System of fuzzy relation equations with inf-→ composition: Complete set of solutions

The problem of solvability of a system of equations with inf-→ composition is considered on finite universes. Equations are expressed using operations of a BL-algebra. We study complete set of solutions of the respective system in the particular case (one equation) and in the general case. In both cases, various conditions of solvability are found and proved. We characterize all maximal solutions and prove that under certain conditions each solution of the system (an equation) is less than or equal to a respective maximal one. As a result, we are able to characterize the complete set of solutions. Examples of single equations and their systems are considered and complete sets of solutions are found for each.