The paradigm of complex probability and Claude Shannon’s information theory - Abdo Abou Jaoude (Systems Science & Control Engineering, 2017)
Andrey Kolmogorov put forward in 1933 the five fundamental axioms of classical probability theory. The original idea in my complex probability paradigm is to add new imaginary dimensions to the experiment real dimensions which will make the work in the complex probability set totally predictable and with a probability permanently equal to one. Therefore, adding to the real set of probabilities $ {\sc{R}} $ the contributions of the imaginary set of probabilities $ \sc{M} $ will make the event in $ \sc{C}= \sc{R} + \sc{M} $ absolutely deterministic. It is of great importance that stochastic systems become totally predictable since we will be perfectly knowledgeable to foretell the outcome of all random events that occur in nature. Hence, my purpose here is to link my complex probability paradigm to Claude Shannon’s information theory that was originally proposed in 1948. Consequently, by calculating the parameters of the new prognostic model, we will be able to determine the magnitude of the chaotic factor, the degree of our knowledge, the complex probability, the self-information functions, the message entropies, and the channel capacities in the probability sets $ \sc{R} $ and $ \sc{M} $ and $ \sc{C} $ and which are all functions of the message real probability subject to chaos and random effects.