The multiple attribute decision making problems are studied, in which the information about attribute weights is partly known and the attribute values take the form of intuitionistic fuzzy numbers. The operational laws of intuitionistic fuzzy numbers are introduced, and the score function and accuracy function are presented to compare the intuitionistic fuzzy numbers. The intuitionistic fuzzy ordered weighted averaging (IFOWA) operator which is an extension of the well-known ordered weighted averaging (OWA) operator is investigated to aggregate the intuitionistic fuzzy information. In order to determine the weights of intuitionistic fuzzy ordered weighted averaging operator, a linear goal programming procedure is proposed for learning the weights from data. Finally, an example is illustrated to verify the effectiveness and practicability of the developed method.
The group decision making problem with linguistic preference relations is studied.The concept of additive consistent linguistic preference relation is defined,and then some properties of the additive consistent linguistic preference relation are studied. In order to rank the alternatives in the group decision making with the linguistic preference relations,the weighted average is first utilized to combine the group linguistic preference relations to one linguistic preference relation,and then the transformation function is proposed to transform the linguistic preference relation to the multiplicative preference relation,and thus the Saaty's eigenvector method(EM) of multiplicative preference relation is utilized to rank the alternatives in group decision making with the linguistic preference relations.Finally,an illustrative numerical example is given to verify the proposed method.A comparative study to the linguistic ordered weighted averaging(LOWA) operator method is also demonstrated.
