On the evaluation of the degree of progress to goal in a multi-purpose self-organization process

M. O. Olatinwo, A. G. Adeagbo-Sheikh

In this paper, we establish a result on the degree of progress to goal for a multi-purpose self-organization process. Our method of presentation is based on the convex combination of the various distance functions of the different self-organizing systems involved, the notions of the convexity of functions, triangle inequality, trace of a matrix, elementary idea of probability theory as well as the concept of regular curves. Just as in Olatinwo [8,9,10], the transition probabilities at various time intervals (including initial and final times) are also evaluated here, and then subsequently interpreted as the degrees of progress to goal at such time intervals. Our result, as usual, is in agreement with the axiomatic properties of probability and it is a generalization of Theorem 2A of Olatinwo [8], Theorem 1 of Olatinwo [9] and Theorem 1 of Olatinwo [10].