| In real life,due to the complexity of the decision making environment and the different cognitive levels of the decision makers,most decision making problems are uncertain and vague.Picture fuzzy set happens to be one of the effective tools to deal with such uncertain decision making problems,can simultaneously consider the information of membership,neutrality,non-membership and abstention.Therefor,this paper studies the information set of attribute information portrayed by picture fuzzy set,and uses it to solve picture fuzzy multi-attribute decision making problem.The picture fuzzy geometric aggregation operators is proposed.From the perspective of function,new basic operations between picture fuzzy numbers are defined,and some picture fuzzy geometric aggregation operators are constructed,such as picture fuzzy weighed geometric operator,picture fuzzy ordered weighted geometric operator,picture fuzzy hybrid geometric operator.The excellent properties of the new operator and the relationship between the operators are discussed,and a method of picture fuzzy multi-attribute decision making is given.The decision example illustrate the effectiveness and feasibility of decision method.Construct picture fuzzy aggregation operators that consider the correlation between attributes.Using the idea of information fusion,combining the geometric operator in the classic category,the picture fuzzy power geometric Heronian mean operator and the picture fuzzy weighted power geometric Heronian mean operator are proposed.Push to its mathematical formula,prove its relevent properties with existing mathematical knowledge,and discuss the relationship between the new operators and the existing operators.A decision making method based on picture fuzzy weighted power geometric Heronian mean operator is given.The influence of parameters on decision results is analyzed through decision example.The new method and the exisiting making method are compared and analyzed.The further demonstrates the feasibility and advantages of the method.The results show that the new operator can not only reflect the correlation between the attribute values to be aggregated,but also reflect the integrity of the information in the decision making process.At the same time,the introduction of parameters makes the decision results more flexible,and the decision maker should choose the appropriate parameters to meet different needs according to the actual decision making situation.The paper has 2 figures,7 tables and 53 references. |
