On characterizations of -fuzzy rough approximation operators

Implicator-Conjunctor Based Models of Fuzzy Rough Sets: Definitions and Properties

“…Some authors [8,15,18] actually require lower semicontintuity of T instead of left-continuity, but by a result from [21] these two notions are equivalent for t-norms. Also, some papers [10,11,13,17] consider fuzzy relations from U to W , with both U and W non-empty, finite universes, but here we restrict ourselves to the case U = W . As can be seen, Wu et al [10] were the first to consider general binary fuzzy relations, while Mi and Zhang [11] initiated the use of conjunctors that are not necessarily t-norms.…”

“…As our starting point, we use the axiomatic approach developed by Wu et al [13], who propose axioms to characterise lower and upper approximations, which are generalized here for an implicator-conjunctor pair.…”

“…This idea sparked the seminal proposal in [3], and since then many papers [8][9][10][11][12][13][14][15][16][17][18] have focused on the refinement of this model using both constructive approaches, which propose new definitions of approximation operators, and axiomatic approaches, which set forth a set of axioms or desirable properties, and characterize the operators that satisfy them.…”

“…[19,20]. For all of these reasons, several other authors considered fuzzy rough set models based on general fuzzy relations [10][11][12][13][14][15]17].…”

“…In Section 4, we evaluate the model w.r.t. desirable properties, while in Section 5, we refine the axiomatic approach of Wu et al [13], weakening some of its conditions and proposing an alternative characterization that caters specifically to residual implications. Finally, in Section 6, we conclude and outline future work.…”