Hyper Lattice Implication Algebras and Some of Their Characterizations

Year 2017, Volume: 14 Issue: 1, - , 01.05.2017

Shokoofeh Ghorbani

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.

Keywords

Hyper lattice implication algebra, implication scalar element, fuzzy implication algebra, isomorphism

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