Metamathematics Of Fuzzy Logic

This book presents a systematic treatment of deductive aspects and structuresof fuzzy logic understood as many valued logic emsui generisem. Some importantsyste... » 

This book presents a systematic treatment of deductive aspects and structuresof fuzzy logic understood as many valued logic emsui generisem. Some importantsystems of realvalued propositional and predicate calculus are defined andinvestigated. The aim is to show that fuzzy logic as a logic of imprecisevague propositions does have welldeveloped formal foundations and that mostthings usually named fuzzy inference can be naturally understood as logicaldeduction. br There are two main groups of intended readers. First logiciansthey can see that fuzzy logic is indeed a branch of logic and may find severalvery interesting open problems. Second equally important researchers involvedin fuzzy logic applications and soft computing. As a matter of fact most ofthese are not professional logicians so that it can easily happen that anapplication clever and successful as it may be is presented in a way which islogically not entirely correct or may appear simpleminded. Standardpresentations of the logical aspects of fuzzy controllers are the most typicalexample. This fact would not be very important if only the embon tonem oflogicians were harmed but it is the opinion of the author who is amathematical logician that a better understanding of the strictly logicalbasis of fuzzy logic in the usual broad sense is very useful for fuzzy logicappliers since if they know better what they are doing they may hope to do itbetter. In addition a better mutual understanding between classicallogicians and researchers in fuzzy logic promises to lead to deepercooperation and new results. br emAudienceem mathematicians logicianscomputer scientists specialists in artificial intelligence and knowledgeengineering developers of fuzzy logic. «