Fuzzy multi-criteria decision making method based on fuzzy structured element with incomplete weight information

The fuzzy structured element (FSE) theory is a very useful tool for dealing with fuzzy multi-criteria decision making (MCDM) problems by transforming the criterion value vectors of each alternative into the corresponding criterion function vectors. In this paper, some concepts related to function vectors are first defined, such as the inner product of two function vectors, the cosine of the included angle between two function vectors and the projection of a function vector on another. Then a method based on FSE is developed to solve fuzzy MCDM problems in which the criterion values take the form of general bounded closed fuzzy numbers and the criterion weight information is incomplete certain. In this method, the projections of criterion function vectors on the fuzzy ideal function point (FIFP) are used to rank all the alternatives and then select the most desirable one, and an optimization model is constructed to determine the weights of criteria according to the incomplete weight information. Finally, an example is given to illustrate the feasibility and effectiveness of the developed method.