Axiomatic foundation of the analytic hierarchy process
Management Science
Remarks on the analytic hierarchy process
Management Science
A clarification of “remarks on the analytic hierarchy process”
Management Science
The Analytic Hierarchy Process--An Exposition
Operations Research
Information Sciences: an International Journal
Soft constraint abstraction based on semiring homomorphism
Theoretical Computer Science
Information Sciences: an International Journal
Expert Systems with Applications: An International Journal
A general unified framework for pairwise comparison matrices in multicriterial methods
International Journal of Intelligent Systems
Expert Systems with Applications: An International Journal
A fuzzy extension of Saaty's priority theory
Fuzzy Sets and Systems
A method for repairing the inconsistency of fuzzy preference relations
Fuzzy Sets and Systems
The Analytic Hierarchy Process and the Theory of Measurement
Management Science
Group consensus algorithms based on preference relations
Information Sciences: an International Journal
On the decomposition of value functions11Research supported in part by NSERC.
Operations Research Letters
Hi-index | 0.07 |
In decision making and group decision making, multiplicative reciprocal judgment matrices and additive reciprocal judgment matrices are used as two kinds of important preference information. In this paper, semirings are applied to the discussion of judgment matrix properties. First, two special semirings are constructed. Second, the properties of the consistent judgment matrices are given as a set of equations (all in the semiring sense), which include idempotency equations and fixed point equations. We find that there exists one and only one specially constrained fixed point as the priority vector of a consistent judgment matrix. Third, optimization models for inconsistent judgment matrices are presented. Finally, we offer some simple illustrative examples.