Interval Multiple Attribute Decision Making Research

Multiple attributes decision making (also be named as multiple objects decision making for limited projects) is an important branch of modern decision science. Its theory and method are widely applied to a good many areas, such as economics, management, engineering, military affairs, and so forth. In the fundamental research aspect, the multi-attribute decision-making since its birth have been always the research topics which the academic circles pays attention. In recent years, the uncertainty multi-attribute decision-makings have aroused academic circle's widespread interest, and interval multi-attribute decision-making is one of them. Because the decision-maker frequently must face the complex thing and the uncertain environment, or because of their fuzzy thought, the decision-maker frequently cannot or difficult to produce a crisp number of the decision information, but often easy to produce the upper limit and the lower limit of the decision information, that is to say, easy to produce the decision information in the form of interval numbers. The multi-attributes decision-making problem is often a qualitative question, and its fuzziness is more remarkable, which results in that interval multi-attribute decision-making arouses the academic circles enormous interest. Therefore, the research on interval multi-attribute decision-making has important theoretic significance and higher practical application value.The interval multi-attribute decision-making is composed by two parts: modeling part, synthesis and application part. This article is organized according to the two parts.1. ModelingFirst, we introduced how to compute interval weight vector using interval AHP, which is proposed by Wei Yi-qiang, a Chinese scholar. Then aims at the existing literature rarely propose any reasonable consistency test standard for interval judgment matrix, we proposed a reasonable test standard. This standard not only has a successive relation with the traditional standard for crisp judgment matrix, but also gives certain relaxing to the fuzziness which results from interval numbers. And detail argumentation of the relaxing degree has made in the article.Next, if the judgment matrix dissatisfied consistency test, it needs to be adjusted. This article first introduced the existing adjust methods for judgment matrix of crisp AHP. Then a method named as foresight algorithm, is proposed for judgment matrix of crisp AHP, according to the thought that "adjust the most inconsistent element towards the direction which can improve the consistency of judgment matrix mostly". Compared with the existing methods, this method has a bigger superiority in maintaining primitive judgment information. Therefore, we extend the foresight algorithm to an interval one, to adjust the inconsistent interval judgment matrix of interval AHP. In this way, the modeling completes.2. Synthesis and application According to the multi-attribute decision-making application, this part divides into two parts again: ranking and rating.Ranking: We first briefly introduced the existing ranking methods of interval multi-attribute decision-making, and made a brief commentary. We discovered that the interval number evaluation exactly divides its value range into three parts, which is very similar to dividing the universe into three parts in the Set-Pair-Analysis theory. By referencing to the thought that dividing the universe into three parts, we proposed a new ranking method for interval multi-attribute decision-making, which is named as A Set-Pair-Analysis based method for interval multi-attribute decision-making. We not only gave the detail process, but also analyzed the rationality of the ranking criteria for the ranking method and illustrated the process by a sample. Compared with the existing methods, the proposed method is more simply and conveniently, and its ranking rule has more intuitional meanings. Furthermore, by summarizing the proposed method, we gained a byproduct, which is "A Set-Pair-Analysis based ranking method for interval numbers", to rank the general interval numbers.Rating: We first briefly introduced the rating problem, and then we present in detail the enterprise credit rating, a common case of rating. After outlining some enterprise credit rating methods, we introduced a survey on enterprise credit rating in our country. Then we attempted to apply interval multi-attribute decision-making to the enterprise credit rating problem, and illustrated the process by the case of small-medium-enterprise (SME) credit rating. We mainly introduced establishing the rating index system, computing the corresponding interval weight vector, and how to evaluation the credit of the SME.Finally, we pointed out some deficiencies in this article that needs improvement and the direction of further research..