It shall be the duty of the Board of Zoning Appeals to hear and determine appeals made for exceptions to and variations in the application of the zoning ordinances in harmony with the intent and purposes thereof, and from any ordinances, regulations, rule, restriction or limitation or order of administrative official or agency in connection with such matter. Action of the Board of Zoning shall be by affirmative vote of not less than three (3) members thereof and its decision shall be final.