A new approach to fuzzy reasoning

J. Weisbrod
1998 Soft Computing - A Fusion of Foundations, Methodologies and Applications  
Over the last years fuzzy control has become a very popular and successful control paradigm. The basic idea of fuzzy control is to incorporate human expert knowledge. This expert knowledge is speci ed in a rule based manner on a high and granular level of abstraction. By using vague predicates a fuzzy rule base neglects useless details and concentrates on important relations. Following L.A. Zadeh's famous principle of incompatibility, this technique is most promising when applied to large and
more » ... mplex problems. Nevertheless, nowadays most fuzzy rule bases are small and represent simple knowledge. From our point of view this surprising and somewhat disappointing observation is due to a major lack of understanding how to handle a fuzzy rule base. In this paper we present a new theory for fuzzy reasoning. This theory is twofold. In general, a fuzzy rule base is both partially inconsistent and partially incomplete. This is the price to pay for abstraction and granularization. We show, that if a fuzzy rule base maximizes consistency at the cost of completenes, the well known possibilistic approach to fuzzy inference is the right choice. For a fuzzy rule base, that maximizes completeness at the cost of consistency, we derive a new type of inference called {reasoning. Together, both mechanisms form an embracing theory for fuzzy reasoning in general. We propose a combined approach to be applied in order to manage complex rule bases.
doi:10.1007/s005000050037 fatcat:cm4jnorqxzbuvin67iwntce73m