Duration: 3.5 year PhD project, January 2020-June 2023
Deadline: 26th July 2019
We request expressions of interest (one brief paragraph on the nature of your expertise in the area) for the ‘Aggregating ordinal and numerical uncertainties’ project.
This research requirement seeks to find new mathematical concepts and theory that would support a meaningful aggregation of numerical and ordinal uncertainty. The research may wish to draw on (and extend) the set representations of measure theory, the semi-algebraic sets of algebraic statistics and lattice theory  towards a foundational reconsideration and understanding of aggregating variables. The algebraic statistics contribution may emerge from its consideration of partially ordered sets and lattices. Additionally, the past application of possibility-theory to interval analysis and its quantitative and qualitative representation may offer a partial insight to a solution. The research should not take an empirical approach (offering limited generalisation) but create innovative, theoretical models that may then be tested against real or simulated data. The work should be aware of the specific issues (such as contradiction) in Defence that should be accommodated within a research solution. Initial interest is in the application of solutions to the domains of maritime domain awareness. We do not seek extensions to extant techniques from Dempster-Shafer Theory (DST), Transferrable Belief Model (TBM) or fuzzy logic (possibility theory).