Algorithms for solving fuzzy relational equations in a probabilistic setting (Q803132)

The author discusses methods suitable for finding approximate solutions to fuzzy relational equations defined in finite universes of discource and taking the form of either a system of equations \(X_ k\cdot R=Y_ k\), \(k=1,2,...,K\) (with R being an unknown fuzzy relation), or a single equation \(X\cdot R=Y\) (with X being looked for). The key idea of the proposed algorithms is to incorporate some statistics concerning the solution of a single equation and utilize it in the final process of approximation of the unknown fuzzy relation (set). Numerical considerations support the established algorithms.