![Sample our Engineering & Technology journals, sign in here to start your access, latest two full volumes FREE to you for 14 days]({"type":"image" , "src" : "/sda/5933/TOC-Subject-Sample-2021-Engineering-Tech.jpg"})
Abstract
The set of solutions of the $-fuzzy relation equation over finite spaces with values from linear lattice is considered. It is shown, that there exist solutions with various known types of the fuzzy transitivity, while the maximum solution has a special new type of so-called α-transitivity. An interesting convergence property of natural powers of the maximum solution is presented. That result and analogous ones, which hold for other types of transitive solutions, are applied for the analysis of the convergence of fuzzy systems described by $-fuzzy relation equations. In such a way, a new conceptual model for the behaviour of fuzzy systems is provided.