This paper discusses a fundamental problem in the Analytic Hierarchy P
rocess of T.L. Saaty, vis. inverse inconsistency, previously addressed
only indirectly in the, literature. A mechanism for handling this is
suggested. More importantly, it is demonstrated how the problem is les
s significant in the Modified Analytic Hierarchy Process devised by Do
negan et al. The related problem of dependence upon the irrelevant alt
ernative is also examined and a list of statistically significant Rand
om Indexes for the modified process is presented.