Abstract. The author proposes a method of elements ranking in multi-functional system using the fuzzy relations theory. The problem is formulated as an automatic classification based on the transitive closure of the fuzzy similarity relation. This allows splitting the set of system elements into disjoint classes, which are similar in importance. The expert information about multi-functional system is given in the form of fuzzy relation of influence of the element’s failures on the system’s functions performance. To calculate the degree of element’s influences on the functions performance we use the comparison of all influences with the least influence by 9-point Saaty scale. The proposed method relaxes the assumption about the independence and the binary-state (up-down) of elements. The possible fields of applications are multi-functional systems with ill-defined structures such as organizational, ergatic, military, etc.

Keywords: multi-functional system, uncertainty, importance of element, fuzzy relation, automation classification.