The concept of \textit{fuzzy set} of [\textit{L. A. Zadeh}, Inf. Control 8, 338--353 (1965; Zbl 0139.24606)] motivated the development of fuzzy real analysis. In particular, the notion of \textit{fuzzy number} was introduced and basic operations with such new structures were considered (see, e.g., [\textit{D. Dubois} and \textit{H. Prade}, in: Analysis of fuzzy information, Vol. 1: Math. logic, 3--39 (1987; Zbl 0663.94028)] for a convenient overview). The paper under review considers an important issue with fuzzy numbers, i.e., the way(s) of their comparison. Given two real numbers \(a\) and \(b\), it is easy to tell whether \(a\leqslant b\) or \(b\leqslant a\) (or both, if \(a=b\)). In case of fuzzy numbers, the answer is not at all that trivial, and there already exist numerous fuzzy number comparison techniques (see, e.g., the above paper of Dubois and Prade [loc. cit.]). The authors of the present paper suggest two alternative ways of comparing fuzzy numbers. Both of them rely on the level sets of a fuzzy number (recall that given a fuzzy set \(\mu_A:X\rightarrow[0,1]\) in a set \(X\), where \([0,1]\) is the unit interval, for every \(\alpha\in[0,1]\), the \textit{\(\alpha\)-level set} of \(\mu_A\) (denoted by the authors \(A(\alpha)\)) is defined as the set \(\{x\in X\,|\,\alpha\leqslant\mu_A(x)\}\)). The first of the proposed methods applies a specific defuzzification procedure to the given fuzzy numbers, getting thus real numbers, which are then easy to compare. The second method assigns a value (from the unit interval \([0,1]\)) to the statement ``\(A\leqslant B\)'', where \(A\) and \(B\) are some fuzzy numbers. If this value is greater than or equal to \(0.5\), then one says that ``fuzzy number \(A\) is less than or equal to fuzzy number \(B\)''. Both methods are applied to the so-called \textit{triangular fuzzy numbers}, and, moreover, it is shown that the presented fuzzy number comparison techniques have the property of transitivity, i.e., \(A\leqslant B\) and \(B\leqslant C\) together imply \(A\leqslant C\). The paper is well written, contains all of its required preliminaries (which are quite straightforward), is easy to read, and will be of interest to all the researchers, who apply the theory of fuzzy numbers in their everyday work.