An extension of some results on the degree of progress to goal in self-organization process

In this paper, we establish some results for the degree of progress to goal at any stage during a self-organization process by considering several self-organizing systems with their corresponding distance functions, gk (t), k = 1, 2, …, s. We employ some properties of curve as well as the convex combination of the distance functions to determine the degree of progress to goal at any stage of the resulting self-organization process. The probability of reaching the goal at any stage of the resulting self-organization process is considered as its degree or level of progress to goal during this process.

The results obtained are in agreement with the axiomatic properties of probability.