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Weakly linear systems of fuzzy relation inequalities and their applications: A brief survey

Ignjatović Jelena (Faculty of Sciences and Mathematics, Niš)
Ćirić Miroslav (Faculty of Sciences and Mathematics, Niš)

Weakly linear systems of fuzzy relation inequalities and equations have recently emerged from research in the theory of fuzzy automata. From the general aspect of the theory of fuzzy relation equations and inequalities homogeneous and heterogeneousweakly linear systems have been discussed in two recent papers. Here we give a brief overview of the main results from these two papers, as well as from a series of papers on applications of weakly linear systems in the state reduction of fuzzy automata, the study of simulation, bisimulation and equivalence of fuzzy automata, and in the social network analysis. Especially, we present algorithms for computing the greatest solutions to weakly linear systems.

Keywords: fuzzy relations, fuzzy relational systems, fuzzy relation inequalities, fuzzy relation equations, matrix inequalities, residuals of fuzzy relations, fuzzy equivalence relations, complete residuated lattices, post-fixed points