Hyper Lattice Implication Algebras and Some of Their Characterizations
Shokoofeh Ghorbani · DergiPark (Istanbul University) · 2017
In this paper, we introduce the concept of hyper lattice implication algebras which is establishedby combining the concept of hyper lattices and hyper implication algebras. We give some important examplesof hyper lattice implication algebras and obtain some of their properties. Then, we characterize hyper latticeimplication algebras in which 1 is an implication scalar element. We prove that the implication reduction ofhyper lattice implication algebras is a regular commutative fuzzy implication algebra, if 1 is an implicationscalar element. Finally, we define the notion of isomorphisms between two hyper lattice implication algebrasand obtain all of the hyper lattice implication algebras of order 2.