L-fuzzy lattices: An introduction

Abstract

The paper introduces lattice-valued fuzzy lattices. Two types of L-fuzzy lattices are defined, and their connection is observed. The first type of fuzzy lattices is obtained via fuzzification of the membership to the carrier, and the second via fuzzification of the ordering relation in a crisp lattice. It is proved that the two approaches are equivalent, similarly as in the crisp lattice theory.