On the evidential reasoning rule for dependent evidence combination

Evidential Reasoning(ER)rule,which can combine multiple pieces of independent evidence conjunctively,is widely applied in multiple attribute decision analysis.However,the assumption of independence among evidence is often not satisfied,resulting in ER rule inapplicable.In this paper,an Evidential Reasoning rule for Dependent Evidence combination(ERr-DE)is developed.Firstly,the aggregation sequence of multiple pieces of evidence is determined according to evidence reliability.On this basis,a calculation method of evidence Relative Total Dependence Coefficient(RTDC)is proposed using the distance correlation method.Secondly,as a discounting factor,RTDC is introduced into the ER rule framework,and the ERr-DE model is formulated.The aggregation process of two pieces of dependent evidence by ERr-DE is investigated,which is then generalized to aggregate multiple pieces of non-independent evidence.Thirdly,sensitivity analysis is carried out to investigate the relationship between the model output and the RTDC.The properties of sensitivity coefficient are explored and mathematically proofed.The conjunctive probabilistic reasoning process of ERr-DE and the properties of sensitivity coefficient are verified by two numerical examples respectively.Finally,the practical application of the ERr-DE is validated by a case study on the performance assessment of satellite turntable system.

Regression model for estimation of attribute reliability

In this paper,a regression model is developed to estimate attribute reliability in the evidential reasoning(ER)context.By analysing the difference between attribute weight and attribute reliability,a general qualitative definition of attribute reliability is provided.The reliability of an attribute is quantitatively measured in consistence with the qualitative definition in the context of the ER approach.A regression model is then constructed to generate attribute reliabilities by minimising the maximum differences between the real value of attribute reliability and its estimation.Within the post-optimal solution space of attribute reliabilities,an optimisation model is constructed to determine the expected utilities of each alternative in order to generate solutions to multiple attribute decision analysis problems.Asale place selection problem in Qingyang County of Chizhou in Anhui province of China is analysed using the proposed regression model to demonstrate its detailed implementation process,validity and applicability.