Generalized additive-multiplicative risk estimation model based on fuzzy and interval initial data

Abstract

Among the mathematical models of risk research, an important place is occupied by additive-multiplicative models of risk estimation. The components of such models are: three-stage hierarchical risk systems (built for a specific applied situation); partial risk estimators (determined by experts for a specific project, product, etc.); indicators of the weight of specific types of partial risks (found on the basis of a survey of experts in a particular application area); algorithms for calculating group risk estimators based on partial risk estimators and general risk estimator based on group risk estimators. As examples, three-stage hierarchical risk systems are considered in the production of a new innovative product and in the implementation of projects for the development of rocket and space technology. An algorithm for an additive-multiplicative model for risk estimation of a general form is proposed. Estimates of partial risks are products of weighting indicators by severity indicators, which corresponds to the well-known method of risk estimation in the form of the product of average damage by the probability of an undesirable event. Group risk estimators are built additively from i partial risk estimators, and the final overall risk estimator is calculated multiplicatively from group risk estimators. In previous works of the author, a special case of an additive-multiplicative risk estimation model was considered, in which, in particular, the components of the model were interpreted in terms of probability theory. It is proposed to carry out estimators of partial risks and weight coefficients on the basis of interval mathematics and fuzzy theory. The rules of arithmetic operations on interval and triangular fuzzy numbers are given. The application of the algorithm of the additive-multiplicative risk estimation model based on triangular fuzzy numbers is demonstrated using the example of risk estimation for the implementation of innovative projects. Within the framework of interval mathematics, risk estimators are considered in the implementation of projects for the development of rocket and space technology. The approach developed in this research article corresponds to the main provisions of the theory of stability of mathematical models of real phenomena and processes and to the results of systemic fuzzy interval mathematics.