PROBABILITY OF FUZZY SET THEORY AND PROBABILITY AMPLITUDE OF QUANTUM NEURONS (SIMILARITIES AND PHYSICAL QUANTITIES OF QUANTUM NEURAL NETWORKS)

摘要

We have proposed the method of the neural network based on quantum theory (wave equation and path integrals) of polaritons, and made some relation's tools and descriptions for calculations for arbitrary neural circuits developed. The most important difference between the common (classical) neural network and quantum one existed in whether there were interferences between both systems. The quantum system had essentially many interferences' relationships in its system, and so its probability was related to the probability amplitude, wave functions and propagators, which were commonly complex functions. On the other hand, the classical probability never contained any interferences since it had in the real number field. And concretely we showed how those quantum methods, whose system contained much interference, were applied to the Bayes' theory, entropy of information theory, and the two-step neural network of multi channels. And we found that our quantum neural network and polariton's model were connected with the common quantum information theory, classical neural system and information theory, and quantum network contained many branches of soft science. Moreover, when we attempt to practice that calculation on classical fuzzy probability and quantum amplitude, we immediately find that fuzzy probability is equivalent to Choquet integral. However, we recognize the difference between Choquet integral and path integral. As Choquet integral is always real number, but quantum integral means complex number. Thus, Choquet integral has sometimes divergence of integral values in spite of finite integral value of quantum computation. Thus, we showed that our methods were related to various areas as applications of fuzzy controls, classical neural systems, the classical information theory and so on.