Dynamic Uncertain Causality Graph for Knowledge Representation and Reasoning: Continuous Variable, Uncertain Evidence, and Failure Forecast

A new approach for uncertain causality representation and probabilistic reasoning named as dynamic uncertain causality graph (DUCG) was presented previously, in which only the discrete variables and certain evidence were addressed. In this paper, the free mixtures of discrete and continuous variables as well as uncertain evidence are addressed. The general idea to deal with continuous variables is to transform them into fuzzy discrete variables along with their corresponding uncertain causalities, and then treat them as ordinary discrete variables, which involves how to deal with fuzzy evidence. It is pointed out that uncertain evidence is either: 1) fuzzy evidence that is an observed certain value of a continuous variable falling into a fuzzy area across two or more fuzzy discrete states of a variable or 2) soft evidence that can only be understood as a probability distribution over the states of a variable. The algorithm for utilizing uncertain evidence in inference is presented, in which uncertain evidence is treated as a virtual child variable of the observed variable without changing the knowledge and inference algorithm encoded in DUCG. It is proved that the two types of uncertain evidence are the same in nature and can be treated indiscriminatingly. Moreover, this method dealing with fuzzy evidence in DUCG can be used for failure forecasting of systems. Examples are provided to illustrate the methodology.