Closure properties for fuzzy recursively enumerable languages and fuzzy recursive languages

Article type: Research Article

Authors: Silva Farias, Antonio Diego^{a; b; *} | de Araújo Lopes, Luiz Ranyer^b | Bedregal, Benjamín^b | Santiago, Regivan H.N.^b

Affiliations: [a] Federal Rural University of Semi-Arid – UFERSA, Universitary Campus of Pau dos Ferros, São Geraldo, Pau dos Ferros, RN, Brazil | [b] Department of Informatics and Applied Mathematics – DIMAp, Federal University of Rio Grande do Norte – UFRN, Universitary Campus of Lagoa Nova, Natal, RN, Brazil

Correspondence: [*] Corresponding author. Antonio Diego Silva Farias. Tel.: +55 84 99939 9065; E-mail: antonio.diego@ufersa.edu.br.

Abstract: There are several variations of fuzzy Turing machines in the literature, many of them require a t-norm in order to establish their accepted language. This paper generalize the concept of non-deterministic fuzzy Turing machine - NTFM, replacing the t-norm operator for several aggregation functions. We establish the languages accepted by these machines, called fuzzy recursively enumerable languages or simply LFRE and show, among other results, which classes of LFRE are closed under unions and intersections.

Keywords: Turing machines, fuzzy turing machines, fuzzy languages, aggregation functions

DOI: 10.3233/JIFS-152489

Journal: Journal of Intelligent & Fuzzy Systems, vol. 31, no. 3, pp. 1795-1806, 2016