Static criteria for fuzzy systems quality evaluation

Abstract

In consensus research, it is necessary to find criteria to assign confidence factors to the knowledge-based systems involved in a consensus algorithm. Those factors must reflect the confidence that we can have on each system's assertions. A whole class of such criteria are static ones (we call them quality criteria), that is, criteria based on the structure of the systems more than on any performance measure.

In the present work, we propose, justify and formalize three static quality evaluation criteria for fuzzy systems: Completeness, Redundancy and Consistence. They are based on similar ones existing in classical logic, but they are generalized to the fuzzy domain. This is mainly done by making use of the subsethood theorem of Kosko's Set-as-Points framework, a very convenient way to assign geometric meaning to fuzzy sets.