Discrete-valued belief structures combination and normalization using evidential reasoning rule
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Discrete-valued belief structures combination and normalization using evidential reasoning rule Xing-Xian Zhang 1,2 & Ying-Ming Wang 1,3 & Sheng-Qun Chen 4 & Lei Chen 1
# Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Discrete-valued belief structures (DBSs) (known as discrete belief structures) are universal in real life, differ from precise-valued belief structures, and interval-valued belief structures (IBSs). However, the combination of different discrete belief structures presents a problem that has yet to be solved. Therefore, this study investigated the respective counter-intuitive types of behavior associated with the combination of discrete belief structures within the frameworks of the Dempster-Shafer theory. (DST) evidential reasoning (ER) for the purpose of constructing a more general method for the combination and normalization of discrete evidence. Finally, an experimental application is provided to indicate that the proposed method is suitable for combining and normalizing conflict-free/conflicting discrete evidence, and can effectively solve problems involving group decision-making (GDM) with uncertain preference ordinals, such as in a software selection problem. Keywords Discrete-valued belief structure . Dempster-Shafer theory . Evidential reasoning . Group decision-making . Uncertain preference ordinals
1 Introduction The Dempster-Shafer theory (DST), developed by Dempster [1] and Shafer [2], has thus far attracted widespread interest and been successfully extended to areas such as audit risk assessment [3], target recognition [4], expert systems [5], environmental impact assessment [6], classification [7, 8], reliability analysis [9], water distribution systems [10], ecommerce security [11], multiple attribute decision analysis (MADA) [12–14], regression analysis [15, 16], and safety analysis [17, 18].
* Ying-Ming Wang [email protected] 1
Decision Sciences Institute, Fuzhou University, Fuzhou 350116, People’s Republic of China
2
School of Architecture and Engineering, Tongling University, Tongling 244061, People’s Republic of China
3
Key Laboratory of Spatial Data Mining & Information Sharing of Ministry of Education, Fuzhou University, Fuzhou 350116, People’s Republic of China
4
School of Information Enginnering, Fujian Business University, Fuzhou 350506, People’s Republic of China
The evidential reasoning (ER) approach, which has been under development since first proposed by Yang and Singh [12] in 1994, is generally employed to analyze multiple attribute decision-making (MADM) problems characterized by uncertainties [19], including fuzziness, ambiguities, and ignorance. Furthermore, in the last two decades, the ER approach has been widely applied in different fields such as navigational risk assessment [20], data classification [21], smart home subcontractor selection [22], trauma outcome prediction [23], medical quality assessment [24], and bridge condition assessment [25]. Yang and Xu [26] generalized the ER approach by considering both local and
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