Hyper Lattice Implication Algebras and Some of Their Characterizations

Abstract

In this paper, we introduce the concept of hyper lattice implication algebras which is established by combining the concept of hyper lattices and hyper implication algebras. We give some important examples of hyper lattice implication algebras and obtain some of their properties. Then, we characterize hyper lattice implication algebras in which 1 is an implication scalar element. We prove that the implication reduction of hyper lattice implication algebras is a regular commutative fuzzy implication algebra, if 1 is an implication scalar element. Finally, we define the notion of isomorphisms between two hyper lattice implication algebras and obtain all of the hyper lattice implication algebras of order 2.