\(TL\)-filters of integral residuated \(l\)-monoids
The paper deals with a fuzzification of filters on integral residuated lattice-ordered monoids. Analogously to the crisp case, a description of the fuzzy filter generated by a fuzzy subset is given. Then the relation between fuzzy filters and homomorphisms in the underlying variety is discussed. In particular, an image of a fuzzy filter under a homomorphism is a fuzzy filter. The same is true also for preimages of fuzzy filters. Finally, it is shown that there is a correspondence between the set of fuzzy filters and the set of \(T\)-congruences. More precisely, it is proved that each fuzzy filter induces a \(T\)-congruence and vice versa.
scientific article; zbMATH DE number 5127727
scientific article