Rank inclusion in criteria hierarchies

Another Potential Strong Shortcoming of Ahp

In the last twenty years many features of Saaty's Analytical Hierarchy Process (AHP) have been criticised, especially the additive hierarchical composition of conventional AHP, which leads to the possibility of occurrence of the Rank Reversal phenomenon (adding an irrelevant alternative may cause a reversal in the ranking at the top). In the context of a variable number of alternatives this ran...

Rank Inclusion in Criteria

Lower bounds on matrix factorization ranks via noncommutative polynomial optimization

We use techniques from (tracial noncommutative) polynomial optimization to formulate hierarchies of semidefinite programming lower bounds on matrix factorization ranks. In particular, we consider the nonnegative rank, the positive semidefinite rank, and their symmetric analogues: the completely positive rank and the completely positive semidefinite rank. We study the convergence properties of o...

Rank Bounds for a Hierarchy of Lovász and Schrijver

Lovász and Schrijver [17] introduced several lift and project methods for 0-1 integer programs, now collectively known as Lovász-Schrijver (LS) hierarchies. Several lower bounds have since been proven for the rank of various linear programming relaxations in the LS and LS+ hierarchies. In this paper we investigate rank bounds in the more general LS∗ hierarchy, which allows lifts by any derived ...

Extracting the criteria for faculty members rank promotion through the application of comparative study of selected universities

The faculty promotion system, due to its special nature, is recognized as one of the prominent policy tools in the field of higher education. The criteria and principles for rank promotion represent the missions, policies and programs of the academic system. Therefore, authorities try to better organize the promotion system. Due to these characteristics, academic and scientific policymakers hav...