Folding Theory Applied to Residuated Lattices

Residuated lattices play an important role in the study of fuzzy logic based on -norms. In this paper, we introduce some notions of -fold filters in residuated lattices, study the relations among them, and compare them with prime, maximal and primary, filters. This work generalizes existing results in BL-algebras and residuated lattices, most notably the works of Lele et al., Motamed et al., Haveski et al., Borzooei et al., Van Gasse et al., Kondo et al., Turunen et al., and Borumand Saeid et al., we draw diagrams summarizing the relations between different types of -fold filters and -fold residuated lattices.