Study On The Order Preserving Problem Of Uncertain Multi-attribute Decision Making

Decision-making is common in human daily life,and affects people's lives.With the development of the society and the times,all kinds of decision-making problems become more and more complex.In the existing uncertain decision theory,some decision methods which result in the inconsistency between the ranking results and the preference of decision makers have defects,which produces the inconsistency of decision information in the decision-making process.Based on this,this paper studies a series of order preserving problems of uncertain multi-attribute decision-making.The main contents are as follows:(1)In this paper,we propose the concepts of additive dominance and multiplicative dominance of interval numbers.By using the advantage degree of interval numbers to make indirect comparison of interval numbers,a consistent fuzzy preference relation is constructed to ensure the consistency of decision information and the consistency of the whole decision-making process,and overcome the decision-making errors caused by the inconsistency of decision information.On this basis,a multi-attribute decision-making method of interval numbers based on thedominance is proposed to improve the ranking theory of interval numbers.(2)In this paper,the concepts of indirect weak transitivity of a fuzzy preference relation and a morbid fuzzy preference relation are put forward respectively.It is proved that if a fuzzy preference relation has indirect weak transitivity,there is a consistent fuzzy preference relation,which makes the scheme order relation determined by its elements is consistent with the scheme order relation determined by the original fuzzy preference relation elements.This paper presents an improved method to deal with morbid fuzzy preference relations and two new ranking algorithms to deal with inconsistent fuzzy preference relations.On the basis of theoretical research,this paper gives relevant examples for the new methods proposed,and demonstrates the feasibility of the methods.At the same time,it also makes a comparative analysis among the methods proposed in this paper and the common methods,and proves that the methods proposed in this paper are able to keep the consistency of decision-making process and overcome the fact that the common methods may lead to the inconsistency between the ranking result and the decision maker's preference.