A Novel<i>Z</i>-Network Model Based on Bayesian Network and<i>Z</i>-Number

Abstract

Z-number is an effective model to describe uncertainty in the real world. Under the condition that uncertainty reasoning is an important issue to process information, how to achieve Z-valuation uncertainty reasoning is a problem. As a Z-number involves both fuzzy and probabilistic uncertainty, main difficulty in the problem to be solved is accomplishing both two uncertainties' reasoning. In this paper, a novel Z-network model and its associated reasoning algorithm are proposed to overcome the difficulty. Structure of the proposed Z-network that contains three basic structures is directed acyclic graph, and this is similarly with Bayesian network (BN). Process of reasoning algorithm involves two parts: first, Bayesian reasoning is applied to establish an optimization model for probabilistic uncertainty reasoning in a Z-number; second, the arithmetic approach of discrete Z-number on if-then rule and maximum entropy approach are proposed for fuzzy uncertainty reasoning. Z-network is essentially an extended model on the basis of BN and properties of a Z-number for Z-valuation uncertainty reasoning. In application, a novel framework of dependence assessment in human reliability analysis is proposed based on Z-network, and a case study demonstrates its effectiveness.