Fuzzy heterogeneous networks are recently introduced feed-forward neural network models composed of neurons of a general class whose inputs and weights are mixtures of continuous variables (crisp and/or fuzzy) with discrete quantities, also admitting missing data. These networks have net input functions based on similarity relations between the inputs to and the weights of a neuron. They thus a...

This paper deals with closure properties of models of fuzzy attribute implications. Fuzzy attribute implications are particular IF-THEN rules which can be interpreted in data tables with fuzzy attributes and/or ranked data tables over domains with similarity relations. We show that models of any set of fuzzy attribute implications form a fuzzy closure system with hedge. Conversely, we show that...

The notion of a transitive closure of a fuzzy relation is very useful for clustering in pattern recognition, for fuzzy databases, etc. It is based on translating the standard definition of transitivity and transitive closure into fuzzy terms. This definition works fine, but to some extent it does not fully capture our understanding of transitivity. The reason is that this definition is based on...

An usual and effective way to define a similarity relation is from a function of distance. Nevertheless, if we consider only usual distances, then some natural kinds of similarity relations cannot be obtained. In this paper, we analyze some of these kinds of similarity relations, and we find non-usual distances in order to obtain these ones.

A Self Organising Fuzzy Controller for linear or non-linear processes with a minimum knowledge about the process is developed with the only assumption that the output of the process is monotonic with respect to the input (as most industrial processes are). Beginning with an empty rule-base a fuzzy process model is progressively on-line built. In this way the controller gradually learns how to c...

Data mining techniques have been proven as effective tools in the search of hidden or implicit knowledge in a database. Commonly, real world problems must be modeled, for example, by means of fuzzy logic, resulting in flexible database models applications and extensions of existing analysis techniques and tools. In this work, a methodology based on fuzzy data mining is applied on a particular p...

Fuzzy equality relations or indistinguishability operators generalize the concepts of crisp equality and equivalence relations in fuzzy systems where inaccuracy and uncertainty is dealt with. They generate fuzzy granularity and are an essential tool in Computing with Words (CWW). Traditionally, the degree of similarity between two objects is a number between 0 and 1, but in many occasions this ...

In this paper, we discuss rough inclusions defined in Rough Mereology – a paradigm for approximate reasoning introduced by Polkowski and Skowron – as a basis for common models for rough as well as fuzzy set theories. We justify the point of view that tolerance (or, similarity) is the motif common to both theories. To this end, we demonstrate in Sect. 6 that rough inclusions (which represent a h...

This paper constitutes a re nement of the fuzzy uni cation algorithm based on fuzzy compatibility relations, which we have developed with the aim of including the data type fuzzy set in a logic programming environment which supports a family of in nitely-valued logics. To be precise, we treat the problem of fuzzy uni cation by focusing on the distinction between general and speci c knowledge. F...