Role of Consistency in Analytic Hierarchy Process – Consistency Improvement Methods V. Shyam Prasad 1 * and P. Kousalya 2 1 Department of Mathematics, Gurunanak Institutions Technical Campus, Hyderabad – 501506, Telangana, India; Shyamnow4u@gmail.com 2 Department of Mathematics, Anna University, Sardar Patel Road, Guindy, Chennai – 600025, Tamil Nadu, India; Kousalya29@yahoo.com 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 devia- tion 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. *Author for correspondence 1. Introduction e AHP was originally introduced by Professor omas. L. Saaty in 1970, since then it has been used in many decision mak- ing situations. Consistency plays a vital role in AHP. It accepts some small Inconsistency in decisions (i.e., 10%). Pair wise comparison matrix obtained by decision maker must satisfy Saaty’s Consistency Ratio condition , if not decision maker has to revise his decisions and improve the Consistency Ratio to acceptable range (i.e., < 10%). ere are vital methods to develop the Consistency Ratio of com- parison matrix to acceptable range. Pelaez 1 postulated a New Measure of Consistency for Positive Reciprocal Matrices which is easily applicable Indian Journal of Science and Technology, Vol 10(29), DOI: 10.17485/ijst/2017/v10i29/100784, August 2017 ISSN (Print) : 0974-6846 ISSN (Online) : 0974-5645 to other types of reciprocal matrices; it is a function of the matrix size. e practical approach introduced by Xu Zehui 2 to improve the Consistency of Judgment matrix in the AHP, Which utilizes the eigen vector to revise a pair of its entries each time without disturbing the order of the matrix. Another method proposed by Dagi Ergu 3 to improve the consistency ratio of pairwise comparison matrix in ANP identifies the location of inconsistent ele- ments in comparison matrices. 2. Over View of AHP Analytic Hierarchy Process, a decision making approach designed for different multi criteria decision making Keywords: Analytic Hierarchy Process, Consistency, Multi Criteria, Pair Wise Comparison Matrix, Positive Reciprocal