Fuzzy Optimization and Decision Making

, Volume 17, Issue 2, pp 195–209 | Cite as

Deriving crisp and consistent priorities for fuzzy AHP-based multicriteria systems using non-linear constrained optimization

  • Raman Kumar GoyalEmail author
  • Sakshi Kaushal


Fuzzy optimization models are used to derive crisp weights (priority vectors) for the fuzzy analytic hierarchy process (AHP) based multicriteria decision making systems. These optimization models deal with the imprecise judgements of decision makers by formulating the optimization problem as the system of constrained non linear equations. Firstly, a Genetic Algorithm based heuristic solution for this optimization problem is implemented in this paper. It has been found that the crisp weights derived from this solution for fuzzy-AHP system, sometimes lead to less consistent or inconsistent solutions. To deal with this problem, we have proposed a consistency based constraint for the optimization models. A decision maker can set the consistency threshold value and if the solution exists for that threshold value then crisp weights can be derived, otherwise it can be concluded that the fuzzy comparison matrix for AHP is not consistent for the given threshold. Three examples are considered to demonstrate the effectiveness of the proposed method. Results with the proposed constraint based fuzzy optimization model are more consistent than the existing optimization models.


MCDM Fuzzy AHP Genetic Algorithms Pairwise comparison judgements Priority vector 



The authors would like to thank University Institute of Engineering and Technology, Panjab University, Chandigarh, India for providing the research facilities for carrying out this research. The author Raman Kumar Goyal would also like to thank Technical Education Quality Improvement Programme (TEQIP)-II for providing the financial assistance during the course of study.


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© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Department of Computer Science and Engineering, University Institute of Engineering and TechnologyPanjab UniversityChandigarhIndia

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