The Research On Partitioned Aggregation Operators Based On Two-dimension Linguistic Numbers

In view of the complicated and changeable subjective factors and practical problems of decision-makers,such as knowledge background and way of thinking,decision-makers sometimes fail to express their evaluation results quantitatively.The linguistic variables(language phrases for range)in expression of fuzzy information in particular is intuitive,convenient and reasonable advantages such as qualitative information,fuzzy multi-attribute decision making based on linguistic variables has been rapid development and become an important part of fuzzy multiple attribute decision making.The use of I and II language variables in two dimensional language variables can more accurately reflect the evaluation of a certain thing by the decision maker,so it has received more attention.According to the two-dimensional linguistic variables,we define the improved operation rules of two-dimensional linguistic variables,and put forward four kinds of two-dimensional partition based ensemble operators and corresponding multiple attribute decision making methods.The main work and results of this paper are as follows:1.Based on two dimensional linguistic variables,the operation rules of I dimensional variables are improved.The operation rules and properties of two dimensional linguistic variables are proposed,and their properties and distance formulas are proved.2.Based on the traditional information integration operator,a new partition information integration operator is proposed in view of the existing problems,including partitioned Bonferroni Mean operator,partitioned Heronian Mean operator,partitioned Maclaurin Symmetric Mean operator and partitioned Muirhead Mean operator.3.Four aggregation operators based on the 2DLVs are proposed,such as 2DLPBM,2DLPHM,2DLPMSM and 2DLPMM operators.We also research the properties of these operators,such as,commutativity,idempotence,boundness.At the same time,the corresponding multiple attribute decision making method based on 2DLVs is given.The case of investment company selection proves that the method is effective,and further analyzes the influence of different parameter values on the final decision results.