Interval Multi-attribute Group Decision-making Method Research

Multi-attribute decision-making problem is the important branch of contemporary decision science. Its theory and method apply to many domains such as economy, administration and military widely. In theoretical research, multi-attribute decision-making has been research topics concerned by academic world since its inception. However, in actual decision-making there are a large number of uncertain multi-attribute group decision-making problems due to the complexity of decision-making problems. This decision-making variables use of currently interval numbers such as uncertain information model to express, and also reduce irrational decision-making factors by assembling expert groups` preference. The method of interval multi-attribute group decision-making problems is comparatively in line with the ambiguity and uncertainties of human thinking. This method can assemble wisdom of group experts and is suitably to deal with the complexity decision-making problems in modern society. It is worth to be researched deeply. There are three problems in the process of interval multi-attribute group decision-making: puts interval numbers in order, assembles expert groups` different form preference information and determines attribute weights. The work of this paper on the basis of previous scholars is as follows:1. A kind of assembly model which is based on projection method is proposed in connection with expert groups'interval multiplication preference information and interval reciprocal preference information. Firstly, the interval multiplication judgment matrix is unified into the interval reciprocal judgment matrix. Secondly, this paper transforms interval reciprocal judgment matrix to reciprocal judgment matrix and discusses the conformity and maintenance in transformation processes. Finally, a method in view of projection model is given to assemble preference information of groups.2. It is put forward how to determine attribute weights in the environment of interval multi-attribute group decision-making. Firstly, expert groups set up interval judgment matrix toward attribute preferences. Secondly, attribute subjective weights can be obtained by way of assembling. Finally, this paper defines interval numbers mean deviations and establishes mean difference maximization model to get attribute objective weights.3.Because of objectivity of subjective empowering method being poor and weights determined through objective empowering method running counter to the degree of practical significance probably, this article proposes two attribute weights combinatorial optimization methods that simple linear weighting method and maximum entropy-based optimization method.Simple linear weighting method is relatively simple and intuitional. It is favorable to judge for decision-makers according to their own preferences. Then maximum entropy-based optimization method needs strong mathematical background.This paper provides interval multi-attribute group decision-making methods of the basic framework and basic decision-making flow and applies the method into E-commerce site selection problem to demonstrate its feasibility.