This chapter concerns an issue of comparing fuzzy numbers. The relationship of similarity is probably the most widely used and most difficult to determine the measure of compliance precisely. Analysis of the similarity between two objects is an essential tool in biology, taxonomy, and psychology, and is the basis for reasoning by analogy. This chapter describes methods for determining the similarity used in fuzzy logic. Many of them were dedicated only to triangular or trapezoidal fuzzy numbers. This was a computing inconvenience and raised the question about the axiological basis for such comparisons. The authors have proposed two new approaches to comparing fuzzy numbers using one of the known fuzzy number extensions that are Ordered Fuzzy Numbers (OFNs). This has allowed us to simplify operations and eliminate said dualism. Two order-sensitive defuzzification methods are presented in the chapter. For OFN numbers with positive order (compliant with the direction of the OX axis increase) the results of defuzzifications are results for numbers of different notations, for example, L-R, whereas for numbers with negative orders, the defuzzification result changes. An important part of the chapter is a catalogue of the shapes of numbers in OFN notation. This is probably the first summary of basic shapes of those numbers with the results of defuzzifications using several methods.

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