The concepts of grey probability, grey probability distribution, grey probability density, grey expectation and grey variance are defined based on the theory of probability and grey system approach. The method of grey\|stochastic risk for system risk analysis is established.

The concepts of grey probability, grey probability distribution, grey probability density, grey expectation and grey variance are applied based on the theory of probability and grey system approach. Directing towards stochastic and grey uncertainties of environmental system, a method for determining the level of non-sudden environmental risk is presented based on the concept of grey probability.

Directing towards the grey uncertainty of probability itself,the concepts of grey probability,the grey degree of grey probability,grey probability distribution,grey probability density,grey expectation and grey variance are defined based on the theory of probability and grey system approach. The Dempster Shafer theory and Dempster's and Shafer's approachs to inference,that can be used to estimate the parameters of grey probability distribution,are introduced.

The concepts of grey probability, grey probability distribution, grey probability density, grey expectation and grey variance are defined based on the theory of probability and grey system approach. The method of grey\|stochastic risk for system risk analysis is established. In this method, the uncertainty of system risk is attributed to grey uncertainty of system, the variables of system performance function are treated with grey probability distributions and the system hazard...

The concepts of grey probability, grey probability distribution, grey probability density, grey expectation and grey variance are defined based on the theory of probability and grey system approach. The method of grey\|stochastic risk for system risk analysis is established. In this method, the uncertainty of system risk is attributed to grey uncertainty of system, the variables of system performance function are treated with grey probability distributions and the system hazard is quantified with grey\|stochastic risk. The grey\|stochastic risk can be transformed into ordinary stochastic risk and computed using advanced first\|order second\|moment method. An example of application is given.

The concepts of grey probability, grey probability distribution, grey probability density, grey expectation and grey variance are applied based on the theory of probability and grey system approach. Directing towards stochastic and grey uncertainties of environmental system, a method for determining the level of non-sudden environmental risk is presented based on the concept of grey probability. In this method, the non-sudden environmental risk is attributed to stochastic uncertainty...

The concepts of grey probability, grey probability distribution, grey probability density, grey expectation and grey variance are applied based on the theory of probability and grey system approach. Directing towards stochastic and grey uncertainties of environmental system, a method for determining the level of non-sudden environmental risk is presented based on the concept of grey probability. In this method, the non-sudden environmental risk is attributed to stochastic uncertainty and grey uncertainty of environmental system. The variables influencing on environmental capacity and the consumption of environmental discharge are treated with grey probability distributions, and the non-sudden hazard of environmental system is quantified with the level of environmental risk expressed in the form of grey probability. The level of environmental risk can be transformed into ordinary probabilistic environmental risk and computed using advanced first-order second-moment method. An example of application for calculating the risks of organic pollute in the Cangxi reach of the Jialing River is given. The results can fully reflect and quantify the stochastic and grey uncertainties influencing on environmental quality.

The river water environment system is a system with many uncertainties. The risk assessment quantifying the influence of uncertainties on river water quality have been paid attention to widely. However, the most of research on risk assessment for river water quality confined to quantify stochastic uncertainty of the river water environmental system using the method of statistics. The research on quantifying the risk due to grey uncertainty of the river water environmental system is done less. Based on the...

The river water environment system is a system with many uncertainties. The risk assessment quantifying the influence of uncertainties on river water quality have been paid attention to widely. However, the most of research on risk assessment for river water quality confined to quantify stochastic uncertainty of the river water environmental system using the method of statistics. The research on quantifying the risk due to grey uncertainty of the river water environmental system is done less. Based on the theory of probability and grey system approach, the concepts of grey probability, grey probability distribution, grey probability density, grey expectation and grey variance are defined in this paper. The concept of grey stochastic risk for water quality concentrations exceeding the standard values is presented to quantify the influence of stochastic uncertainty and grey uncertainty on river water quality. The assessment models of grey stochastic risk for water quality concentrations exceeding the standard values are established. In the assessment model for the individual parameter, the contaminant concentration is modeled as a random variable with a grey probability distribution and the risk for contaminant concentration exceeding the standard value is expressed with grey probability-the grey stochastic risk for water quality concentrations exceeding the standard values. In the model of comprehensive assessment for multiple parameters, the river water environmental system is considered as the reliability system to undertake useful function, and the result that the concentration of anyone of water quality parameters exceeds the standard value shows that the useful function of river water environmental system cannot be guaranteed. Lastly, the comprehensive risks for water quality concentrations exceeding the standard values are computed by using the approach of reliability system. An example of application to evaluate the grey stochastic risks for heavy metals concentrations exceeding the standard values in the Yellow River at the Huayuankou section is given. The results provide more information and are satisfactory.