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

Linguistic variable has the advantages that using it to express the fuzzy information will be more convenient and reasonable. The multi-attribute group decision making(MADM) based on the two-dimension linguistic variable develops quickly and becomes a very important part of MADM. It will be more accurately that the two-dimension linguistic variable uses two dimensions to display the people’s evaluations.On the basis of two-dimension uncertain linguistic variables, we further propose a trapezoidal fuzzy two-dimension linguistic variable(TTLV). And we establish some aggregation operators based on the TTLV to supply new theories and approaches for solving MADM problems.(1) Based on the two-dimension linguistic variable,we further propose a trapezoidal fuzzy two-dimension linguistic variable(TTLV) by extending the I dimension linguistic uncertain information to trapezoidal fuzzy number. And the operation rules and properties,distance measure, expectation are introduced.(2) Three aggregation operators based on the TTLV are proposed, including TTFLGWA, TTFLGOWA, TTFLHWA operators.We also research the properties of these operators, such as, idempotence, monotonicity, boundness. The steps of the multi-attribute group decision making method based on TTLV are proposed, and we also analyze the influence of the different values of parameter.(3) Some Bonferroni Mean operators based on the TTLV are introduced, including TTFLBM, TTFLWBM, TTFLGBM, TTFLWGBM operators. We also study the properties and special cases of these operators mentioned above.The steps of the multi-attribute group decision making method based on TTFLWGBM are proposed and analyze the influence of the different values of parameter.(4) The trapezoidal fuzzy two-dimension linguistic prioritized ordered weighted aggregation operator(TTFLPOWA) which combining the prioritized operator and TTLV considers a number of aggregation operators in which exists a prioritization relationship between the arguments. The steps of the multi-attribute group decision making method based on TTFLPOWA are proposed, and we make a comparation with the grey incidencedecision-making method to verify its usefulness.