Geometry of risk analysis (morphogenetic system)

Abstract

We know that risk analysis is based on the estimation of catastrophic events. Now to obtain a good estimation we must create suitable model of the risk. With samples of data we can use different mathematical models as linear or non linear regression methods, neural network methods, genetic methods and more recent hybrid models consisting of the information diffusion approximate reasoning method and back propagation neural network. In this paper, we present a new frame-work denoted morphogenetic system to study risk analysis. We show that morphogenetic system is a generalization of the tensor calculus used to formalize the non Euclidean geometrical representation. Now, we take suggestion from the electrical circuit analysis to create the morphogenetic model for the estimation. In the electrical circuit, we have the vector of voltages and vector of currents. The relation between voltages and currents is given by Ohms rule and the impedance matrix. The relation is a multi input and multi output (MIMO) system given a set of samples for voltages and currents we can estimate the impedance matrix of the circuit. Now, we know that the electrical circuit is controlled by a limited set of voltage or current sources. The aim of this papers is to give the rule by which from arbitrary voltages in the circuit we compute the voltage sources and also the associated current sources. We also give the method to compute the currents by the current sources and also the voltages by the impedance matrix. All the process from arbitrary voltages, voltage sources, current sources, current in the circuit and voltage in the circuit is denoted the projection operator in the morphogenetic system. Electrical circuits are a prototype of the morphogenetic system. We show that fuzzy inferential processes can be modeled by morphogenetic systems to improve models to estimate risks.