Generate two-dimensional belief function based on an improved similarity measure of trapezoidal fuzzy numbers

Yangxue Li, Danilo Pelusi, Yong Deng

Abstract: Dempster–Shafer evidence theory plays a significant role in addressing uncertain information in various data fusion application systems. Recently, a new framework to model uncertain and partially reliable information on the basis of Dempster–Shafer evidence theory is put forward, called two-dimensional belief function (TDBF). A TDBF consists of two classical belief functions, \(T=(m_A,m_B)\), where \(m_B\) is a measure of reliability of \(m_A\). In this paper, an approach for determining TDBF is presented based on the improved similarity measure of fuzzy numbers. The improved similarity measure is more logical, flexible and can obviously improve the effectiveness in classification problem. Compared to the classical belief function, the TDBF can achieve better classification effective. The processes of the determine approach are expounded through a classification problem of Iris data. The validity of the determine approach is further illustrated by the classification of Wheat data.