On Closure Operators in Fuzzy Algebras and Fuzzy Deductive Systems

Abstract

The starting point of this paper is the classical wellknown theorem due to G. BIRKHOFF,P.HALL,andJ.SCHMIDT which establishes a one-to-one correspondence between compact closure operators, inductive closure operators, inductive closure systems, and closure operators generated in universal algebras (and generated in deductive systems, respectively). In the paper presented we make first steps in order to generalize this important theorem to the fuzzy set theory and fuzzy algebra (and fuzzy deductive systems, respectively).