An application used here to demonstrate the proposed method is in Section 4. The way to develop the CAHP is given in Section 3. In Section 2, we present the procedure of the AHP and uncover the limitation on the issue of correlation between criteria. The rest of this paper is organized as follows. It should be highlighted that the tradition AHP can be considered as the special case when we reduce our model to single-objective programming model. In addition, we propose a numerical example to demonstrate the proposed model and compare the result with the traditional AHP. A biobjective programming model is proposed to derive the result. The purpose of this paper is to propose the correlated analytic hierarchy process (CAHP) which can account for the correlation between criteria in the AHP. Hence, the AHP/ANP cannot be used in this situation. All we can say is that risk and return are correlated with each other. In addition, there is no evidence that risk can affect return and vice visa. However, it is irrational to assume that risk and return are independent of each other in the real world. The problem above can be solved by the AHP, because of the independent subcriteria. Two major criteria, that is, risk and return, are considered and can be divided into many independent subcriteria, respectively. Assume an investor is considering constructing a portfolio in a stock market. Let us consider the following investment situation to describe the insufficiency of the AHP/ANP as follows. The correlation between criteria is commonly observed in the realistic problems. Hereafter, the AHP/ANP is the most common tool in the field of decision making to deal with various effects between criteria. Hence, Saaty proposed the analytic network process to account for the effects of outer-dependence, inner-dependence, and feedback. However, there are other effects, such as inner-dependence and feedback, which should be considered to present the relationship between criteria. As we know, the AHP is used to derive the weights of criteria when they are independent and outer-dependent by the upper-level criteria. For example, Yu proposed a revised model to release the assumption of reciprocal matrix in the AHP and Huang extended the AHP to consider the fuzzy environments.Īlthough the past papers elaborated much work on the extension of the AHP, they seem to ignore the issue of correlation between criteria. To extend the capability of the AHP for dealing with more sophisticated problems, many methods have been proposed to revise or modify the limitations and defects of the AHP. The AHP should be the most popular method used in dealing with multicriteria decision making (MCDM) problems in the field of operations research/management science (OR/MS), according to the published journal papers. On the basis of dealing with MADM problems, the analytic hierarchy process (AHP) was proposed by Saaty to derive the relative weights according to the appropriate hierarchical system. Determine the best alternative according to the synthetic utility values, which are the aggregation value of relative weights and performance scores corresponding to alternatives. Obtain the relative weights and performance score of each attribute with respect to each alternative. Construct a hierarchy system for evaluation (as shown in Figure 1). Roughly speaking, the procedures of MADM can be comprised of five main steps as follows. Since Bernoulli proposed the concept of utility function to reflect human persuading, such as maximum satisfactory, and von Neumann and Morgenstern presented the theory of game and economic behavior model, which expanded the studies on human being economic behavior for multiple attribute decision making (MADM) problems, from that moment on, more and more literatures engaged in this field. Finally, a numerical example is given to justify the proposed method and compare the result with the AHP. Furthermore, the traditional AHP can be considered as the special case of the proposed model when the correlation effect between criteria is ignored. In addition, a biobjective programming model is proposed to derive the result. Hence, in this paper, we extend the AHP to consider the correlation effect. However, besides outer-dependence, correlation is another common effect between criteria which cannot be accounted for neither by the AHP nor by the analytic network process (ANP). Hence, only the effect of outer-dependence can be considered in the AHP. Construct a hierarchy system for evaluation by decision makers. The analytic hierarchy process (AHP) has been the most popular tool for the field of decision making in the past 30 years, because of its simplicity and rationality.
0 kommentar(er)
