Uncertain inference network in evidential reasoning
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Uncertain inference network in evidential reasoning Lijie Hu1 · Jinwu Gao2 · Giuseppe Fenza3 · Yanghe Feng4 · Carmen De Maio5 Received: 30 July 2020 / Revised: 17 August 2020 / Accepted: 28 August 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract As a dominant method in evidential reasoning, Bayesian network has been proved powerful in discrete fields. Although Bayesian network performs reliable in continuous variables and interval estimations, it relies on discretizing continuous variables or building an approximate model to conduct, which causes information loss and accuracy reduction. In order to bridge this gap, this paper introduces two inference rules combined with four inference rules proposed by other scholars. Then we propose a concept of uncertain inference network that consists of six basic structures matching inference rules to represent relationships and logic connection among the evidence. Evidence is represented by uncertain sets that can apply to continuous variables using membership functions to represent vague concepts. Furthermore, a numeric experiment for a forensic investigation of fire incidents is given to compare the results of uncertain inference network and Bayesian network. We found three merits in the case study. First, an uncertain inference network has simpler data access for each node because Bayesian network depends on conditional probability tables while uncertain inference network only relies on membership function. Second, an uncertain inference network has a more wide application because it can perform continuous variables with certain mathematical formulas without discretizing or approximating. Third, an uncertain inference network has a more accurate result because Bayesian network gives a point estimation with a 0–1 value while uncertain inference network conducts an interval estimation with a range value. Keywords Evidential reasoning · Uncertain inference network · Uncertain set · Bayesian network
* Yanghe Feng [email protected] Lijie Hu [email protected] Jinwu Gao [email protected] Giuseppe Fenza [email protected] Carmen De Maio [email protected] 1
School of Mathematics, Remin University of China, Beijing 100872, China
2
School of Economics, Ocean University of China, Qingdao 266100, China
3
Department of Business Sciences Management and Innovation Systems, University of Salerno, 84084 Fisciano, SA, Italy
4
College of Systems Engineering, National University of Defense Technology, Changsha 410073, China
5
Department of Information Engineering and Electrical and Applied Mathematics, University of Salerno, 84084 Fisciano, SA, Italy
1 Introduction In the actual court judgment process, the judges usually make decisions according to two methods. One is the Civil Law, which based on a similar case conducted before, the trial could be understood by the principle known as stare decisis [1, 2]. The other is the maritime law, that is, to make judgments in accordance with written legal provisions and relevant regul
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