Simplification of decision making matrix in fuzzy multiple attribute decision making

In the multiple attribute decision making, the computational intensity of problems quickly increases with the number of attributes increases. In this paper, we will introduce the simplification theory and technology of decision matrix in fuzzy multiple attribute decision making, and propose an attribute reduction algorithm. The purpose of this algorithm is to find all of the simplest order-preserving attribute subsets and the order-preserving attribute core of the corresponding multiple attribute decision making problem. One of the simplest order-preserving attribute subsets will be exploited as a substitute of the original attribute set. Thus the original multiple attribute decision making problem could be simplified and unnecessary cost related to redundant attributes could be saved. Finally, an illustrative numerical example is given to demonstrate our approach. And through this example, a dissimilarity between the attribute reduction in decision making and the knowledge reduction in rough set theory is discovered.