Logical structure of fuzzy IF-THEN rules
This paper provides a logical basis for manipulation withfuzzy IF-THEN rules. Our theory is wide enough and it encompasses not only finding a conclusion by means of the compositional rule of inference due to Lotfi A. Zadeh but also other kinds of approximate reasoning methods, e.g., perception-based deduction, provided that there exists a possibility to characterize them within a formal logical system. In contrast with other approaches employing variants of multiple-valuedfirst-order logic, the approach presented here employsfuzzy type theory of V. Novdk which has sufficient expressive power to present the essential concepts and results in a compact, elegant and justifiable form. Within the effectively formalized representation developed here, based on a complete logical system, it is possible to reconstruct numerous well-known properties of CRI-related fuzzy inference methods, albeit not from the analytic point of view as usually presented, but as formal derivations of the logical system employed. The authors are confident that eventually all relevant knowledge about fuzzy inference methods based on fuzzy IF-THEN rule bases will be represented, formalized and backed up by proof within the well-founded logical representation presented here. An immediate positive consequence of this approach is that suddenly all elements of a fuzzy inference method based on fuzzy IF-THEN rules are 'first class citizeng of the representation: there are clear, logically founded definitions for fuzzy IF-THEN rule bases to be consistent, complete, or independent. (c) 2006 Elsevier B.V. All rights reserved.
fuzzy if-then rules compositional rule of inference type theory fuzzy logic fuzzy relation equations fuzzy type theory