Common solutions to some extended system of fuzzy ordered variational inclusions and fixed point problems

The main aim of this work is to use the XOR-operation technique to find the common solutions for a new class of extended system of fuzzy ordered variational inclusions with its corresponding system of fuzzy ordered resolvent equations involving the $\oplus$ operation and fixed point problems, which are slightly different from corresponding problems considered in several recent papers in the literature and are more advantageous. We establish that the system of fuzzy ordered variational inclusions is equivalent to a fixed point problem and a relationship between a system of fuzzy ordered variational inclusions and a system of fuzzy ordered resolvent equations is shown. We prove the existence of a common solution and discuss the convergence of the sequence of iterates generated by the algorithm for a considered problem. The iterative algorithm and results demonstrated in this article have witnessed, a significant improvement for many previously known results of this domain. Some examples are constructed in support of the main results.