Number-free Mathematics Based on T-norm Fuzzy Logic

Abstract--The paper presents a form of rendering classical mathematical notions by formal theories over suitable t-norm fuzzy logics in such a way that references to real numbers are eliminated from definitions and theorems, being removed to the standard semantics of fuzzy logic. Several examples demonstrate how this move conceptually simplifies the theory in exchange for non-classical reasoning, facilitates certain generalizations, and puts the concepts into a different perspective. The formal framework employed for the number-free formalization of mathematical concepts is that of higher-order fuzzy logic, also known as Fuzzy Class Theory. Keywords--Continuity, Fuzzy Class Theory, limit, metric, realvalued function, similarity.

• Type: Journal
• Year: 2009
• Where: EUSFLAT
• Authors: Libor Behounek
• Keywords: EUSFLAT 2009, Fuzzy Class Theory, Fuzzy Logic, T-norm Fuzzy Logics