Extensions of the analytic hierarchy process in fuzzy environment

The aim of this paper is to extend the analytic hierarchy process (AHP) to the fuzzy environment. Firstly, starting from the viewpoint of actual application, considering the method of group decision-making in complex systems and the fuzziness of judgment in pairwise comparison of projects, we constr...

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Bibliographic Details
Published in:Fuzzy sets and systems 1992-12, Vol.52 (3), p.251-257
Main Authors: Ruoning, Xu, Xiaoyan, Zhai
Format: Article
Language:English
Subjects:
Analytic hierarchy process (AHP)
Applied sciences
continuous scale interval
criterion
Decision theory. Utility theory
Exact sciences and technology
judgment matrix
Operational research and scientific management
Operational research. Management science
positive bounded closed fuzzy number
scale
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Summary:The aim of this paper is to extend the analytic hierarchy process (AHP) to the fuzzy environment. Firstly, starting from the viewpoint of actual application, considering the method of group decision-making in complex systems and the fuzziness of judgment in pairwise comparison of projects, we construct the fuzzy judgement matrix by using a set-valued statistics method on continuous judgment matrix and prove that every element of the fuzzy judgment scale can be represented by a positive bounded closed fuzzy number. After a discussion of the properties of a positive bounded closed fuzzy number, the fuzzy weight vector of projects can be introduced by applying the fuzzy extension principle to the altered gradient eigenvector method. Thus, the rank-ordering of projects is given. Finally, we also give an example to apply our model.
ISSN:0165-0114
1872-6801
DOI:10.1016/0165-0114(92)90236-W