Fuzzy logarithmic least squares ranking method in analytic hierarchy process

✍ Scribed by Xu Ruoning; Zhai Xiaoyan

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 529 KB
• Volume: 77
• Category: Article
• ISSN: 0165-0114
• DOI: 10.1016/0165-0114(95)00073-9

✦ Synopsis

We have discussed the extensions of analytic hierarchy process in fuzzy environment and presented a procedure for constructing the fuzzy judgment matrix. This paper continues the discussion and goes further into the problem about extracting the fuzzy weights from the fuzzy judgment matrix by logarithmic least squares method, which is a main ranking method in analytic hierarchy process. First, we define the metric of the fuzzy judgment space and develop the expression form of logarithmic least squares method in fuzzy environment. Next, we derive the associated normal equations from the problem of fuzzy logarithmic least squares and prove that the solutions of fuzzy logarithmic least squares model are equivalent to the solutions of its normal equations. Finally, for every t e (0, I l, we can get its explicit solutions by solving the normal equations. The technique proposed in this paper is rather simple to realize and can be used for dealing with actual problems.