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

**Abstract**

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

**Abstract**

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

**Abstract**

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.