Autocratic decision making using group recommendations based on ranking interval type-2 fuzzy sets

Abstract

In this paper, we propose a new autocratic decision making method using group recommendations based on ranking interval type-2 fuzzy sets. First, the proposed method calculates the ranking values of interval type-2 fuzzy sets appearing in the weighting vectors and the evaluating matrices given by decision makers, respectively, to construct the ranking weighting vectors and the ranking evaluating matrices of the decision makers, respectively. Then, it constructs the weighted evaluating matrix of each decision maker and calculates the aggregated evaluating value of each alternative with respect to each decision maker for constructing the aggregated evaluating matrix of all decision makers. Then, it gets the numerical preference order of the alternatives with respect to each decision maker represented by a preference vector. Then, it calculates the aggregated group evaluating value of each alternative with respect to all decision makers to get the numerical preference order of the alternatives with respect to all decision makers represented by a group preference vector. Then, it calculates the similarity degree between the obtained preference vector of each decision maker and the obtained group preference vector of all decision makers. Then, it gets the normalized aggregated evaluating value of each alternative with respect to each decision maker to construct the normalized aggregated evaluating vector of each decision maker. Then, it gets the normalized aggregated group evaluating value of each alternative with respect to all decision makers to construct the normalized aggregated group evaluating vector of all decision makers. Finally, it calculates the similarity degree between the obtained normalized aggregated evaluating vector of each decision maker and the obtained normalized aggregated group evaluating vector of all decision makers for changing the weights of the decision makers until the group consensus degree is larger than or equal to a predefined consensus threshold value. We apply the proposed method to deal with the “system analysis engineers” selection problem, the cars selection problem and the “table tennis players” selection problem. The proposed method can overcome the drawbacks of the existing group decision making methods in interval type-2 fuzzy sets environments.