Multiattribute decision-making based on TOPSIS technique and novel correlation coefficient of q-rung orthopair fuzzy sets

The correlation coefficient is a powerful tool to measure the relationship between two variables and is very useful in decision-making. In this paper, we propose a new multiattribute decision-making (MADM) method for q-rung orthopair fuzzy number (q-ROFN) environment. For this, we propose a novel correlation coefficient for q-rung orthopair fuzzy sets (q-ROFSs), which measures the strength of the relationship between two q-ROFSs. We also present the various properties of the proposed correlation coefficient of q-ROFSs. Moreover, we also develop the weighted correlation coefficient of q-ROFSs. Afterward, we propose a new MADM method under the q-ROFNs environment based on the proposed weighted correlation coefficient of q-ROFSs and the “Technique for Order Preference by Similarity to Ideal Solution” (TOPSIS) method. The proposed MADM method can overcome the shortcomings of the existing MADM methods of the q-ROFNs environment, where they cannot distinguish the ranking orders (ROs) of the alternatives. The proposed MADM method provides a very useful method to deal with MADM problems in the q-ROFNs environment.