Neutrosophic Vague Binary BCK/BCI-algebra

Abstract

Ineradicable hindrances of the existing mathematical models widespread from
probabilities to soft sets. These difficulties made up way for the opening of “neutrosophic set
model’. Set theory of ‘vague’ values is an already established branch of mathematics. Complex
situations which arose in problem solving, demanded more accurate models. As a result,
‘neutrosophic vague’ came into screen. At present, research works in this area are very few. But it
is on the way of its moves. Algebra and topology are well connected, as algebra and geometry.
So, anything related to geometric topology is equally important in algebraic topology too. Separate
growth of algebra and topology will slow down the development of each branch. And in one sense
it is imperfect! In this paper a new algebraic structure, BCK/BCI is developed for ‘neutrosophic’ and
to ‘neutrosophic vague’ concept with ‘single’ and ‘double’ universe. It’s sub-algebra, different kinds
of ideals and cuts are developed in this paper with suitable examples where necessary. Several
theorems connected to this are also got verified.