Joint propagation of probability and possibility in risk analysis: Towards a formal framework

This paper discusses some aspects of fuzzy random variables obtained by propagating uncertainty in risk analysis when some input parameters are stochastic, while others are deterministic but the information about them is partial and is represented by possibility distributions. Our knowledge about the probability of events pertaining to the output of the risk analysis model can be either represented by a fuzzy probability or by a probability interval obtained by viewing a fuzzy random set as a regular random set by means of α-cuts. It is shown that this interval is the average cut of the fuzzy probability of the event, thus legitimating the propagation method. Besides the independence assumptions underlying the probability possibility propagation methods are discussed and illustrated by examples. This approach can be extended to input parameters that are both stochastic and imprecisely observed. Key-words: Random sets, possibility distributions, fuzzy random variables, independence. 1...

• Type: Journal
• Year: 2007
• Where: IJAR
• Authors: Cédric Baudrit, Inés Couso, Didier Dubois
• Keywords: Fuzzy Probability, Fuzzy Random, Fuzzy Random Variables, IJAR 2007