The Preference Ranking Organization METHod for Enrichment of Evaluations and its descriptive complement geometrical analysis for interactive aid are better known as the Promethee and Gaia methods. Based on mathematics and sociology, the Promethee and Gaia method was developed at the beginning of the 1980s and has been extensively studied and refined since then. It has particular application in decision making, and is used around the world in a wide variety of decision scenarios, in fields such as business, governmental institutions, transportation, healthcare and education. Rather than pointing out a "right" decision, the Promethee and Gaia method helps decision makers find the alternative that best suits their goal and their understanding of the problem. It provides a comprehensive and rational framework for structuring a decision problem, identifying and quantifying its conflicts and synergies, clusters of actions, and highlight the main alternatives and the structured reasoning behind.