The computation and application of random consistency index

Analytic hierarchy process (AHP) is a method frequently used in mathematical modeling. Its consistency must be tested, after the positive reciprocal matrix of paired comparison is constructed. The formal test results of random consistency indices were of lower order. In practical application, for various factors are often involved, the computation of the test results of random indices of higher order is often complicated. Using Matlab software, we resolved the problem that positive reciprocal Matrix of any order be generated at random, thus we solved the problem that how to calculate random consistency index of high-order the better. The method is also applied to “the mathematical modeling of coal-mining safety alarm system”, with ideal results.