Fuzzy relational equations employing Dragonfly operations

This article studies solvability of system of fuzzy relational equations where the antecedents and the consequents may suffer from missing values. We use the operations from the Dragonfly algebra that we have recently proposed as a specific algebra for partial fuzzy set theory for dealing with missing values especially when constructing fuzzy relational compositions. To investigate the solvability of the new system, we build an implicative model mirroring the shape of the standard implicative model and then we focus on the possible difference between the inferred outputs using such a model and the consequents appearing in the system of fuzzy relational equations. Furthermore, assuming the solvability of the system and some additional conditions, we show that it is possible to determine a solution of the system derived from the built implicative model by slight modifications.