The Research On The Consistency About The Positive Reciprocal Judgment Matrix In AHP

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 scientific method of decision making, whichcombines the qualitative judgment and quantitative analysis. With thedevelopment of society, due to the completeness in the theory, the rigorousnessin the structure, the simplicity and practicability in solving problems, AHP hasbeen widely applied in city programming, economic engineering and evaluatingresults of scientific researches, etc. One of the keys about the application onAHP is how to establish a reasonable judgment matrix by the comparison on theboth elements below the single criterion, but the consistency level of thejudgment matrix is just the important embody of the reasonable degree, So theconsistency problem becomes the core problem in the AHP theory and itsapplications.In this paper, the positive reciprocal judgment matrix's consistency problem is analyzed and studied. The main research works are as follows:In Chapter 1, the basic aspects of the AHP are stated, such as its production,developments, the basic steps while applied, the main research content and itsforeground etc. Then, the recent researches on the consistency in AHP areconcluded, and the main research contents are also involved.In Chapter 2, three different concepts about consistency are summarized.After pointing out the membership among them, the paper expounds the presentconditions of country and overseas; Aiming at the study about the basicconsistency of the judgment matrix, the careful comparison analysis among thepresent methods is given, then the paper proposed the new method to modify theconsistency, which has nothing to do with the weight vectors. After analyzingthe feasibility of the new method, the examples are compared to elaborate themethod; Focusing on the rank consistency of the comparison matrix, the authorpoints out the lack in the theorem of the old method and proposes a way tocheck the rank consistency, which can be used to find out all the elements thatleads to the rank inconsistency.In Chapter 3, the new concepts about the interval judgment matrix such asthe kernel matrix, the intersection of its own, the standard kernel matrix and theconsistent level etc. are proposed out on the basis of the old definitions, somenew theorems with the certificate are given together. The paper also proposed aparticular way to check the interval judgment matrix's consistency; Thedefinition of the rank consistency about the interval judgment matrix is described in the chapter; At last two kinds of methods to modify the matrix'sinconsistency are proposed, meanwhile the analysis between the practicalexamples is given, too.In the end, the research works are summarized, and some suggestions aboutthe research on the consistency in AHP are made.