The concept of lattice plays a significant role in mathematics and other domains where order properties play an important role. In fact, a Boolean algebra, which is a special case of a Lattice, is of fundamental importance in Computer science. The notion of Fuzzy sets as an extension of Crisp sets is a model to handle uncertainty in data. Following it, the notions of fuzzy lattices have been introduced by many researchers [1, 11]. One of the approaches is the introduction of a fuzzy partially ordered relation on a crisp set which satisfies the lattice property. Intuitionistic fuzzy sets [2] are generalisations of the notion of fuzzy sets. So far the notion of Intuitionistic fuzzy lattices has neither been introduced nor studied. In this paper, we introduce the notions of intuitionistic fuzzy lattices, intuitionistic fuzzy Boolean algebra and study their properties. In this process, we provide an alternate definition of antisymmetric property of intuitionistic fuzzy relations and compare it with the existing ones.
展开▼
