Ranking interval numbers: a review

It is important to rank interval numbers in uncertain decision-making field. Ranking methods of interval numbers are analyzed systematically. Rankings is classified into nine classes. Characteristics and drawbacks of each are discussed. Ranking by possibility degree widely used in uncertain multiple-attribute decision-making is examined in some detail. Different formulas of possibility degree are presented, their features and properties are discussed. Six different possibility formulae are proven equivalent. The popular methodology of ranking a set of interval numbers by possibility degree matrix is investigated. Result obtained by this ranking method is sometimes contrary to the meaning of possibility degree or violates rank preservation. Revised ranking by Boolean matrix is discussed.