Minimal solutions of generalized fuzzy relational equations: Probabilistic algorithm based on greedy approach

The paper deals with generalized fuzzy relational equations that are defined within a recently introduced framework of sup-preserving aggregation structures. Generalized fuzzy relational equations subsume all previously studied types of fuzzy relational equations, namely those that are based on sup-t-norm and inf-residuum compositions. The paper contributes to previous studies of generalized fuzzy relational equations by presenting a method for constructing all minimal solutions and, consequently, for determining the whole solution set for any given generalized fuzzy relational equation that is solvable and for which every solution is bounded from below by a minimal solution. Moreover, in the paper we present a simple probabilistic algorithm for finding all minimal solutions.