Fuzzy homomorphisms of rings (Q1187450)

The authors start with a new definition of the concepts: fuzzy function, fuzzy surjective function and fuzzy injective function. The relations between these new concepts and the ones introduced by \textit{C. V. Negoiţă} and \textit{D. A. Ralescu} [Applications of fuzzy sets to systems analysis (1975; Zbl 0326.94002)] are not outlined. The composition of fuzzy functions is defined in accordance to the definition of composition of fuzzy relations. A fuzzy homomorphism between two rings is then defined as a fuzzy function satisfying some compatibility conditions with the ring operations. Based on these notions the authors find some fuzzifications of important classical theorems among them the fundamental theorems of fuzzy homomorphisms and some theorems related to a fuzzy ideal of a ring.