Developing a rough set based approach for group decision making based on determining weights of decision makers with interval numbers

The goal of this paper is to propose a novel approach for determining the weights of decision makers (DMs) in group settings with a rough set group method, in which each decision maker's decision matrix is in interval numbers. In this paper, we first build a lower rough group decision (LRGD) and an upper rough group decision (URGD) from a rough group decision. Then, we define the average matrix of LRGD as a Lower positive ideal solution (Lower PIS), and the average matrix of URGD as an Upper positive ideal solution (Upper PIS) based on the Technique for Order Preference by Similarity to Ideal Solution method. Next, the average matrix of the Lower PIS and Upper PIS is regarded as the positive ideal solution (PIS), and the farthest distance from the PIS is regarded as the negative ideal solution (NIS). After that, each DM's weight is derived from the distances from the DM's decision to the PIS and NIS. Comparisons with existing methods are also made. Finally, an example of air quality evaluation is provided to clarify the availability of the proposed method.