A New Soft Likelihood Function Based on D Numbers in Handling Uncertain Information
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A New Soft Likelihood Function Based on D Numbers in Handling Uncertain Information Ye Tian1 • Xiangjun Mi1 • Lili Liu1 • Bingyi Kang1
Received: 31 March 2020 / Revised: 31 May 2020 / Accepted: 17 June 2020 Taiwan Fuzzy Systems Association 2020
Abstract How to effectively deal with uncertain information has traditionally been a concern. The D numbers theory overcomes the limitations of Dempster–Shafer theory and further strengthens the ability of uncertainty modeling. Recently, Yager et al. proposed a soft likelihood function which can effectively combine probability information. Related research has enriched and expanded its connotation, but there are still problems to be solved. This paper conducted further research and proposed a new soft likelihood function based on D numbers. Comparison and discussion illustrate the rationality and superiority of the proposed methodology. Keywords D numbers Soft likelihood functions Ordered weighted average Uncertain information fusion Reliability
1 Introduction Uncertainty information processing has received widespread attention. Perceiving a variety of information and being able to effectively process it is an important basis for intelligent information processing, especially in artificial intelligence that simulates human thinking in complex external environments. Due to the complexity of the real world, the information to be faced is often vague, uncertain, and partially reliable. In order to model effectively, many important theories are proposed, such as fuzzy set & Bingyi Kang [email protected]; [email protected] 1
College of Information Engineering, Northwest A&F University, Yangling 712100, Shaanxi, China
theory [1–5], fuzzy neural network [6–8], belief structures [9–12], entropy function [13–17], Z-number [18–21] and Dempster–Shafer theory [22–25]. Since no prior information is required, Dempster–Shafer theory (D–S theory) is considered as an alternative to Bayesian probability theory, which has shown excellent capabilities in the process of reasoning with uncertain information and has been widely used [26–28]. However, it still has some flaws [29]. D–S theory requires that the elements in the frame of discernment are mutually exclusive, and the basic probability assignment (BPA) information must be complete. However, in many cases, this exclusivity hypothesis cannot be accurately guaranteed, and in real life, the large amount of information obtained is liable to be incomplete. In addition, the computational complex degree with exponential increasing and the onevote veto mechanism also limits its further development. Recently, Deng et al. proposed D numbers [29], which effectively solved the above problems and was regarded as a further extension of D–S theory. D numbers provide a more flexible and effective method to deal with uncertainty information, so it has been widely used in many fields such as such as supplier selection [30], evaluation analysis [31–34], combination with game theory [35, 36], supply chain management practices [37],
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