Andrew Geschke presented honours thesis

Andrew presented his honours thesis today (a project supervised by Dale Nimmo and with help from me for the R-code optimization code) looking at how urban population density affects biodiversity of birds.

Linear program for ecology

Recently worked with Dale Nimmo and our honours student Andrew on optimizing abundance (or the geometric mean of abundance) based on land types.  I found it a really interesting problem, as trying to using a general solver generally just didn’t work.  The optimization is essentially with respect to the objective:

∏_i=1…n  (∑w_j x_ij)

and so non-linear.  However by representing the geometric mean as the sum of logs and, in turn, the logarithmic function as the max min of linear functions then we’re able to solve it linearly.  I also looked at a bilevel approach for maximizing Shannon’s diversity.

The code is available here:

Strict-stability bilevel fitting code

Here is an example of the code we used for a recent conference paper.  If you have any questions about it, please get in touch.  We are currently extending the code to look at data missing from multiple dimensions.

AGOP 2015, Katowice, Poland

Had an amazing time in Katowice.  Every single talk was interesting and so it was nice that, with no parallel sessions, it was possible to see every talk!  As it was a smaller conference, with a little over 50 participants, I also had the benefit of being very well looked after by Michal and Marek.  I took advantage of being so close to a concert by my favourite band who were playing in Slovakia to visit Zilina and see them live!  The conference proceedings are here (along with many great photos).

IFSA-EUSFLAT 2015, Gijon, Spain

IFSA-EUSFLAT had over 200 attendees (maybe near 300) this year and with its Spanish location was easily accessible to the European fuzzy sets community.  It was nice to see many colleagues again and walking along the beach to reach the conference made it very easy to get out of bed.  The last day of the conference was my birthday and the afternoon was spent visiting the very beautiful nearby town of Oviedo with Marek and his students. There were a couple of sessions on aggregation functions, but in addition to this I found almost every session had talks I was interested in!  The proceedings are here:


Conversation article published

I wrote an article for The Conversation about misconceptions around AI and tried to also incorporate some introductory information about Fuzzy Logic.  The Conversation is an interesting medium to publish through, aimed at a general audience.

Conference Papers for 2015

Summer was busy preparing three conference papers.

The first, for IFSA-EUSFLAT continued on from Laura’s summer project with AMSI and was based on some analytical results about how much consensus-weighting systems were able to offset the impacts of biased experts.

The second was a collaboration with Javier Montero and his team, which we have been meaning to get started for a long time, on strict-stability of aggregation functions.  We looked at using the theory of strict-stability to guide some linear programming approaches (and bilevel approaches) to fitting weights when there are data missing.  This was submitted to AGOP.

The third followed on from the findings of the IFSA paper and some other work I had done previously on consensus.  The basic idea is that current methods for fuzzifying the pairwise preference matrix allow decision makers to allocate extreme scores, and this means that the process is sensitive to preferences expressed by biased (or just extreme) experts.  A key to address this is to rethink the way we interpret and define the preference relation.  This was submitted to FUZZIEEE, which unfortunately I won’t be able to attend this year but Tim will be attending and so will present this work.

Title: Biased experts and similarity based weights in preferences aggregation

Authors: Gleb Beliakov, Simon James, Laura Smith, Tim Wilkin


In a group decision making setting, we consider the potential impact an expert can have on the overall ranking by providing a biased assessment of the alternatives that differs substantially from the majority opinion. In the framework of similarity based averaging functions, we show that some alternative approaches to weighting the experts’ inputs during the aggregation process can minimize the influence the biased expert is able to exert.

Title: Learning stable weights for data of varying dimension

Authors: Gleb Beliakov, Simon James, Daniel Gómez, J. T. Rodríguez and Javier Montero


In this paper we develop a data-driven weight learning method for weighted quasi-arithmetic means where the observed data may vary in dimension.

Title: Construction and aggregation of preference relations based on fuzzy partial orders

Authors: Gleb Beliakov, Simon James and Tim Wilkin


In group decision-making problems it is common to elicit preferences from human experts in the form of pairwise preference relations. When this is extended to a fuzzy setting, entries in the pairwise preference matrix are interpreted to denote strength of preference, however once logical properties such as consistency and transitivity are enforced, the resulting preference relation requires almost as much information as providing raw scores or a complete order over the alternatives. Here we instead interpret fuzzy degrees of preference to only apply where the preference over two alternatives is genuinely fuzzy and then suggest an aggregation procedure that minimizes a generalized Kemeny distance to the nearest complete or partial order. By focusing on the fuzzy partial order, the method is less affected by differences in the natural scale over which an expert expresses their preference, and can also limit the influence of extreme scores.