Classification of Ordered Semigroups Through Neutrosophic Generalized bi-ideals with Applications

Abstract

An icebreaking theory known as neutrosophic theory opened a new direction for researchers of philosophy, logics, set theory and probability/statistics. Neutrosophy put the point base for a entire household of new mathematical speculations that summarized classical and fuzzy correspondence theories. In this article, we introduced the conception of neutrosophic fuzzy ideal theory of ordered semigroups based on belongs to relation and quasi-coincident with relation. Particularly, neutrosophic fuzzy generalized bi-ideal (resp. bi-ideal) of type (∈, ∈ ∨q) have been developed and detail symposium on multi-dimension of the neutrosophic said ideals in ordered semigroup has given. Further, a verity of depictions of ordered semigroups in expression of (∈, ∈ ∨q)- fuzzy generalized bi-ideals have been constructed and several related examples have been formulated. Finally, the lower parts of neutrosophic (∈, ∈ ∨q)-fuzzy generalized bi-ideals were proposed and ordered semigroups have been discussed by the properties of these newly developed neutrosophic fuzzy generalized bi-ideals