Semantics for Fuzzy Disjunctive Programs with Weak Similarity
Dušan Guller · 2002
In the paper, we present declarative, model, and fixpoint semantics for fuzzy disjunctive programs with weak similarity — sets of graded strong literal disjunctions. We shall suppose that truth values (degrees) constitute a regular residuated lattice L = (L, ≤, *, ⇒, ∪, ∩, 0, 1). A graded strong literal disjunction will be viewed as a pair (d, c) where d is a formula of the form ¬(d 1 & … & d n ), i.e. a negation of a strong conjunction of literals d i ; and c is a truth value belonging to the lattice L. A graded literal disjunction can be understood as a means of representation of incomplete and imprecise information, where the incompleteness is formalised by its strong literal disjunction (a negation of a strong conjunction of literals), while the impreciseness by its truth degree. Such programs may contain the binary predicate symbol for weak similarity, denoted as ∼, which is the fuzzy counterpart of the ‘classical’ equality.