Algebraic fuzzy systems (Q809113)

Since Goguen and Rosenfeld, respectively, proposed L-fuzzy sets (1967) and fuzzy groups (1971), some scholars developed these structures and suggested a lot of new ideas. Here, a general theory of algebraic fuzzy systems is discussed, based on the notion of a fuzzy \({\mathcal S}\)-subset, which is the basic idea of this paper, corresponding to the class \({\mathcal S}\) of subsets of a nonempty set X assuming truth values in a complete Brouwerian lattice. I feel that this work is interesting as it gives a reasonable frame for algebraic fuzzy systems. Of course, this paper gives some important results, for example, all fuzzy \({\mathcal S}\)-subsets of X form a closure fuzzy set system on X iff \({\mathcal S}\) is a closure set system on X.