An extension of VIKOR method for multi-attribute decision-making under Pythagorean hesitant fuzzy setting

Pythagorean hesitant fuzzy set plays a significant role to deal with vagueness and hesitation which can be precisely and perfectly defined in terms of the opinions of decision-makers. In this paper, we proposed a broad new extension of classical VIKOR method for multi-attribute decision-making (MADM) problems with Pythagorean hesitant fuzzy information. Basically VIKOR method of compromise ranking determines a compromise solution, which provides a maximum group utility for the majority and a minimum of an individual regret for the opponent and is an effective tool to solve MADM problems. To do this first we give some basic definitions and analogous concepts, and the basic steps of classical VIKOR method are introduced. Different situations of attribute weight information are considered. If attribute weights are partly known a linear programming model is set up based on the idea that reasonable weights should make the relative closeness of each alternative evaluation value to the Pythagorean hesitant fuzzy positive ideal solution as large as possible. If attribute weights are unknown completely, an optimization model is set up based on the maximum deviation method. We describe a MADM problem and present the steps of VIKOR method under the Pythagorean hesitant fuzzy environment. Finally, a numerical example is presented to illustrate feasibility and practical advantages of the proposed method.