Fuzzy sets and applications
Fuzzy ideals on a distributive lattice
Fuzzy Sets and Systems
Information Sciences—Intelligent Systems: An International Journal
Fuzzy sets and fuzzy logic: theory and applications
Fuzzy sets and fuzzy logic: theory and applications
The lattices of fuzzy ideals of a ring
Fuzzy Sets and Systems
Partially ordered and relational valued fuzzy relations I
Fuzzy Sets and Systems - Special issue on fuzzy relations, part 1
Fuzzy Sets and Systems: Theory and Applications
Fuzzy Sets and Systems: Theory and Applications
| Hi-index | 0.00 |
The features of fuzzy lattices valued by lattices can be observed in the light of more general results from fuzzy algebraic and fuzzy relational structures. By approaching directly the problem of defining the notion of a fuzzy lattice, several directions can be taken. In this paper we present an idea and two of its variations to define what is referred to as LM fuzzy lattices. The idea is to fuzzify the membership functions of elements of the carrier of an ordinary, crisp, lattice. L1M fuzzy lattices require for the cuts of the structure to be sublattices of the lattice whose carrier's membership function has been the subject of fuzzification. More generally, L2M fuzzy lattices require that the cuts are lattices themselves, not insisting on being substructures of the crisp lattice. The structure of the families of cuts in both cases are presented, as well as an algorithm to construct LM fuzzy lattice with a given set of cuts. Alternative approaches to defining fuzzy lattices are discussed at the end of the paper.