An approach toward defining L-fuzzy lattices

• Published in: 1998 Conference of the North American Fuzzy Information Processing Society - NAFIPS (Cat. No.98TH8353) pp. 221 - 225
• Main Author: Trajkovski, G.
• Format: Conference Proceeding
• Language: English
• Published: IEEE 1998
• Subjects: Absorption; Algebra; Fuzzy sets; Lattices; Level set; Physics; Topology
• ISBN: 9780780344532; 0780344537
• DOI: 10.1109/NAFIPS.1998.715569

The paper deals with one possible approach that can be used in the process of defining lattice valued fuzzy lattice (L-fuzzy lattice). The idea of fuzzification of the ordering of a crisp lattice to obtain a weakly reflexive lattice valued ordering relation is developed in order to obtain a structure whose level sets are crisp lattices. At this point, two different treatments of the problem can be effectuated, and therefore two definitions of L-fuzzy lattices can be offered. The theorems for synthesis of those structures are also given, as well as an illustrating example.