We investigate here the possibility of approximating a language starting from a partial knowledge of its strings. This is understood as the possibility to read only a bounded part of a string: a preex or a subword. In this way, indiscernibility relations among strings (they are equivalence or tolerance relations) are introduced, which lead to lower and upper approximations of languages. By vary...

Theory exploration is a term describing the development of a formal (i.e. with the help of an automated proof-assistant) approach to selected topic, usually within mathematics or computer science. This activity however usually doesn’t reflect the view of science considered as a whole, not as separated islands of knowledge. Merging theories essentially has its primary aim of bridging these gaps ...

Abs t rac t . Vagueness for a long time has been studied by philosophers, logicians and linguists. Recently researchers interested in AI contributed essentially to this area. In this paper we present a new approach to vagueness, called rough set theory. The starting of the theory theory is the assumption that fundamental mechanisms of human reasoning are based on the ability to classify object ...

In many data mining applications, cluster analysis is widely used and its results are expected to be interpretable, comprehensible, and usable. Rough set theory is one of the techniques to induce decision rules and manage inconsistent and incomplete information. This paper proposes a method to construct equivalence classes during the clustering process, isolate outlier points and finally deduce...

Conventional clustering algorithms categorize an object into precisely one cluster. In many applications, the membership of some of the objects to a cluster can be ambiguous. Therefore, an ability to specify membership to multiple clusters can be useful in real world applications. Fuzzy clustering makes it possible to specify the degree to which a given object belongs to a cluster. In Rough set...