Abstract and concrete categories
Abstract and concrete categories
On relationship between modified sets, topological spaces and rough sets
Fuzzy Sets and Systems
Relational interpretations of neighborhood operators and rough set approximation operators
Information Sciences—Informatics and Computer Science: An International Journal
Applying modifiers to knowledge acquisition
Information Sciences—Informatics and Computer Science: An International Journal - Special issue computing with words
On the structure of rough approximations
Fundamenta Informaticae
Completion of ordered structures by cuts of fuzzy sets: an overview
Fuzzy Sets and Systems - Logic and algebra
Representing ordered structures by fuzzy sets: an overview
Fuzzy Sets and Systems - Logic and algebra
Modal-Like Operators in Boolean Lattices, Galois Connections and Fixed Points
Fundamenta Informaticae
Set Operations for L-Fuzzy Sets
RSEISP '07 Proceedings of the international conference on Rough Sets and Intelligent Systems Paradigms
Logics from Galois connections
International Journal of Approximate Reasoning
Topology vs generalized rough sets
International Journal of Approximate Reasoning
The relationship between L-fuzzy rough set and L-topology
Fuzzy Sets and Systems
Approximation of sets based on partial covering
Theoretical Computer Science
| Hi-index | 0.21 |
The paper presents the essential connections between modal-like operators, topologies and fuzzy sets. We show, for example, that each fuzzy set determines a preorder and an Alexandrov topology, and that similar correspondences hold also for the other direction. Further, a category for preorder-based fuzzy sets is defined, and it is shown that its equivalent subcategory of representatives is isomorphic to the categories of preordered sets and Alexandrov spaces. Moreover, joins, meets and complements for the objects in this category of representatives are determined. This suggests how to define for fuzzy subsets of a certain universe the lattice operations in a canonical way.