The concept of Fuzzy set was opened up a new horizon in Mathematical Sciences.In fuzzy set theory, a fuzzy set which assigns to each object a grade of membership ranking between 0 and 1. This single value combines both evidence and nonevidence without indicating howmuch there is of each. But it is felt by several decission makers and researchers that proper decission making the evidence and non evidence both necessary.To counter this problem, the vague set theory is introduced which it has both the grade of membership and grade of nonmembership functions and these are generalization of fuzzy...