Journal of Algebraic Hyperstructures and Logical Algebras Volume 3, Number 2, (2022), pp. 1-15 Possibility operators over n-valued Gödel logic A. Figallo-Orellano 1 and J.S. Slagter 2 1,2 Departamento de Matemática, Universidad Nacional del Sur (UNS), Bahia Blanca, Argentina aldofgallo@gmail.com, juan.slagter@uns.edu.ar Abstract In the area of fuzzy logic, expansions of these logics by Δ operator have been intensively studied; the interest of Δ operator is due to the fact that it presents a fuzzy behav- ior, the associated systems were studied in propositional and frst-order level. On the other hand, the possibil- ity operators that defne Łukasiewicz-Moisil algebras have been studied over diferent classes of algebras; these op- erators are known as Moisil’s operators in the literature. One of these operators coincides with Δ, showing there are other operators with fuzzy behavior. In this paper, we present the study of Moisil’s operators over an exten- sion of a fuzzy logic; namely, n-valued Gödel logic, thus opening the possibility to explore more fuzzy operators. Article Information Corresponding Author: A. Figallo-Orellano; Received: April 2022; Accepted: Invited paper; Paper type: Original. Keywords: n-valued Gödel logic, Δ op- erator, Moisil operators, frst- order logics. A Title 1 Introduction Moisil introduced n-valued Łukasiewicz algebras or n-valued Łukasiewicz-Moisil algebras, see, for instance, [3]. Recall that the standard n-valued Łukasiewicz-Moisil algebras is defned by C n whose universe is {0, 1 n , 2 n , ··· , n − 1 n , 1}, endowed with the operations x ∧ y := min{x,y}, x ∨ y := max{x,y}, ∼ x := 1 − x and the operators σ i are defne as follows: σ i ( j n )= { 0 if i + j<n 1 if i + j ≥ n . https://doi.org/10.52547/HATEF.JAHLA.3.2.1