Nonstandard conjunctions and implications in fuzzy logic

János C. Fodor, Tibor Keresztfalvi
1995 International Journal of Approximate Reasoning  
We 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
more » ... classes of nonstandard conjunctions and implications are formulated so that all of them satisfy the proposed axioms.
doi:10.1016/0888-613x(94)00012-r fatcat:gnx645obordbni3zxodv6lpg3i