关键词: 多属性决策, 层次分析法, 摆幅置权, 目标参照方案, 属性公度价值

Abstract: For multi-attribute hierarchies with non-specific attributes included, Saaty (1986,2006) has presented an approach of multiple attribute decision-making (MADM) to alternative evaluations/decisions, called the analytic hierarchy process (AHP), which has four specific types or application formats, namely AHP in the distributive mode (shorted as DIS-AHP), AHP in the absolute mode (ABS-AHP), AHP in the ideal mode (IDE-AHP) and AHP in the supermatrix mode (SUP-AHP). While AHP has widely been applied to real-world complex decisions, it, as well as its four specific types, has also suffered from a lot of academic criticisms, such as shortness of scientific rationality for lack of the reference-point of ratio comparisons, unclearness in the weights' meaning, and incapability of keeping alternative-evaluation ranking unchanged when an alternative is deleted from or a new alternative is added to the alternative set. To solve these shortcomings of AHP, three study efforts are made. First, based on the judgment mode of swing weighting (SW), and the approach to measure commensurable satisfaction values (CSV) of attribute performances in a MADM, a prescriptive approach to measure attribute-performances' CSVs in a MADM, called the prescriptive CSV approach, is presented to support the SW judgments on non-specific attributes in a multi-attribute hierarchy. The CSV of an alternative performance x_i(x_i ≥ x_i,1) on the i^th specific attribute is given by Mξ_i^**(α_i^*)(x_i-x_i,1)^α_i*/?_i^**+MF_i(x_i|π_i), where M denotes the number of target alternatives for reference, F_i(x_i|π_i) does the cumulative probability of x_i relative to the attribute-performance distribution π_i of target alternatives for reference in the i^th specific attribute, x_i,1 does the reference point given by the decision maker, and α_i^*,ξ_i^**(α_i^*),?_i^** are parameters determined by a linear programming model. Second, based on the prescriptive CSV approach, a SW-like judgement mode for weights of attributes in every hierarchy level is presented. Third, based on the SW-like judgement mode for level-attributes' weights and the multiple-attribute value theory, a new approach to alternative evaluations/decisions with a multi-attribute hierarchy, called targets-oriented AHP (ToAHP), is presented. Compared with AHP, ToAHP has the following three advantages. Firstly, ToAHP can guarantee that attribute weights given by the decision maker are of clear meanings because of the adoption of SW judgments on every level attributes. Secondly, ToAHP is constructed on the robust basis of multiple attribute value theory, rather than simply on the primitive notions as AHP is, and thus whether or not the proposition of absolute preference independence adopted in ToAHP, as is also done in AHP, is applicable can be tested. Thirdly, ToAHP takes such an one-by-one procedure to evaluate alternatives that can not only keep the alternative ranking unchanged even if the alternative set is changed, but also is intrinsically of strict mathematical basis to guarantee rationally the unchanged alternative ranking. A case study shows that, on comparable conditions of input information, ToAHP is greatly superior to SUP-AHP, which is the most believable one among the four specific formats of AHP. For the mentioned-above reasons, ToANP can be considered as a better substitute of AHP when AHP is required to solve real-world complex decisions.

Key words: multiple attribute decision-making, analytic hierarchy process, swing weighting, target alternative for reference, commensurable satisfaction value of attribute performance