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 toolfor dealing with fuzzy multi-criteria decision making (MCDM)problems by transforming the criterion value vectors of eachalternative into the corresponding criterion function vectors. Inthis paper, some concepts related to function vectors are firstdefined, such as the inner product of two function vectors, thecosine of the included angle between two function vectors and theprojection of a function vector on another. Then a method based onFSE is developed to solve fuzzy MCDM problems in which thecriterion values take the form of general bounded closed fuzzynumbers and the criterion weight information is incompletecertain. In this method, the projections of criterion functionvectors on the fuzzy ideal function point (FIFP) are used to rankall the alternatives and then select the most desirable one, andan optimization model is constructed to determine the weights ofcriteria according to the incomplete weight information. Finally,an example is given to illustrate the feasibility andeffectiveness of the developed method.