to value; to make a valuation or official estimate of for the purpose of taxation.-to apportion a sum to be paid by (a person, a community, or an estate), in the nature of a tax, fine, etc.; to impose a tax upon (a person, an estate, or an income) according to a rate or apportionment.-to determine and impose a tax or fine upon (a person, community, estate, or income); to tax; as, the club assessed each member twenty-five cents.-to fix or determine the rate or amount of.