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

Abstract

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