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Role of Consistency in Analytic Hierarchy Process – Consistency Improvement Methods

Affiliations

  • Department of Mathematics, Gurunanak Institutions Technical Campus, Hyderabad – 501506, Telangana, India
  • Department of Mathematics, Anna University, Sardar Patel Road, Guindy, Chennai – 600025, Tamil Nadu, India

Abstract


Background / Objectives: Analytic Hierarchy Process is considered to be one of the applicable decision making techniques developed by Thomas. L. Saaty in 1970s. Consistency plays vital role in AHP. The objective is to improve the Consistency Ratio of Pair wise Comparison Matrix if it is more than 10%. Methodology: The research paper focuses on consistency in Analytic Hierarchy Process and two methods of consistency to improve the consistency ratio of pairwise comparison matrix. Findings: In this paper we used two methods to improve the C.R of Comparison Matrix. It has been observed that the first method identifies the location of inconsistent elements in comparison matrix which may deviate the order of comparison matrix to change. The second method improves the consistency ratio of comparison matrix without deviation in the order of matrix. Applications: Multiplication of matrices, Dot product of Vectors and Definitions of Pair Wise comparison Matrix have been used to identify the Inconsistent Elements and MATLAB is used to find the Eigen Values of Comparison Matrix.

Keywords

Analytic Hierarchy Process, Consistency, Multi Criteria, Pair Wise Comparison Matrix, Positive Reciprocal

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References


  • Pelaez JI, Lamata MT. A new measure of consistency for positive reciprocal matrices. International Journal of Computers and Mathematics with Applications, Elsevier, ScienceDirect. 2003 Dec; 46(12):1839–45. Crossref
  • Deturck DM. The approach to consistency in the analytic hierarchy process. Mathematical Modeling, Elsevier, ScienceDirect. 1987; 9(3–5):345–52. Crossref
  • Ishizaka A, Lusti M. An expert model to improve the consistency of AHP matrices. International Transactions in Operational Research. 2004 Jan; 11(1):97–105. Crossref
  • Zeshui X. A practical method for improving consistency of judgment matrix in the AHP. Journal of System Sciences And Complexity. 2004 Apr; 17(2):169–75.
  • Ergu D, Kou G, Shi Y, Peng Y. A simple method to improve the consistency of pair – wise comparison matrix in ANP. European Journal of Operational Research, Elsevier, ScienceDirect. 2011 Aug 16; 213(1):246–59. Crossref
  • Kousalya P, Rabindranath V, Vizayakumar K. Student absenteeism in engineering colleges: evaluation of alternatives using AHP. Journal of Applied Mathematics and Decision Sciences. 2006 Sep 24; 2006:1–26. Crossref
  • Prasad VS, Kousalya P. Consistency of pair wise comparison matrix in analytic hierarchy process-an illustration. Mathematical Sciences International Research Journal. 2015; 4(1):137–43.
  • Prasad VS, Kousalya P. Selection of a leader for a company by using prioritization methods of analytic hierarchy process – an illustration. Journal of Advances in Mathematics. 2014 Aug; 10(7):3619–27.
  • Prasad VS, Kousalya P. Analytic hierarchy process – an efficient decision making technique. Global Journal of Pure and Applied Mathematics. 2015; 11(2):224–8.
  • Saaty TL. Decision making with the AHP-why the principal eigenvector necessary. European Journal of Operational Research, Elsevier, ScienceDirect. 2003 Feb 16; 145(1):85– 91. Crossref
  • Saaty TL. Theory and applications of analytic network process-decision making with benefits, opportunities, costs and risks. pittsburg, Pennsylvania: RWS publications; 2005 Jul 1. p. 352.
  • Saaty TL. The analytic network process. Decision Making with the Analytic Network Process, International Series in Operations Research and Management Science, Springer. 2006; 95:1–26.
  • Crossref
  • Golany B, Kress M. A multi criteria evaluation of methods for obtaining weights from ratio – scale matrices. European Journal of Operational Research, Elsevier, ScienceDirect.1993 Sep 10; 69(2):210–20.
  • Crossref
  • Mikhailov L. A fuzzy programming method for deriving priorities in the analytic hierarchy process. Journal of Operational Research Society. 2000 Mar; 51(3):341–9. Crossref. Crossref
  • Zahedi F. A simulation study of estimation methods in the analytic hierarchy process. Socio-Economic Planning Sciences, Elsevier, ScienceDirect. 1986; 20(6):347–54. Crossref
  • Saaty TL. Eigen vector and logarithmic least squares. European Journal of Operational Research, Elsevier, ScienceDirect.1990 Sep 5; 48(1):156–60. Crossref
  • Srdjevic B. Evaluation of storage reservoir purposes by means of multi criteria optimization models. Journal of Water Resources Vodoprivreda. 2002; 34(195–200):35–45.
  • Watson SR, Freeling A. Comment on: assessing attribute weights by ratios. OMEGA: International Journal of Management Science. 1983; 11:1–13.

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