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This chapter provides an introduction to multi-criteria decision making methods and specifies the focus of the book. It identifies critical issues related to multi-criteria decision making methods based on fuzzy pairwise comparison matrices and large-dimensional pairwise comparison matrices and derives the key research questions of the book. It provides a motivational example demonstrating the necessity of using constrained fuzzy arithmetic in the fuzzy extension of pairwise comparison methods. The example is explained in simple words and is easily understandable also to non-expert readers. This example is highly recommended to anyone interested in fuzzy pairwise comparison methods or in general in fuzzy arithmetic.