Nonstandard conjunctions and implications in fuzzy logic

AbstractWe point out possible disadvantages of considering exclusively t-norms and t-conorms as proper models for conjunction and disjunction in fuzzy logic. We draw up a general framework for particular investigations, expressed by the so-called closure property. We suggest a constructive approach to the axiomatics of generalized modus ponens (GMP). As a consequence, a system of functional equations is obtained. Idempotent as well as nonidempotent conjunctions fulfilling this system are studied. Three classes of nonstandard conjunctions and implications are formulated so that all of them satisfy the proposed axioms