Relations d'équivalence co-analytiques
In this paper, by defining a pair of classical sets as a relative set, an extension of the classical set algebra which is a counterpart of Belnap's four-valued logic is achieved. Every relative set partitions all objects into four distinct regions corresponding to four truth-values of Belnap's logic. Like truth-values of Belnap's logic, relative sets have two orderings; one is an order of inclusion and the other is an order of knowledge or information. By defining a rough set as a pair of definable...
Fuzzy classification systems is defined in this paper as an aggregative model, in such a way that Ruspini classical definition of fuzzy partition appears as a particular case. Once a basic recursive model has been accepted, we then propose to analyze relevance and redundancy in order to allow the possibility of learning from previous experiences. All these concepts are applied to a real picture, showing that our approach allows to check quality of such a classification system.
Some constructions of spaces with/without dense subspaces satisfying stronger separation axioms are presented.