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Rough Sets and Infomorphisms: Towards Approximation of Relations in Distributed Environments

Skowron A., Stepaniuk J., Peters J.F.

Fundamenta Informaticae

2003

Vol. 54, nr 2,3

263-277

We discuss the relationships between information systems and classifications as well as between infomorphisms and definability of relations (between whole objects and their parts) in information systems. Infomorphisms between information systems (classifications) IS1 and IS2 make it possible to define some formulas over IS2 by means of formulas over IS1. The remaining formulas over IS2 can be approximatively defined by means of formulas over IS1. The approximation operations are defined using the rough set approach. We present definitions and examples of such approximations.

Towards an Ontology of Approximate Reason

Peters J.F., Skowron A., Stepaniuk J., Ramanna S.

Fundamenta Informaticae

2002

Vol. 51, nr 1,2

157-173

This article introduces structural aspects in an ontology of approximate reason. The basic assumption in this ontology is that approximate reason is a capability of an agent. Agents are designed to classify information granules derived from sensors that respond to stimuli in the environment of an agent or received from other agents. Classification of information granules is carried out in the context of parameterized approximation spaces and a calculus of granules. Judgment in agents is a faculty of thinking about (classifying) the particular relative to decision rules derived from data. Judgment in agents is reflective, but not in the classical philosophical sense (e.g., the notion of judgment in Kant). In an agent, a reflective judgment itself is an assertion that a particular decision rule derived from data is applicable to an object (input). That is, a reflective judgment by an agent is an assertion that a particular vector of attribute (sensor) values matches to some degree the conditions for a particular rule. In effect, this form of judgment is an assertion that a vector of sensor values reflects a known property of data expressed by a decision rule. Since the reasoning underlying a reflective judgment is inductive and surjective (not based on a priori conditions or universals), this form of judgment is reflective, but not in the sense of Kant. Unlike Kant, a reflective judgment is surjective in the sense that it maps experimental attribute values onto the most closely matching descriptors (conditions) in a derived rule. Again, unlike Kant's notion of judgment, a reflective judgment is not the result of searching for a universal that pertains to a particular set of values of descriptors. Rather, a reflective judgment by an agent is a form of recognition that a particular vector of sensor values pertains to a particular rule in some degree. This recognition takes the form of an assertion that a particular descriptor vector is associated with a particular decision rule. These considerations can be repeated for other forms of classifiers besides those defined by decision rules.