Optimization-Based TOPSIS Method with Incomplete Weight Information under Nested Probabilistic-Numerical Linguistic Environment

With the development of the economic and technology, decision-making problems are more and more complex and uncertain. Experts have difficulty in expressing evaluation information because of different research background and insufficient cognition of knowledge structure. Attribute weight information has been often incomplete in decision-making problems. Considering that nested probabilistic-numerical linguistic term sets (NPNLTSs) are flexible to express qualitative and quantitative information, in this paper, we firstly establish an optimization model based on distance measures to obtain the attribute weight. Combined with a classical decision-making method, an optimization-based TOPSIS method with NPNLTSs is proposed to deal with complex decision-making problems. After that, a case study about the river health assessment is given to show the effectiveness and practicability of the proposed method. Finally, some comparative analysis and discussion are provided from three aspects, including the impact for the results without weight optimization, the impact for the results under other uncertain environments, and the impact for the results using other decision-making methods. As a result, the proposed optimization-based TOPSIS method is effective and reliable. The optimization-based TOPSIS method proposed in this paper provides a new way to deal with uncertain and practical problems, which makes a technically sound contribution to the decision-making field.