There are three properties of relation,
1. Reflexive
2. Symmetric
3. Transitive
and if all properties are satisfy by a relation then its known as Equivalence. Now if the relation is reflexive + anti-symmetric + transition then its known as Partial Order Relation.. My question is that is there a relation like, when irreflexive + anti-symmetric + anti-transitive (don't know if its exist, means the negation of transitive) then what we call it ?
No there is no such thing as anti-transitive. You might define it as xRy∧yRz⇒¬xRz, but it wouldn't be a very interesting property. The negation of transitive xRy∧yRz⇏xRz, which just says the relation is not transitive, would be even less interesting. Note that for instance anti-symmetric is not the negation of symmetric either (By Marc van Leeuwen)