TOLERANT FUZZY PATTERN MATCHING : AN INTRODUCTION

The fuzzy pattern matching technique has been developed in the framework of fuzzy set and possibility theory in order to take into account the imprecision and the uncertainty pervading values which have to be compared to requirements (which may be fuzzy) in a pattern matching process. This paper restates the basic principles and extends them to situations where (sub)patterns are only required to be satisfied up to a given tolerance (which may be fuzzy), or where the different subparts of a compound pattern may have various levels of importance. Both cases correspond to a weakening of elementary patterns. which can be expressed by a fuzzy relations modelling an approximate equality or an uncertain strict equality respectively. We also study the more sophisticated case where some elementary patterns have not to be satisfied with the highest priority provided that weaker requirements remain satisfied. The fuzzy pattern matching technique applies in a variety of problems including the evaluation of soft queries with respect to a fuzzy database, the evaluation of the fuzzy condition parts of rules in approximate reasoning, or the evaluation of the belonging of an ill-known object to a flexible class in classification problems.