Filters of residuated lattices and triangle algebras

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. Key words: filters, interval-valued structures, residuated lattices 1991 MSC: 03B45, 03B47, 03B50, 03B52, 06F05, 08A72

• Type: Journal
• Year: 2010
• Where: ISCI
• Authors: Bart Van Gasse, Glad Deschrijver, Chris Cornelis, Etienne E. Kerre
• Keywords: Congruence Relations, Formal Fuzzy Logic, ISCI 2010, Lattices 1991 Msc