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Geometry Of Risk Analysis (morphogenetic System)

机译：风险分析的几何（形态发生系统）

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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.
机译：我们知道风险分析是基于灾难性事件的估计。现在要获得良好的估计，我们必须创建合适的风险模型。对于数据样本，我们可以使用不同的数学模型，如线性或非线性回归方法，神经网络方法，遗传方法以及由信息扩散近似推理方法和反向传播神经网络组成的最新混合模型。在本文中，我们提出了一个新的框架，称为形态发生系统，以研究风险分析。我们表明，形态发生系统是张量演算的推广，用于对非欧几里得几何表示形式进行形式化。现在，我们从电路分析中提出建议，以建立用于估计的形态发生模型。在电路中，我们有电压矢量和电流矢量。电压和电流之间的关系由欧姆定律和阻抗矩阵给出。该关系是一个多输入多输出（MIMO）系统，给出了一组电压和电流样本，我们可以估算电路的阻抗矩阵。现在，我们知道电路由一组有限的电压或电流源控制。本文的目的是给出一个规则，通过该规则，我们可以根据电路中的任意电压来计算电压源以及相关的电流源。我们还给出了通过电流源计算电流以及通过阻抗矩阵计算电压的方法。来自任意电压，电压源，电流源，电路中的电流以及电路中的电压的所有过程都被表示为形态发生系统中的投影算子。电路是形态发生系统的原型。我们表明，可以通过形态发生系统对模糊推理过程进行建模，以改进模型来估计风险。

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