In Fuzzy Formal Concept Analysis (FFCA), concept lattices are computed by scaling the problem and applying ordinary FCA algorithms. In this paper, the CbO family of algorithms is extended to work natively in the fuzzy setting, they are proved to be correct and output the whole set of formal concepts, which makes them mathematically equivalent to the scaling approach. However, experimental results demonstrate the performance improvement of these methods compared to scaling. The paper also discusses a new fuzzy strategy based on blacklisting redundant truth values to enhance the performance of algorithms by taking advantage of the structure of the residuated lattice.

This article delves into the process of fuzzifying time series, which entails converting a conventional time series into a time-indexed sequence of fuzzy numbers. The focus lies on the well-established practice of fuzzifying time series when a predefined degree of uncertainty is known, employing fuzzy numbers to quantify volatility or vagueness. To address practical challenges associated with volatility or vagueness quantification, we introduce the concept of informed time series. An algorithm is proposed to derive fuzzy time series, and findings include the examination of structural breaks within the realm of fuzzy time series. Additionally, this article underscores the significance of employing topological tools in the analysis of fuzzy time series, accentuating the role of these tools in extracting insights and unraveling intricate relationships within the data. • Introduces fuzzification of time series with informed time series. • Fuzzy time series captures uncertainty with fuzzy numbers. • Shows fuzzification can maintain stationarity despite structural breaks. • Dynamic time warping extended for fuzzy time series analysis. • Applications include stock market prediction and pattern recognition.

The Carve algorithm uses a divide-and-conquer strategy to compute the concept lattice of a formal context. The decomposition phase of the Carve algorithm discovers hierarchical structure in an amenable formal context, which the synthesis phase then exploits to construct the concept lattice from those of the component sub-contexts. In this paper, the problem of computing a sound and complete set of attribute implications via a refinement of the Carve decomposition is studied. Indeed, a set of rules is devised to obtain a set of valid implications which is proved to be complete. The refined decomposition and these rules are implemented in the novel Carve+ algorithm, whose runtime compares favorably with direct computation of the Duquenne–Guigues base of implications via the NextClosure algorithm.

In this paper, we present a novel approach for sentiment analysis that uses Formal Concept Analysis (FCA) to create dictionaries for classification. Unlike other methods that rely on pre-defined lexicons, our approach allows for the creation of customised dictionaries that are tailored to the specific data and tasks. By using a dataset of tweets categorised into positive and negative polarity, we show that our approach achieves a better performance than other standard dictionaries.

In this paper, we present a probabilistic neural model, which extends Kohonen's self-organizing map (SOM) by performing a probabilistic principal component analysis (PPCA) at each neuron. Several SOMs have been proposed in the literature to capture the local principal subspaces, but our approach offers a probabilistic model while it has a low complexity on the dimensionality of the input space. This allows to process very high-dimensional data to obtain reliable estimations of the probability densities which are based on the PPCA framework. Experimental results are presented, which show the map formation capabilities of the proposal with high-dimensional data, and its potential in image and video compression applications.

The aim of this work is to present a segmentation method to detect moving objects in video scenes, based on the use of a multivalued discrete neural network to improve the results obtained by an underlying segmentation algorithm. Specifically, the multivalued neural model (MREM) is used to detect and correct some of the deficiencies and errors off the well-known Mixture of Gaussians algorithm. Experimental results, using video scenes publicly available from the Internet, show an increase of the visual quality of the segmentation, that could improve for subsequent analysis phases, such as object tracking or behavior studies.

In this work, we propose the use of a multivalued recurrent neural network with the aim of graph drawing. Particularly, the problem of drawing a graph in two parallel lines with the minimum number of crossings between edges is studied, and a formulation for this problem is presented. The neural model MREM is used to solve this problem. This model has been successfully applied to other optimization problems. In this case, a slightly different version is used, in which the neuron state is represented by a two dimensional discrete vector, representing the nodes assigned to a given position in each of the parallel lines. Some experimental simulations have been carried out in order to compare the efficiency of the neural network with a heuristic approach designed to solve the problem at hand. These simulations confirm that our neural model outperforms the heuristic approach, obtaining a lower number of crossings on average.