Abstract
A general theory of algebraic fuzzy systems is developed by introducing the notion of a fuzzy L -subset, corresponding to a set L of subsets of a nonempty set X assuming truth values in a complete Brouwerian lattice. It is observed that the set FL of all fuzzy L -subsets of X is a closure (algebraic closure) fuzzy set system if and only if L is a closure (algebraic closure) set system on X . A fuzzy L -subset generated by a fuzzy subset is described. Modularity and distributivity of the complete lattices L and FL are discussed. A method to construct fuzzy L -subsets from certain family of members of L is established. Certain applications of the general theory are mentioned.
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