Incorporating a Discrete Renewal Random Sum in Computational Intelligence and Cindynics

Abstract

The paper concentrates on the formulation and stochastic derivation of a renewal random sum of discrete, independent and identically distributed random variables. An interpretation of the formulated discrete renewal random sum in the discipline of computational intelligence is also established. Moreover, it is shown that such an interpretation can contribute to the investigation of the evolution of a complex system going through a crisis arising from the occurrences of a major risk. The paper makes use of generalization, discovery, association, abstraction which constitute the fundamental characteristics of the discipline of computational intelligence and the mathematical structure of a wide class of discrete random sums, taking values in the set of nonnegative integers, in order to provide analysts and decision makers with strong analytical tools for supporting intelligence behaviour of complex systems in the environment of a major risk. The results of the paper makes clear the significance to undertake new research activities for formulating and interpreting classes of random sums as particularly useful analytical tools of computational intelligence with interesting practical applications in significant areas of the new discipline of cindynics.