-space increases the contrast in the image and homogenizes images. In addition to theoretical results, we illustrate the scale-space's behaviour in ad-hoc 1D signals and in greyscale images. Finally, to validate the potential application of this theoretical approach, we show that the proposal can be used as a preprocessing that performed before a neural network technique, increasing the accuracy in a classification task.
Journal paper accepted
15/03/21/09:42 Filed in: Journal paper
N. Madrid and M. Ojeda-Aciego. A Measure of Consistency for Fuzzy Logic Theories. Mathematical Methods in the Applied Sciences, 2021. To appear
ABSTRACT Fuzzy logic has shown to be a suitable framework to handle contradictions in which, unsurprisingly, the notion of inconsistency can be defined in different ways. This paper starts with a short survey of different ways to define the notion of inconsistency in fuzzy logic systems. As a result, we provide a first notion of inconsistency by means of the absence of models. Subsequently, we define two measures of consistency that belong purely to the fuzzy paradigm; in the sense that both measures coincide with the crisp notion of consistency when the set of truth values is {0,1}. Accordingly, we can state that the two provided measures of consistence are notions of consistence based on degrees, bringing back the spirit of fuzzy logic into the notion of consistency.
ABSTRACT Fuzzy logic has shown to be a suitable framework to handle contradictions in which, unsurprisingly, the notion of inconsistency can be defined in different ways. This paper starts with a short survey of different ways to define the notion of inconsistency in fuzzy logic systems. As a result, we provide a first notion of inconsistency by means of the absence of models. Subsequently, we define two measures of consistency that belong purely to the fuzzy paradigm; in the sense that both measures coincide with the crisp notion of consistency when the set of truth values is {0,1}. Accordingly, we can state that the two provided measures of consistence are notions of consistence based on degrees, bringing back the spirit of fuzzy logic into the notion of consistency.
Conference paper accepted
15/03/21/09:11 Filed in: Conference paper
D. López-Rodríguez, P. Cordero, M. Enciso, Á. Mora. Clustering and identification of core implications. Int Con on Formal Concept Analysis (ICFCA), Strasbourg, 2021.
ABSTRACT FCA exhaustively uses the notion of cluster, by grouping attributes and objects and also providing a strong algebraic structure to them by means of the concept lattice. Our proposal explores how we can cluster implications. This work opens a research line in the direction of studying the knowledge inside the clusters computed from the Duquenne-Guigues basis. Some alternative measures to induce the clusters are analyzed, taking into account the information that directly appears in the appearance and in the semantics of the implications. This work also allows us to show to the FCA community the fcaR package, having the main methods of FCA and of the Simplification Logic. The paper ends with a motivation of the potential applications of performing clustering on the implications.
ABSTRACT FCA exhaustively uses the notion of cluster, by grouping attributes and objects and also providing a strong algebraic structure to them by means of the concept lattice. Our proposal explores how we can cluster implications. This work opens a research line in the direction of studying the knowledge inside the clusters computed from the Duquenne-Guigues basis. Some alternative measures to induce the clusters are analyzed, taking into account the information that directly appears in the appearance and in the semantics of the implications. This work also allows us to show to the FCA community the fcaR package, having the main methods of FCA and of the Simplification Logic. The paper ends with a motivation of the potential applications of performing clustering on the implications.