Probabilistic Implications

Implications over Probabilistic Attributes

We consider the task of acquisition of terminological knowledge from given assertional data. However, when evaluating data of realworld applications we often encounter situations where it is impractical to deduce only crisp knowledge, due to the presence of exceptions or errors. It is rather appropriate to allow for degrees of uncertainty within the derived knowledge. Consequently, suitable met...

Probabilistic Formal Concepts with Negation

The probabilistic generalization of formal concept analysis, as well as it’s comparison to standard formal analysis is presented. Construction is resistant to noise in the data and give one an opportunity to consider contexts with negation (object-attribute relation which allows both attribute presence and it’s absence). This generalization is obtained from the notion of formal concepts with it...

Probabilistic Implicational Bases in FCA and Probabilistic Bases of GCIs in EL⊥

A probabilistic formal context is a triadic context the third dimension of which is a set of worlds equipped with a probability measure. After a formal definition of this notion, this document introduces probability of implications with respect to probabilistic formal contexts, and provides a construction for a base of implications the probabilities of which exceed a given lower threshold. A co...

Laws of Contraposition and Law of Importation for Probabilistic Implications and Probabilistic S-implications

Fuzzy implications based on semicopulas

Recently, two new families of fuzzy implication functions called probabilistic implications and probabilistic S-implications were introduced by Grzegorzewski [6, 7, 9]. They are based on conditional copulas and make a bridge between probability theory and fuzzy logic. In this paper we generalize these two classes and propose a new kind of construction methods for fuzzy implications which are ba...