α—Fuzzy Relation Equations and Decomposable Fuzzy Relations
In this Ch., we investigate a new type of fuzzy relation equation defined on finite sets and with membership functions on a complete Brouwerian lattice. We characterize the entire set of the solutions when the fuzzy equation is assigned on a linear lattice. We also study when a fuzzy relation is pointwise decomposable in the intersection (resp. union) of two fuzzy sets and we show that such relations are max-min transitive (resp. compact). Finally, properties of convergence of powers of these fuzzy relations are established.
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