An Improved Method to Transform Triangular Fuzzy Number Into Basic Belief Assignment in Evidence Theory

Abstract

Dempster-Shafer evidence theory (D-S theory) is a developing theory to solve the uncertain problems and it has an important impact on many fields such as information fusion, expert systems, and machine learning. One of the main points of D-S theory is about how to generate a reliable basic belief assignment. Furthermore, the data collected from the multi-sources may be influenced by noise or other factors which cause conflicts in practical applications. Since the fuzzy number is useful to construct the target model for generating basic belief assignments, in this paper, an improved method to obtain basic belief assignment is proposed based on the triangular fuzzy number and k-means++ algorithm. First, the k-means++ clustering method is used to construct the target model. Then, the difference degree between the target model and sample model is calculated to generate the initial basic belief assignments. After that, the conflicts will be resolved by using the discount coefficient method. Finally, Dempster's combination rule is used to combine initial basic belief assignments to obtain the final result. The applications in recognition problems of the Iris data set and Wine Quality data set illustrate that the proposed method is effective to generate the basic belief assignments and keeps a high recognition rate even under a noisy environment.

Keywords

• Basic belief assignment
• Dempster-Shafer evidence theory
• triangular fuzzy number
• white Gaussian noise