Research On Orthopair Fuzzy Information Aggregation Operators Based Multiple Attribute Decision Making Methods

As decision making problems are becoming more and more intricate,improving the reliability and scientificity of decision making is a fundamental and important issue in modern decision making science.Decision making is driven by information,i.e.information drives management and decision.Thus,managing,representing and integrating decision making information experts is a fundamental hot issue in multiple attribute decision making.When using multiple attribute decision making theories to make choices,the primary issue is to represent decision makers'evaluation information accurately.Due to the complexity and fuzziness of decision making problems and the limitations of human cognitive process,it is difficult for decision makers to express their evaluations by crisp numbers.Intuitionistic fuzz sets,Pythagorean fuzzy sets,and generalized orthopair fuzzy sets have been widely used to express decision makers'evaluation values in multiple attribute decision making.As intuitionistic fuzzy sets,Pythagorean fuzzy sets and generalized orthopair fuzzy sets are characterized by membership and non-membership degrees,they are called orthopair fuzzy sets uniformly.Up to present,researches on orthopair fuzzy sets based multiple attribute decision making have achieved great success,especially researches on multiple attribute decision making with intuitionistic fuzzy information.However,researches on Pythagorean fuzzy information and generalized orthopair fuzzy information based multiple attribute decision making problems have not been widely conducted yet.Thus,the information aggregation methods of orthopair fuzzy information with their applications in multiple attribute decision making are investigated in this paper.We firstly study Pythagorean fuzzy sets,propose their aggregation operators and based on which some new multiple attribute decision making methods are proposed.We further study aggregation technologies of generalized orthopair fuzzy information,and employ the developed operators in multiple attribute decision making.The main works and novelties of this paper are as follows:(1)The aggregation methods of Pythagorean fuzzy information are investigated.To reflect the interrelationship between attributes,the Bonferroni mean is extended to Pythagorean fuzzy sets and some Pythagorean fuzzy Bonferroni mean operators are proposed and applied in multiple attribute decision making.Additionally,as the interrelationship exits among multiple attributes in multiple attribute decision making,we extend the proposed Pythagorean fuzzy Bonferroni mean operators and develop the generalized Pythagorean fuzzy Bonferroni mean operators and the dual generalized Pythagorean fuzzy Bonferroni mean operators.Based on the power average operator,some series of interval-valued Pythagorean fuzzy aggregation operators are proposed,which have the ability of the negative effect of decision makers'unreasonable evaluations on the ranking results,and apply the proposed operators in practical multiple attribute decision making problems.Operational rules and aggregation operators of Pythagorean fuzzy numbers based on Schweizer-Sklar t-norms and t-conorms are proposed and their desirable properties are studied.(2)Aggregation operators of generalized orthopair fuzzy information based on Maclaurin symmetric mean and Muirhead mean are proposed and their properties are investigated.Based on the proposed generalized orthopair fuzzy aggregation operators,a novel approach for multiple decision making is proposed,whose effectives is proved through numerical example.Considering that decision makers prefer to utilize interval-values to denote the membership and non-membership degrees of their evaluation values,motivated by interval-valued intuitionistic fuzzy set and interval-valued Pythagorean fuzzy sets,the traditional generalized orthopair fuzzy sets are extended to interval-valued generalized orthopair fuzzy sets.The definition of interval-valued generalized orthopair fuzzy sets and comparison method of generalized interval-valued orthopair fuzzy numbers are given.In addition,operations of interval-valued generalized orthopair fuzzy numbers based on Dombi t-norm and t-conorm are provided.We further investigate interval-valued generalized orthopair fuzzy aggregation operators based on Muirhead mean.Furthermore,we investigate decision making problems in hesitant fuzzy and generalized orthopair fuzzy environment,propose new generalized dual hesitant fuzzy aggregation operators and study generalized dual hesitant fuzzy sets based MADM problems.(3)Multiple attribute decision making based on generalized orthopair linguistic information is investigated.Generalized orthopair fuzzy sets are combined with linguistic variables and uncertain linguistic variables,respectively,and the notions of interval-valued generalized orthopair linguistic sets and generalized orthopair uncertain linguistic sets are provided.In the interval-valued generalized orthopair linguistic sets and generalized orthopair uncertain linguistic sets,the membership of membership and non-membership degrees of linguistic variables and uncertain variables are represented by generalized orthopair fuzzy numbers.Based on Muirhead mean operator,we introduce a series of interval-valued generalized orthopair linguistic aggregation operators and investigate their properties detailedly.Based on Heronian mean operator,a family of generalized orthopair uncertain linguistic aggregation operators are introduced.Multiple attribute decision making methods based on interval-valued generalized orthopair linguistic information and generalized orthopair uncertain linguistic information are presented.The validity of the proposed methods is illustrated through numerical example.