Sec. 11. INVESTIGATIONS. The board shall consider all cases for the retirement and pension of the members of the fire and police departments rendered necessary or expedient under the provisions of this law, and all applications for pensions by widows and the children and of dependent relatives, and the said trustees shall give written notice to persons asking a pension to appear before said board and offer such sworn evidence as he or they may desire. Any person who is a member of either of said departments and who is a contributor to said fund may appear either in person or by attorney and contest the application for participation in said fund by any person claiming to be entitled to participate therein, and may offer testimony in support of such contest. The president or chairman of said board shall have authority to issue process for witnesses and administer oaths to said witnesses and to examine any witness as to any matter affecting retirement or a pension under the provisions of this law. Such process for witness shall be served by any member of the police or fire department and upon the failure of any witness to attend and testify, he or she may be compelled to attend and testify, as in any judicial proceeding.