When members of an organization feel involved in the decision-making process and perceive that process as fair, they are more likely to accept tough decisions?

That statement is true.

When members are involved in the decision-making process, they would more likely to understand the current problem that company face and the options that the organization could afford to take. This would make the members much more likely to understand the reason behind though decisions that are taken by the organization.

Yes. With the increased perception of transparency in the process, organization members are less likely to feel that their opinion and general well-being is neglected in the decision-making process, and their involvement in the process means that they themselves are in part responsible for the formulation of any tough decision made. This responsibility, coupled with the emotional and time investment needed to make tough decisions, means that organization members are cognizant of and willing to acknowledge the rationale behind the necessity of any tough decisions made.