This paper has been published in International Journal of Mathematical Problems in Engineering. vol. 2014 doi:10.1155/2014/989726. 2014. As: Haiqing Zhang, Aicha Sekhari, Yacine Ouzrout, and Abdelaziz Bouras. An Approach to Modify an Inconsistent Pairwise Comparison Matrix with Fuzzy or Crisp Elements to Fit Consistency Requirements Haiqing Zhang 1* , Aicha Sekhari * , Yacine Ouzrout * and Abdelaziz Bouras † * *DISP laboratory, University Lumiè re Lyon 2, France 160 Bd de l’Université 69676 Bron Cedex †Computer Science Dept., Faculty of Engineering Qatar University, Box. 2731, Doha, Qatar {aicha.sekhari, yacine.ouzrout}@univ-lyon2.fr abdelaziz.bouras@qu.edu.qa Abstract. Satisfying consistency requirements of pairwise comparison matrix (PCM) is a critical step in decision making methodologies. An algorithm has been proposed to find a new modified consistent PCM in which it can replace the original inconsistent PCM in analytic hierarchy process (AHP) or in fuzzy AHP. This paper defines the modified consistent PCM by the original inconsistent PCM and an adjustable consistent PCM combined. The algorithm adopts a segment tree to gradually approach the greatest lower bound of the distance with original PCM to obtain the middle value of adjustable PCM. It also proposes a theorem to obtain the lower value and the upper value based on two conditions: one is minimum fuzziness to reduce uncertainty factors that come from adjustable PCM, and the other one is maximum maintain of similarity to keep the original PCM’s pattern. The experiments for crisp elements show that the proposed approach can preserve more the original information than Cao et al. and Xu and Wei in the same consistent value. The convergence rate of our algorithm is significantly faster than the two references with respect to different parameters. The experiments for fuzzy elements show that our method could obtain suitable modified fuzzy PCMs by analyzing two effective parameters and two consistency indices. Keywords: AHP, Fuzzy AHP, pairwise comparison matrix, Preserve information, Uncertainty, Decision Making, Inconsistency 1 Introduction Analytic Hierarchy Process (AHP) is developed by Saaty [1], which is a multi-criterion decision-making methodology widely used in many real problems [11-12]. The AHP expresses the relative importance of criteria by pairwise comparisons and converts the values of pairwise comparisons to priorities. Fuzzy AHP methodology [13] is an advanced AHP methodology, which is used to tackle the uncertainty and inaccurate problems in multi-criteria decision-making process. Fuzzy AHP derives the fuzzy priorities of criteria from pairwise comparisons matrix with triangular (or trapezoidal) fuzzy elements. To make sure the priorities of each criterion are accurate and sensible, the consistency of Pairwise Comparison Matrix (PCM) with crisp or fuzzy elements must be achieved. 1 Corresponding Author. E-mail address: haiqing.zhang.zhq@gmail.com