Filters of residuated lattices and triangle algebras |
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Authors: | B Van Gasse G Deschrijver EE Kerre |
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Affiliation: | Fuzziness and Uncertainty Modelling Research Unit, Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281 (S9), 9000 Gent, Belgium |
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Abstract: | 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. |
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Keywords: | Filters Interval-valued structures Residuated lattices |
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