Analysis of normalization technique on multi objective preference analysis method

Abstract

Normalization is a critical step in multi-criteria decision analysis (MCDA) because it influences ranking consistency and decision reliability. This study evaluates the effects of four normalization techniques linear max, linear max-min, linear sum, and semi-linear vector, within the multi objective preference analysis (MOPA) framework using a tourism development case involving 18 alternatives and 8 decision criteria with both cost and benefit attributes. The techniques were compared based on ranking behavior, discriminative capability, and robustness using statistical and non-parametric validation. The results show that linear max-min normalization provides the strongest discriminative performance and the most significant statistical results, while semi-linear vector demonstrates high ranking stability and balanced sensitivity. In contrast, linear sum and linear max exhibit lower discriminative capability under the evaluated conditions. Kendall's tau and robustness analyses further confirm that normalization choice significantly affects ranking consistency and decision reliability. These findings provide practical guidance for selecting appropriate normalization techniques and support the development of more reliable MCDA-based decision-making models for complex applications, including sustainable tourism planning.