Soft quantization of the production's knowledgebases for multi-agent systems

In multi-agent systems, agents communicate using message on the BlackBoards, “White” and “Yellow” pages. It is assuming that the messages contain not only data, but also knowledge. The approaches to the knowledge quantization (soft knowledge coding) are considering in this article. We have proved the statements that allow you to perform isomorphic transformations for the classical additive fuzzy models, working in the field of real numbers, to their analogs able to function in the finite Galois fields also. The homeomorphism (topological isomorphism) considered fuzzy and neuro-fuzzy models. Given author's soft coding algorithm for knowledgebase. The existence of such isomorphic and homeomorphic transformations lead to the possibility of an adequate quantization the agent's knowledgebase, presented in the form of an additive fuzzy and neuro-fuzzy systems in both metric and topological spaces.