Tolerance Spaces

In traditional approaches to knowledge representation, notions such as tolerance measures on data, distance between objects or individuals, and similarity measures between primitive and complex data structures such as properties and relations, elementary and complex descriptors, decision rules, information systems, and relational databases, are rarely considered. This is unfortunate because many complex systems which have knowledge representation components receive and process data which is incomplete, noisy, and uncertain. There is often a need to use tolerance and similarity measures in processes of data and knowledge abstraction. This is a particular problem in the area of cognitive robotics where data input by sensors has to be fused, filtered and integrated with more traditional qualitative knowledge structures. A great many levels of knowledge abstraction and data reduction must be used as one tries to integrate newly acquired data with existing data which has previously been abstracted and represented implicitly in the form of more qualitative data and knowledge structures.