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A method to multi-attribute decision making with picture fuzzy information based on Muirhead mean
The recently proposed picture fuzzy set (PFS) is a powerful tool for handling fuzziness and uncertainty. PFS is character-ized by a positive membership degree, a neutral membership degree, and a negative membership degree, making it more suitable and useful than the intuitionistic fuzzy set (IFS) when dealing with multi-attribute decision making (MADM). The aim of this paper is to develop some aggregation operators for fusing picture fuzzy information. Considering the Muirhead mean (MM) is an aggregation technology which can consider the interrelationship among all aggregated ar-guments, we extend MM to picture fuzzy context and propose a family of picture fuzzy Muirhead mean operators. In addition, we investigate some properties and special cases of the proposed operators. Further, we develop a novel meth-od to MADM in which the attribute values take the form of picture fuzzy numbers (PFNs). Finally, a numerical example is provided to illustrate the validity of the proposed method
A group decision-making model for wastewater treatment plans selection based on intuitionistic fuzzy sets
As the need for environmental protection and resource sustainability has increased in recent times, wastewater treatment has become increasingly important. In this paper, a group decision-making model for plans selection in wastewater treatment is proposed. In order to deal with uncertainties and multiple attributes in wastewater treatment, an intuitionistic fuzzy set is employed to evaluate wastewater treatment plans effectively. A distance measure is defined to obtain an objective weight measuring the expert鈥檚 judgment. More specifically, experts first use group decision-making on the various plans with an intuitionistic fuzzy set. Meanwhile, Due to the decision-makers psychological behavior, the prospect theory is applied. Next, the various plans are ranked by The Order of Preference by Similarity to Ideal Solution (TOPSIS) method and prospect theory. Finally, an illustrative example of wastewater treatment plans selection is used to verify the proposed model