Information Sciences: an International Journal
Boolean filters and positive implicative filters of residuated lattices
Information Sciences: an International Journal
Triangle algebras: A formal logic approach to interval-valued residuated lattices
Fuzzy Sets and Systems
Fuzzy filters and fuzzy prime filters of bounded Rl-monoids and pseudo BL-algebras
Information Sciences: an International Journal
A characterization of interval-valued residuated lattices
International Journal of Approximate Reasoning
The pseudo-linear semantics of interval-valued fuzzy logics
Information Sciences: an International Journal
Advances and challenges in interval-valued fuzzy logic
Fuzzy Sets and Systems
Information Sciences: an International Journal
Mathematical fuzzy logic as a tool for the treatment of vague information
Information Sciences: an International Journal
Pseudo-BCK algebras as partial algebras
Information Sciences: an International Journal
On fuzzy filters of pseudo BL-algebras
Fuzzy Sets and Systems
Fuzzy Sets and Systems
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An important concept in the theory of residuated lattices and other algebraic structures used for formal fuzzy logic, is that of a filter. Filters can be used, amongst others, to define congruence relations. Specific kinds of filters include Boolean filters and prime filters. In this paper, we define several different filters of residuated lattices and triangle algebras and examine their mutual dependencies and connections. Triangle algebras characterize interval-valued residuated lattices.