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Role of Consistency in Analytic Hierarchy Process – Consistency Improvement Methods


  • 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


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.


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

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