Abstract
In this paper we will study fuzzy systems, analyzing their origin, various ways of their characterization and fundamental problems associated with them. A thorough discussion is centered around types of fuzzy systems, their relevancy and its influence on the formulation of so-called direct and inverse tasks. Moreover, a theory of relational equations as applied to system analysis is investigated. Special attention is focussed on links between the theory of fuzzy systems viewed from a standpoint of general system theory and a variety of applications (e.g., control, knowledge-based system, pattern recognition etc.). Then, specific interpretations to direct and inverse problems are given, bearing in mind the selected area of application.