Let Covering be the category of fuzzy coverings, and Partition, partitions. We geometrically construct an isomorphism categories between Partition a full subcategory Covering, which can used to derive bijections partitions coverings with finitely many sets. Also, we establish Covering[n], n sets, whose objects are sets satisfy certain conditions.

Model-based reinforcement learning can be applied to problems with continuous state spaces by discretizing the spaces with crisp or fuzzy partitions. The manual definition of suitable partitions, however, is often not trivial, since fine partitions lead to a high number of states and thus complex discrete problems, whereas coarse partitions can be unsuitable for the representation of the optima...

Two approaches are developed, which are suitable for the optimization of a fuzzy classification scheme through the formation of appropriate space-filling clusters. The first approach is based on the analog Hopfield neural network, while the second one uses real-encoded genetic optimization. Experimental results concerning difficult classification problems show that both proposed approaches are ...

In the present paper a Korovkin-type theorem is proposed for the approximation operators defined by the inverse Ftransforms. These results allow us to choose between a variety of shapes to be used as atoms of the fuzzy partitions used within the F-transform’s framework. In this way we can enlarge considerably the class of F-transforms proposed recently by I. Perfilieva. The new fuzzy partitions...

A new algorithm is proposed to learn fuzzy partitions with a high interpretability degree. The set of input variables, the number of linguistic terms per variable, and the type (triangular or trapezoidal) and parameters of the membership functions are learnt by means of a meta-algorithm that uses a simple learning method to generate a fuzzy rule set from the derived fuzzy partitions. Interpreta...

We explore attribute dependencies in the datasets by using direct and inverse fuzzy transforms. Our algorithm optimizes the fuzzy partitions of the universe of the attributes and moreover establishes if the set of the data points is sufficiently dense with respect to the chosen partitions: two specific regression indexes measure the reliability of our model. The known “El Nino” dataset is the b...

This paper describes a method for fuzzy classification and recognition of two-dimensional (2-D) shapes, such as handwritten characters, image contours, etc. A fuzzy model is derived for each considered shape from a fuzzy description of a set of instances of this shape. A fuzzy description of a shape instance, in its turn, exploits appropriate fuzzy partitions of the two dimensions of the shape....

This article presents a novel fuzzy identification method for dynamic modelling of quadrotor unmanned aerial vehicles. The method is based on a special parameterization of the antecedent part of fuzzy systems that results in fuzzy-partitions for antecedents. This antecedent parameter representation method of fuzzy rules ensures upholding of predefined linguistic value ordering and ensures that ...

In 1993, Yang first extended the classification maximum likelihood (CML) to a so-called fuzzy CML, by combining fuzzy c-partitions with the CML function. Fuzzy c-partitions are generally an extension of hard c-partitions. It was claimed that this was more robust. However, the fuzzy CML still lacks some robustness as a clustering algorithm, such as its inability to detect different volumes of cl...

The discretization of values plays a critical role in data mining and knowledge discovery. The representation of information through intervals is more concise and easier to understand at certain levels of knowledge than the representation by mean continuous values. In this paper, we propose a method for discretizing continuous attributes by means of a series of fuzzy sets, which constitutes a f...