Fuzzy information relations and operators: An algebraic approach based on residuated lattices. (English) Zbl 1177.68211
de Swart, Harrie (ed.) et al., Theory and applications of relational structures as knowledge instruments II. International workshops of COST Action 274, TARSKI, 2002–2005. Selected revised papers. Berlin: Springer (ISBN 978-3-540-69223-2/pbk). Lecture Notes in Computer Science 4342. Lecture Notes in Artificial Intelligence, 162-184 (2006).
Summary: We discuss fuzzy generalisations of information relations taking two classes of residuated lattices as basic algebraic structures. More precisely, we consider commutative and integral residuated lattices and extended residuated lattices defined by enriching the signature of residuated lattices by an antitone involution corresponding to the De Morgan negation. We show that some inadequacies in representation occur when residuated lattices are taken as a basis. These inadequacies, in turn, are avoided when an extended residuated lattice constitutes the basic structure. We also define several fuzzy information operators and show characterizations of some binary fuzzy relations using these operators.
For the entire collection see [Zbl 1151.68001].
For the entire collection see [Zbl 1151.68001].
MSC:
| 68T30 | Knowledge representation |
| 03E72 | Theory of fuzzy sets, etc. |
| 06F05 | Ordered semigroups and monoids |
