Abstract
Although Qiao and Hu intended to propose granular variable precision L-fuzzy rough sets based on residuated lattices, L actually denotes a doubly residuated lattice with an involutive negation. However, there exist doubly residuated lattices without involutive negations. This paper presents a comparative study of variable precision fuzzy rough sets based on residuated lattices, in which we compare variable precision L-fuzzy rough sets with the preexisting models. A variable precision upper L-fuzzy rough approximation operator is proposed with L-fuzzy granules based on L-fuzzy implication on a residuated lattice L instead of a doubly residuated lattice. The variable precision upper L-fuzzy rough approximation operator is investigated with respect to different L-fuzzy relations regardless of proposing an involutive negation on a residuated lattice.
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