  New types of systems of fuzzy relation inequalities and equations, called
weakly linear, have been recently introduced in [J. Ignjatovi\'c, M. \'Ciri\'c,
S. Bogdanovi\'c, On the greatest solutions to weakly linear systems of fuzzy
relation inequalities and equations, Fuzzy Sets and Systems 161 (2010)
3081--3113.]. The mentioned paper dealt with homogeneous weakly linear systems,
composed of fuzzy relations on a single set, and a method for computing their
greatest solutions has been provided. This method is based on the computing of
the greatest post-fixed point, contained in a given fuzzy relation, of an
isotone function on the lattice of fuzzy relations. Here we adapt this method
for computing the greatest solutions of heterogeneous weakly linear systems,
where the unknown fuzzy relation relates two possibly different sets. We also
introduce and study quotient fuzzy relational systems and establish
relationships between solutions to heterogeneous and homogeneous weakly linear
systems. Besides, we point out to applications of the obtained results in the
state reduction of fuzzy automata and computing the greatest simulations and
bisimulations between fuzzy automata, as well as in the positional analysis of
fuzzy social networks.
