Multiple Attribute Decision Making Methods Based On Pythagoras Fuzzy Information

When dealing with complex decision problems,some attribute information may be incomplete or ambiguous.For different decision-making problems,decision makers may use appropriate fuzzy set to model uncertain information.Pythagorean fuzzy set can effectively solve uncertain multiple attribute decision making(MADM)problems.In this paper,we study multiple attribute decision making problems based on Pythagorean fuzzy information and proposed several multiple attribute decision-making methods to solve multiple attribute decision making problems with Pythagorean fuzzy information.The Pythagorean fuzzy MADM method based on DEMATEL and TOPSIS(technique for order preference by similarity to ideal solution)has been studied.Firstly,we defined a new distance formula for Pythagorean fuzzy information by analyzing of the fact that results of traditional Euclidean distance to not match the human intuitive feeling.Then DEMATEL(Decision-Making Trial and Evaluation Laboratory)method is introduced for Pythagorean fuzzy information to consider interaction of the attribute.Graph theory and matrices are used in DEMATEL to analyze the system factors and find the key factors,and the attribute weights are got.Finally,the alternatives can be ranked according to the distance between the alternatives and the positive and negative ideal solution.In this method,the impact of not only data itself but also the relationship between the data on the decision results has been considered.TOPSIS method is used to rank alternatives to avoid complicated computation and the more reasonable decision results can be got.The hesitant Pythagorean fuzzy TODIM(an acronym in Portuguese for Interactive Multi-criteria Decision Making)method is studied.A measurement function is defined according to the space theory,which is used to compare the size of two hesitant Pythagorean fuzzy numbers.The TODIM method based on proposed measurement function in this paper has been developed to solve the hesitant Pythagorean fuzzy multiple attribute decision making problems.The TODIM method can characterize the decision makers' psychological behaviors under risk.The Hamy mean(HM)aggregation operators and Hamacher operations based on Pythagoras fuzzy set are studied.Some Pythagorean fuzzy Hamacher Hamy mean aggregation operators are developed based on the Hamacher operator and Hamy mean aggregation operator: Pythagorean fuzzy Hamacher Hamy mean operator,Pythagorean fuzzy Hamacher dual Hamy mean operator,Pythagorean fuzzy Hamacher weighted Hamy mean operator and Pythagorean fuzzy Hamacher weighted dual Hamy mean operator.The above operators are capable of capturing interrelationships among arguments to be aggregated.They can solve MADM problems more flexible.