Towards Rough Applicability of Rules

In this article, we further study the problem of soft applicability of rules within the framework of approximation spaces. Such forms of applicability are generally called rough. The starting point is the notion of graded applicability of a rule to an object, introduced in our previous work and referred to as fundamental. The abstract concept of rough applicability of rules comprises a vast number of particular cases. In the present paper, we generalize the fundamental form of applicability in two ways. Firstly, we more intensively exploit the idea of rough approximation of sets of objects. Secondly, a graded applicability of a rule to a set of objects is defined. A better understanding of rough applicability of rules is important for building the ontology of an approximate reason and, in the sequel, for modeling of complex systems, e.g., systems of social agents.