n-fold filters in residuated lattice

TL;DR

This paper introduces various n-fold filters in residuated lattices, generalizing existing results in BL-algebras and exploring their interrelations and the structure of n-fold residuated lattices.

Contribution

It defines new n-fold filter concepts in residuated lattices and studies their relationships, extending prior work in BL-algebras and related structures.

Findings

Defined n-fold implicative, positive implicative, boolean, fantastic, normal, and obstinate filters.

Established relations among these n-fold filters.

Presented diagrams illustrating the relationships between filter types and residuated lattices.

Abstract

Residuated lattices play an important role in the study of fuzzy logic based of t-norm. In this paper, we introduced the notions of n-fold implicative filters, n-fold positive implicative filters, n-fold boolean filters, n-fold fantastic filters, n-fold normal filters and n-fold obstinate filters in residuated lattices and study the relations among them. This generalized the similar existing results in BL-algebra with the connection of the work of Kerre and all in [14], Kondo and all in [7], [11] and Motamed and all in [9]. At the end of this paper, we draw two diagrams; the first one describe the relations between some type of n-fold filters in residuated lattices and the second one describe the relations between some type of n-fold residuated lattices.