Possibility operators over n-valued Gödel logic

Abstract

In the area of fuzzy logic, expansions of these logics by $\Delta$ operator have been intensively studied; the interest of $\Delta$ operator is due to the fact that it presents a fuzzy behavior, the associated systems were studied in propositional and first-order level. On the other hand, the possibility operators that define Łukasiewicz-Moisil algebras have been studied over different classes of algebras; these operators are known as Moisil's operators in the literature. One of these operators coincides with $\Delta$, showing there are other operators with fuzzy behavior. In this paper, we present the study of Moisil's operators over an extension of a fuzzy logic; namely, n-valued Gödel logic, thus opening the possibility to explore more fuzzy operators.