Sorting Method And Its Application For The Multi-Attribute Decision Based On Ordered Information Systems

Rough set theory proposed to deal with uncertainty issues usher in a new life with its continuous improvement, Dominance relation as an extension and expansion of rough set theory, it has caused widely concerned because it can better deal with the comparison problem between different programs in the uncertain decision-making. Reasonable and effective sorting methods have been a research focus and difficulty in the field of multi-attribute decision-making. However, current sorting methods often have their individual defects and difficult to obtain unanimous recognition in academic community, and there is fewer sorting method based on dominance relations. In view of this, promoting ordered information system and dominance relation in the multi-attribute decision-making, several sorting methods based on dominance relation are proposed in this paper. The order-preserving reduction, the inconsistent issue of ordered information systems are researched. Some preliminary achievements are got in this paper, which generalize the rough set theory’attribute reduction theory and application in the field of management decision, perfect the sorting method of multi-attribute decision, and enrich the data preprocessing methods and evaluation methods of sorting results’reliability. The mainly research and achievement of this paper are as follow: Firstly, Through access to domestic and foreign research status’make systematically summarizes on the rough set theory, ordered information systems and dominance relation, sorting methods of multi-attribute decision-making. By analyzing achievements and deficiencies of the existing research, the further study direction is determined.Secondly, based on analyzing the deficiencies of existing dominance relation’s sorting methods, the sorting formula is improved and its good mathematical properties are proved. Then the new sorting method based on dominance matrix is proposed. Hereafter, the concept of order-preserving reduction is put forward, and four types of reductions with descending order preserving strength are defined.Thirdly, against the failure that dominance sorting method may face when it applied to practical, by combining the advantages of analytic hierarchy process in dealing index system, the sorting hierarchy process (SHP) based on the combination of dominance sorting method and analytic hierarchy processis is proposed, and an application example of the energy evaluation is given.Lastly, against the possible decision mistakes may cause in inconsistent ordered decision system, the consistent amendment heuristic algorithm (CAA) is proposed by defining two indicators of decision information entropy and inconsistent degree, and simulation experiments are used to verified the algorithm’s feasibility and effectiveness. The algorithm enrich the data’s preprocessing methods and sorting effectiveness evaluation methods.