Some properties of L-fuzzy approximation spaces based on bounded integral residuated lattices

Notes on “Some Properties of <i>L</i>-fuzzy Approximation Spaces on Bounded Integral Residuated Lattices”

“…This result shows that the reflexive and transitive L-relations Thus, by Definition 1.3 and Theorem 4.1(3) in [12], we see that…”

“…In this note, we continue the works in [12]. For a complete involutive residuated lattice, we have supplemented some properties of the L-fuzzy topologies generated by a reflexive and transitive L-relation; showed that the L-fuzzy topologies generated by a reflexive and transitive L-relation satisfy (TC) L or (TC) R axioms; and given out some conditions such that the L-fuzzy topologies generated by two L-relations, which are induced by an L-fuzzy topology, are all the original L-fuzzy topology.…”

The Lattice Structures of Approximation Operators Based on L‐Fuzzy Generalized Neighborhood Systems

“…Particularly, fuzzy rough set theory is an important branch, which can handle more complicated uncertain problems since it has the advantages of both fuzzy set and rough set [22,[32][33][34][35][36][37][38]. Furthermore, replacing the unit interval [0, 1] with a complete lattice L as the range of the membership function [39], the more general L-fuzzy rough sets further extend the theoretical framework and application range of classic rough sets [31,[40][41][42][43][44][45][46]. Fuzzy rough sets have a variety of forms due to the different approaches of fuzzification.…”

Congruences and the discrete Sugeno integrals on bounded distributive lattices

“…This is especially important in domains, where the essential information is either not available, or superfluous, and only the ordinal relationships are of interest. We can mention several recent papers devoted to a deeper study of lattice-based data see, e.g., [6,22]. Aggregation on bounded lattices belongs to basic tools of lattice-based data, and thus a deeper development of aggregation on lattices is an important and hot topic.…”