Complex Evidence Theory And Its Applications

In an uncertain environment,information fusion processes evidence obtained from various information sources comprehensively,generating a detailed and comprehensive estimate for the system under test,which is regarded as one of the key technologies to improve the intelligence of intelligent systems.It is well known that Dempster-Shafer evidence theory can effectively model and handle uncertain information,which promotes the research and application of information fusion.It should be noted,in Dempster-Shafer evidence theory,however,that the work relating to computational complexity of combination rules,reliability hypothesis,and conflict measure still has some limitations.Also,the research on theories(such as probability theory,fuzzy theory)relating to or peering with Dempster-Shafer evidence theory has moved from the expansion of a real plane to a complex space,and has increasingly been engaged in theoretical research and engineering practice.In light of the above,this dissertation first verifies the necessity of establishing complex evidence theory from the perspective of the computational complexity of combination rules and the complex evidence network.After that,a basic framework of complex evidence theory is developed in order to achieve a multi-state evaluation of propositions’ reliability.Then,uncertain information measure and similarity measure are conducted in complex evidence theory.Finally,when complex evidence theory collapses into Dempster-Shafer evidence theory,a divergence measure of basic probability assignment is used to overcome the shortcomings of the work related to conflict measure.As a summary,the following findings are presented in this dissertation.A necessity of moving from evidence theory to complex evidence theory.In DempsterShafer evidence theory,there are defects such as information loss and space limitation in the work related to the computational complexity of the Dempster rule of combination.It is possible to overcome these deficiencies through the development of quantum computer.Based on the parallel idea of quantum computing,this dissertation proposes a quantum model of the Dempster rule of combination.This model includes quantum state preparation of basic probability assignment,measure operations,etc.With the help of IBM’s quantum platform,this method is experimentally verified,as well as compared to other approaches.Experimental results show that the quantum model of Dempster rule of combination can effectively reduce computational complexity.This model provides a preliminary guide for the extension of Dempster-Shafer evidence theory to the complex space.As a further explanation of the necessity of extending evidence theory to complex space,this dissertation establishes a complex evidence network.Complex evidence networks include complex basic probability assignment generation,interference factor calculation,action prediction and other processes.It is then applied to the Prisoner’s Dilemma experiment and compared with other methods.Experimental results show that the complex evidence network can more accurately predict the behavior of the participants in the Prisoner’s Dilemma.In summary,the quantum model of Dempster rule of combination provides guidance for establishing complex evidence theory,and complex evidence network explains the necessity of moving from evidence theory to complex evidence theory.Complex evidence theory breaks the limitation of reliability hypothesis,and simultaneously models the information of support degree of proposition and the reliability information related to the support degree,and then realizes the multi-state evaluation of the reliability information.A prerequisite for the application of Dempster rule combinations is the reliability hypothesis,which requires bodies of evidence that is completely reliable.Several studies have demonstrated that this condition is idealized.To address problems related to the reliability hypothesis,discount model and disjunctive rule are designed.However,discount model and disjunctive rule are not yet able to consider the reliability information of support from the propositional level,thus limiting the status of reliability evaluation.To solve it,based on complex evidence theory proposed in this dissertation,amplitude of the complex basic probability assignment can be interpreted as support degree of a proposition,and phase angle is interpreted as information related to the reliability of the support degree of the proposition.On this basis,complex belief function,complex Dempster rule of combination and etc.are proposed.Mobius transformation is employed to realize the transformation between functions and the matrix expression of complex Dempster rule of combination.Also,in dataset environment,it is proposed to develop a method based on marginal contribution for generating complex basic probability assignment,and this method is experimentally verified.It has been demonstrated that the accuracy of the combined results is improved when reliability information is modeled.Overall,the above work establishes the basic framework of complex evidence theory and realizes multi-state evaluation of the reliability of proposition.In complex evidence theory,this dissertation tries to solve uncertainty measure,conflict measure and management.The first is an uncertainty measure for complex base probability assignment.Compared with basic probability assignment in Dempster-Shafer evidence theory,the information involved in complex basic probability assignment involves discord information,non-specificity information,and phase angle-related information.However,the uncertainty measures in Dempster-Shafer evidence theory cannot simultaneously capture the three characteristics of complex basic probability assignment.To address this problem,this dissertation proposes complex belief entropy,which aims to simultaneously measure the three information.Following this,the properties of complex belief entropy are discussed,and numerical examples are provided to demonstrate its rationality and validity.Additionally,a classification model based on complex belief entropy is proposed,and dataset experiments and comparative experiments are conducted.Experimental results suggest that the classification model based on complex belief entropy can enhance the accuracy of the experimental results.Secondly,this dissertation defines a similarity measure between complex basic probability assignments to quantify consistency,and then evaluates the degree to which these complex basic probability assignments conflict.It discusses the properties of complex similarity measure,as well as demonstrating the rationality and effectiveness of the method through examples.In addition,based on complex similarity measure,a low-time-cost multi-source information fusion model is established,and apply it to dataset experiments,the results demonstrate that it not only improves the accuracy of fusion results,but also reduces the running time related to combination rules.Finally,the classical fusion model in Dempster-Shafer evidence theory is migrated to complex space,and verified by dataset experiments.The above work contributes to the development and application of complex evidence theory to the information fusion.When complex evidence theory collapses into Dempster-Shafer evidence theory,this dissertation complete conflict measure and management.First,a similarity measure of focal elements is defined,aiming to solve the problem of insensitivity to element changes in focal elements.Based on it,a Jensen-Shannon divergence of basic probability assignment is proposed.And discuss the properties of the Jensen-Shannon divergence of basic probability assignments,and then verify its rationality and effectiveness through examples.Lastly,a method of information fusion based on static weights and dynamic weights is proposed using Jensen-Shannon divergence of basic probability assignments.Results from experiments on datasets demonstrate that,in the context of evidence theory,this method can improve the accuracy of fusion results in comparison with other methods.In short,this dissertation explains the necessity of establishing complex evidence theory,establishes complex evidence theory initially,solves some problems of DempsterShafer evidence theory,and provides a practical solution for the development and application of information fusion.