On TL-fuzzy ideals and their L-fuzzy roughness in lattices

Abstract

In this paper, we study TL-fuzzy ideals of lattices.  First, using a left continuous t-norm T on a complete lattice L, we introduce the concept of TL-fuzzy ideals of lattices and study the corresponding relations between TL-fuzzy ideals of two homomorphic lattices and discuss the image and the inverse image of generated TL-fuzzy ideals.  Moreover, we consider the L-fuzzy roughness in lattices based on a complete residuated lattice, which is a generalization of (fuzzy) roughness in lattices.  And we study some related properties of TL-fuzzy ideals with respect to T-upper and θ-lower fuzzy rough approximations.