The papers below have both been accepted for focus sessions at the International Fuzzy Systems Association World Congress to be held in Edmonton, Alberta, Canada.
Title: Aggregating fuzzy implications to measure group consensus
Authors: G. Beliakov, T. Calvo and S. James
We approach the problem of measuring consensus for a set of real inputs by aggregating the fuzzy implication degrees between each pair of inputs. We compare our operator with existing consensus measures in terms of their satisfaction of desirable properties. The appeal of such an approach lies in the interpretability and flexibility that results from component-wise construction which we modeled on the Bonferroni mean. We also outline some intentions for future research.
Title: Learning aggregation weights from 3-tuple comparison sets
Authors: G. Beliakov, S. James and D. Nimmo
An important task in multiple-criteria decision making is how to learn the weights and parameters of an aggregation function from empirical data. We consider this in the context of quantifying ecological diversity, where such data is to be obtained as a set of pairwise comparisons specifying that one community should be considered more diverse than another. A problem that arises is how to collect a sufficient amount of data for reliable model determination without overloading individuals with the number of comparisons they need to make. After providing an algorithm for determining criteria weights and an overall ranking from such information, we then investigate the improvement in accuracy if ranked 3-tuples are supplied instead of pairs. We found that aggregation models could be determined accurately from significantly fewer 3-tuple comparisons than pairs.
The R code relating to these papers will be made available soon.
This paper just accepted for publication in Fuzzy Sets and Systems. We look at aggregation functions whose output does not change when a new input is introduced that is equal to the aggregated value of the original inputs. Some of the more novel results concern the conditions on weighting vectors associated with functions like the OWA that involve a reordering of the inputs.
Title: Stability of weighted penalty-based aggregation functions
Authors: G. Beliakov and S. James
In many practical applications, the need arises to aggregate data of varying dimension. Following from the self-identity property, some recent studies have looked at the stability of aggregation operators in terms of their behavior as the dimensionality is increased from n-1 to n. We use the penalty-based representation of aggregation functions in order to investigate the conditions for weighting vectors associated with some important weighted families, extending on the results already established for quasi-arithmetic means. In particular, we obtain results for quasi-medians and functions that involve a reordering of the inputs such as the OWA and order statistics.
Another AMS review has been recently published. Can be accessed here. The article concerns multivalued fuzzy integrals.
I have received an award for excellence in research for 2012 in the School of Information Technology at Deakin University. The award is in acknowledgement of a number of publications in aggregation functions throughout the year and a successful Central Research Grants Scheme application submitted by Dale Nimmo and myself titled, Reconciling quantified measures of species diversity with human perceptions using aggregation functions. We hope that this research project will allow us to create new environmental indices that are more closely aligned with intuitive understandings of diversity.
Presented a talk on learning the weights of generalized Bonferroni means in the R programming language yesterday as one of the 8 talks on Aggregation Operators at MDAI this year. These talks were:
Using linear programming for weights identification of generalized Bonferroni means in R – Gleb Beliakov and Simon James
An Ordered Weighted Average with a truncation weight on intervals – Yuji Yoshida
Choquet integral on the real line as a generalization of the OWA operator – Yasuo Narukawa
On WOWA Rank Reversal - Wlodzimierz Ogryczak, Patrice Perny, Paul Weng
Combination and soft-normalization of belief functions on MV-algebras – Tommaso Flaminio, Lluis Godo, Tomas Kroupa
Extending concordance and discordance relations to hierarchical sets of criteria in ELECTRE-III method – Luis del Vasto-Terrientes, Aida Valls, Roman Slowinski, Piotre Zielniewicz
An extended LibQUAL+ model based on fuzzy linguistic information – Francisco J. Cabrerizo, Ignacio J. Perez, Javier Lopez-Gijon, Enrique Herrera-Viedma
Measure of Inconsistency for the potential method - Lavoslav Caklovic (not presented)
Gleb Beliakov and I are organizing the Aggregation Operators special session to be held at FUZZIEEE 2013 in Hyderabad, India from July 7-10 next year. I hope India’s central location will encourage participation from the aggregation operators researchers from across the world!
In the past, it’s been hard for me to attend the AUSTMS annual meeting as Deakin’s intra-trimester break doesn’t always align with other universities. It was nice this year that it did, and I was able to attend and participate. As well as Lynn Batten presenting our findings on fear abatement , I also presented some current work on worked example videos and was a panel member for the discussion which took part of the Education Afternoon.
Interactive Panel Discussion: Primary School Mathematics
The Panel was chaired by Lynn Batten and included myself, Terry Mills and Simuzar Hajilarova as panelists. Over the hour, we discussed two topics. Firstly, that there seem to be a number of jumps in the curriculum that results in a number of students struggling with the transition from year 10 to year 11. Secondly, we discussed the involvement/role of AUSTMS in the primary education system.
Use and perceptions of worked example videos for first year students in a Primary Education degree
The abstract for the talk was as follows:
Worked example videos are particularly useful for students when learning mathematics as they can work through the questions at their own pace, pausing as needed, but still learn from the way the demonstrator thinks and solves problems. We created worked example videos each week for a subject taught in the first year of a primary education degree and investigated how students used them and their perceptions. An additional aspect of this undertaking was the inclusion of subtitles to make the videos accessible to hearing impaired and ESL students. This talk will reflect on the process of creating these videos, as well as some initial findings on their success.
* I look to do a more comprehensive analysis of my findings on this topic for submission to Delta 2013. The abstract for our work on anxiety abatement is here.
It was great to be able to finally attend the whole conference, and the associated ECR workshop was also fantastically organised!