Soft Computing

, Volume 22, Issue 5, pp 1641–1650 | Cite as

Fuzzy multi-criteria decision making on combining fuzzy analytic hierarchy process with representative utility functions under fuzzy environment

  • Yu-Jie Wang
Methodologies and Application


In 1980, Saaty proposed the analytic hierarchy process (AHP) to evaluate alternatives with multi-criteria being multi-criteria decision making. Then, numerous approaches engaged on extension of AHP under fuzzy environment named fuzzy analytic hierarchy process (FAHP) for evaluation of multi-criteria alternatives under fuzzy environment being fuzzy multi-criteria decision making (FMCDM). In the current approaches, the extent analysis method proposed by Chang in 1996 was a famous FAHP method for FMCDM. However, computing priorities in matrix by Chang’s method is difficult for comparing pairwise fuzzy numbers, and calculating possibility degrees has drawback for some special fuzzy numbers. To resolve above ties, we combine FAHP with representative utility functions under fuzzy environment. Through combination of FAHP and representative utility functions to FMCDM, our method easily and quickly solves FMCDM problems.


Fuzzy analytic hierarchy process (FAHP) Fuzzy numbers Pairwise comparison matrix Priorities Representative utility functions 



This research work was partially supported by the National Science Council of the Republic of China under Grant No. NSC 101-2410-H-346-001-.

Compliance with ethical standards

Conflict of interest

The author declares that there is no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

Informed consent

Based on above, “Informed consent” is unnecessary.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of Shipping and Transportation ManagementNational Penghu University of Science and TechnologyPenghuTaiwan, ROC

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