Theoretical Study On Interval Number Complementary Judgement Matrix

The analytic hierarchy process (AHP) was introduced in middle 1970s byAmerican professor T.L.Saaty, who made researches on Operations Analysis inPittsburgh University. It is a very practical multi-decision making method whichcombines the quality and the quantity, and makes man's subjective judgment beexpressed and disposed using number. During the decision making, the expertsusually construct judgement matrix with comparing with each other. Because ofthe complexity, uncertainty, thought fuzzy and information incomplete ofreal-word decision problems and the subjective nature of human judgments,judgement sometimes is given by interval number. So people will structure twotypes of interval number judgement matrices: one is reciprocal, the other iscomplementary. Up to now, much research results are reciprocal, but fewconclusions are presented about complementary.In this paper, the theory is analyzed and studied. The main research worksare as follows.In Chapter 1, the basic aspects of the AHP and the recent researches oninterval number complementary judgement matrix are stated, and the mainresearch contents are involved. In Chapter 2, pointing out the defection of definition of consistency, wegive a new one, and discuss the consistency of interval number complementaryjudgment matrix in group.In Chapter 3, the operation rule of interval number reciprocal judgementmatrix is stated, we give the operation rule of interval number complementaryjudgement matrix, and the differences between them are studied.In Chapter 4, based on the additive and multiple consistency of intervalnumber complementary judgement matrix, we give some ranking methods, andget some methods of checking consistency.In the end, the research works are summarized, and some ideas about theresearch on interval number complementary judgement matrix are made.