Fusion of qualitative beliefs based on linguistic labels

In order to model beliefs expressed by natural language, the qualitative belief assignment based on the linguistic labels has been presented in the Dezert-Smarandache Theory (DSmT). However, the combination of qualitative beliefs is only based on the equidistant linguistic labels and the calculation of non-equidistant labels is approximate. To solve the fusion problem of qualitative beliefs denoted by non-equidistant labels, this paper proposed the universal arithmetic operations of linguistic labels, and analyzed the fusion of qualitative beliefs based on the general labels. The new operations which were based on the linear or nonlinear mapping relationship between linguistic labels and numerical values, could be effectively used on 1-tuple or 2-tuple linguistic representation model, and could increase the precision and reliability of the combination of qualitative beliefs or mixed beliefs. The experimental results have proved the validity of universal operations.