An often raised objection to fuzzy logic can be articulated as follows. Fuzzy sets are intended to represent vague collections of objects. On the one hand, boundaries of such collections are inherently imprecise. On the other hand, fuzzy sets are defined by membership degrees which are precise. There is, therefore, an obvious discrepancy between the imprecision of a collection and the precision...

Some difficulties emerging during the construction of fuzzy rule bases are inherited from the type of the applied fuzzy reasoning. In fuzzy systems, when classical methods (e.g. the Compositional Rule of Inference) are applied, the completeness of the fuzzy rule base is required to generate meaningful output. This means, that the fuzzy rule base has to cover all possible inputs. The way of buil...

F TP (Fuzzy Template Predicate) is proposed as a template to incorporate concept-based match into fuzzy production languages. A thesaurus augmented in F TP supports the concept-based match, which is more sophisticated than previous fuzzy match mechanisms. Membership functions for fuzzy linguistic variables and fuzzy numbers are used as an interface to the thesaurus. F TP also has self reening f...

Many compilers, synthesizers, and theorem provers rely on rewrite rules to simplify expressions or prove equivalences. Developing can be difficult: may subtly incorrect, profitable are easy miss, rulesets must rechecked extended whenever semantics tweaked. Large also challenging apply: redundant slow down rule-based search frustrate debugging. This paper explores how equality saturation, a prom...

Current theories of relational learning on structure mapping emphasize the importance of compositional representations, based on the concept’s components and the relations among them. We consider the possibility that relational concepts can also be represented unitarily, whereby the concept is a property of the stimulus as a whole. The distinction between compositional and unitary representatio...

If the given fact for an antecedent in a fuzzy production rule (FPR) does not match exactly with the antecedent of the rule, the consequent can still be drawn by technique such as fuzzy reasoning. Many existing fuzzy reasoning methods are based on Zadeh’s Compositional rule of Inference (CRI) which requires setting up a fuzzy relation between the antecedent and the consequent part. There are so...