Distance and Similarity Measures for Nested Probabilistic-Numerical Linguistic Term Sets Applied to Evaluation of Medical Treatment

Nested probabilistic-numerical linguistic term sets (NPNLTSs), which can be used to express two layers of evaluation information fromqualitativeandquantitativeviews, increase the flexibility of representing the nested uncertain information. In order to enhance and extend the applicability of the NPNLTSs, in this paper, we mainly investigate and develop some different types of distance and similarity measures for NPNLTSs. Firstly, a family of distance and similarity measures between two NPNLTSs with their properties and proofs are proposed. Then, we further establish a variety of weighted distance and similarity measures between two collections of NPNLTSs in discrete case, continuous case and ordered weighted case, respectively. Based on that, an approach based on the proposed measures is put forward to deal with multi-attribute decision-making problems. After that, a practical application concerning the evaluation of medical treatment is given to illustrate the usability andeffectivenessof the proposed approach. Finally, some comparisons and analyses are provided from three angles including the impact of using various decision-making methods, various distance and similarity measures and the changed focal parameters.