Multi-attribute group decision-making method based on time-series q-rung orthopair fuzzy sets

The q-rung orthopair fuzzy set is a powerful and useful tool to deal with uncertainty, but in actual decision-making process, decision-makers are usually required to analyze the actual problem dynamically. Therefore in this paper, we consider the time-series q-rung orthopair fuzzy decision making. First, we introduce the new cosine similarity measure of q-ROFS which combines the cosine similarity measure and the Euclidean distance measure. Then, we combine the advantages of projection method and grey correlation degree, establishing the nonlinear programming model to calculate the weights of attributes. Furthermore, we use the exponential decay model to get the weights formulas of q-ROFS at different times. Then we replace the distance function with grey relational projection and extend TOPSIS method. Based on these, we propose a new MAGDM approach to deal with time-series q-rung orthopair fuzzy problem not only from the point of view of geometry but also from the point of view of algebra. Finally, we give a practical example to illustrate effectiveness and feasibility of the new method.