Some types of filters in BL algebras
Soft Computing - A Fusion of Foundations, Methodologies and Applications
Semi-divisible t-norms on discrete scales
Fuzzy Sets and Systems
States on semi-divisible residuated lattices
Soft Computing - A Fusion of Foundations, Methodologies and Applications - Special issue (pp 315-357) "Ordered structures in many-valued logic"
Soft Computing - A Fusion of Foundations, Methodologies and Applications
Fuzzy Sets and Systems
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The aim of this work is to introduce the concepts of IMTL-filters and strong MTL-filters in MTL-algebras and show that these filters are related to IMTL-algebras and strong MTL-algebras, respectively. We also introduce the concepts of EIMTL and associative filters in MTL-algebras. The relationships between these filters and quotient algebras that are constructed via these filters are described. We clarify that EIMTL, IMTL and fantastic filters coincide in BL-algebras, whereas they have different properties in MTL-algebras; moreover, the relations between them are delineated. We prove that strong filters include some current filters such as implicative, positive implicative and fantastic filters.