Path problem in multi-criteria ranking and generalization of AHP

LIU Kai-di, PANG Yan-jun, ZHOU Shao-ling, MA Li-tao, LI Wen-guo

Systems Engineering - Theory & Practice ›› 2015, Vol. 35 ›› Issue (4) : 973-983.

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Systems Engineering - Theory & Practice ›› 2015, Vol. 35 ›› Issue (4) : 973-983. DOI: 10.12011/1000-6788(2015)4-973

Path problem in multi-criteria ranking and generalization of AHP

  • LIU Kai-di, PANG Yan-jun, ZHOU Shao-ling, MA Li-tao, LI Wen-guo
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Abstract

It is pointed out that multi-criteria ranking metric transformation is realized by matrix multiplication in AHP is wrong. In fact this kind of transformation is concerned with path. Multi-criteria ranking is multipath. Multipath ranking metric transformation is nonlinear and can't use matrix multiplication. So ranking metric is mapped into high dimensional spaces and is expressed by uncertain membership vector. Then ranking metric transformation is changed into membership transformation. It is proved that membership transformation is nonlinear and can be realized by classification weight filter. Nonlinear ranking model of multi-criteria is built up.

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AHP / multi-criteria ranking / ranking metric transformation / nonlinear / classification weight filter

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LIU Kai-di , PANG Yan-jun , ZHOU Shao-ling , MA Li-tao , LI Wen-guo. Path problem in multi-criteria ranking and generalization of AHP. Systems Engineering - Theory & Practice, 2015, 35(4): 973-983 https://doi.org/10.12011/1000-6788(2015)4-973

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