Smarandache defined the notion of neutrosophic topology on the non-standard interval [13, 14, 18, 19, 20].
The concepts of the upper and lower pre-continuous multifunctions was introduced in .In this paper we introduce and study the neutrosophic version of upper and lower pre-continuous multifunctions.
In , Salama presented the principle of Neutrosophic Set (NS) and mathematical theory, to define any situation by a ternary crisp build.
Designing a neutrosophic IDS is a proper solution in handling vague circumstances.
The concept of 'Neutrosophic logic' was developed by Prof.
The neutrosophic set A on the universal set [zeta] categorized into three membership functions called the true membership function [T.sub.A](x), indeterminate membership function[I.sub.A](x) and false membership function[F.sub.A](x) contained in real standard or non-standard subset of ]-0, [1.sup.+][ respectively and satisfy the following condition
Thamaraiselvi and Santhi  pointed out that neutrosophic set , one of the extensions of fuzzy set, is used in different research areas.
Since neutrosophic transportation problems are new area of research, others may be attracted to extend these approaches for solving other types of neutrosophic transportation problems like neutrosophic solid transportation problems, neutrosophic time minimization transportation problems, neutrosophic transshipment problems, and so on.
To express indeterminate and inconsistent information which exists in real world, Smarandache  originally proposed the concept of the neutrosophic
set from a philosophical point of view.
More general is the Neutrosophic
Logic [Smarandache, 1995], where the truth (T) and the falsity (F) and the indeterminacy (1) can be any numbers in [0, 1], then 0 [less than or equal to] T + I + F [less than or equal to] 3.
set is a powerful general formal framework which generalizes the concept of the classic set, fuzzy set , Vague set  etc.
We first define the notion of Smarandache pseudo neutrosophic