KBS paper and RS Book Chapter update accepted

Received two pieces of good news today, with a new paper submitted to Knowledge-Based Systems having been accepted and also an update of our contribution to the Recommender Systems Handbook.

Title: A penalty-based aggregation operator for non-convex intervals

Authors: G. Beliakov and S. James


In the case of real-valued inputs, averaging aggregation functions have been studied extensively with results arising in fields including probability and statistics, fuzzy decision-making, and various sciences. Although much of the behavior of aggregation functions when combining standard fuzzy membership values is well established, extensions to interval-valued fuzzy sets, hesitant fuzzy sets, and other new domains pose a number of difficulties.
The aggregation of non-convex or discontinuous intervals is usually approached in line with the extension principle, i.e. by aggregating all real-valued input vectors lying within the interval boundaries and taking the union as the final output. Although this is consistent with the aggregation of convex interval inputs, in the non-convex case such operators are not idempotent and may result in outputs which do not faithfully summarize or represent the set of inputs. After giving an overview of the treatment of non-convex intervals and their associated interpretations, we propose a novel extension of the arithmetic mean based on penalty functions that provides a representative output and satisfies idempotency.


Title: Aggregation functions for recommender systems (in Recommender Systems Handbook, 2nd Ed. by Springer)

Authors: G. Beliakov, T. Calo and S. James


This chapter gives an overview of aggregation functions and their use in recommender systems.  The classical weighted average lies at the heart of various recommendation mechanisms, often being employed to combine item feature scores or predict ratings from similar users.  Some improvements to accuracy and robustness can be achieved by aggregating different measures of similarity or using an average of recommendations obtained through different techniques.  Advances made in the theory of aggregation functions therefore have the potential to deliver increased performance to many recommender systems.    We provide definitions of some important families and properties, sophisticated methods of construction, and various examples of aggregation functions in the domain of recommender systems.


Consensus and Evenness measures Summer Project

Over the Summer, Laura undertook a project with the IPCI lab on Measures of Consensus and Ecological Evenness.  She presented her results at a seminar earlier this year and her report led to the MDAI contribution.  We look forward to Laura continuing her research in this area.

Conference papers for FUZZIEEE2014 and MDAI2014

We have had the following papers accepted for presentation at FUZZIEEE (part of WCCI) in Beijing in July and Modeling Decisions for Artificial Intelligence (MDAI) in Tokyo in October.  We received particularly positive feedback for all of these which is nice.  The first and third (submitted to FUZZIEEE and MDAI respectively) relate to our project on the relationship between ecology indices and aggregation functions.  We still have a lot of analysis and data to extract from that project so it is nice to have the work viewed positively in its initial stages.  The second paper (submitted to FUZZIEEE) is based on a paper presented by R.R. Yager at IFSA in Canada last year.

Title: Can Indices of Ecological Evenness Be Used to Measure Consensus?

Authors: G. Beliakov, S. James and D. Nimmo


In the context of group decision making with fuzzy preferences, consensus measures are employed to provide feedback and help guide automatic or semi-automatic decision reaching processes. These measures attempt to capture the intuitive notion of how much inputs, individuals or groups agree with one another. Meanwhile, in ecological studies there has been an ongoing research effort to define measures of community evenness based on how evenly the proportional abundances of species are distributed. The question hence arises as to whether there can be any cross-fertilization from developments in these fields given their intuitive similarity. Here we investigate some of the models used in ecology toward their potential use in measuring consensus. We found that although many consensus characteristics are exhibited by evenness indices, lack of reciprocity and a tendency towards a minimum when a single input is non-zero would make them undesirable for inputs expressed on an interval scale. On the other hand, we note that some of the general frameworks could still be useful for other types of inputs like ranking profiles and that in the opposite direction consensus measures have the potential to provide new insights in ecology.


Title: Averaging Aggregation Functions for Preferences Expressed as Pythagorean Membership Grades and Fuzzy Orthopairs

Authors: G. Beliakov and S. James


Rather than denoting fuzzy membership with a single value, orthopairs such as Atanassov’s intuitionistic membership and non-membership pairs allow the incorporation of uncertainty, as well as positive and negative aspects when providing evaluations in fuzzy decision making problems.   Such representations, along with interval-valued fuzzy values and the recently introduced Pythagorean membership grades, present particular challenges when it comes to defining orders and constructing aggregation functions that behave consistently when summarizing evaluations over multiple criteria or experts.   In this paper we consider the aggregation of pairwise preferences denoted by membership and non-membership pairs.  We look at how mappings from the space of Atanassov orthopairs to more general classes of fuzzy orthopairs can be used to help define averaging aggregation functions in these new settings.  In particular, we focus on how the notion of `averaging’ should be treated in the case of Yager’s Pythagorean membership grades and how to ensure that such functions produce outputs consistent with the case of ordinary fuzzy membership degrees.


Title: Single-Preference Consensus Measures Based on Models of Ecological Evenness

Authors: G. Beliakov, S. James and L. Smith


We investigate the relationship between consensus measures used in different settings depending on how voters or experts express their preferences. We propose some new models for single-preference voting, which we derive from the evenness concept in ecology, and show that some of these can be placed within the framework of existing consensus measures using the discrete distance.  Finally, we suggest some generalizations of the single-preference consensus measures allowing the incorporation of more general notions of distance.

Aggregation Operators special session at FUZZIEEE 2014

We are inviting submissions to our proposed special session on Aggregation Operators at FUZZIEEE to be held in Beijing from July 6-14, 2014 as part of the World Congress on Computational Intelligence.

Aggregation Operators (AGOPs) play a key role in fuzzy sets theory as fuzzy logic connectives, and also have wide-ranging applications in decision making, classification and data analysis. Traditional aggregation operators such as the arithmetic mean and median are now acknowledged as particular cases of more general families of aggregation operations, such as the ordered weighted averaging (OWA) operator and Choquet integral. Triangular norms and conorms, uninorms, symmetric sums, to name a few, are widely used families of AGOP. With the growing need to deal with large amounts of data and uncertainty, research on practical applications and their associated challenges is of increasing interest.

This special session will be dedicated to theoretical and practical aspects of AGOPs. Specific topics include, but are not limited to:
– practical constructions of AGOPs,
– real-world applications,
– parameter and weights identification,
– weighting functions for AGOPs,
– AGOPs with specific properties,
– interval-valued and intuitionistic AGOPs,
– theoretical analysis,
– fuzzy measures and integrals.

Style and paper submission guidelines can be found here.

Papers can be submitted here.

Please select “S34: FZ34: Aggregation Operators” from the drop-down box where it says Main research topic.

The current due date for submission is December 20, 2013 – although there is usually a two week extension on this.

Survey on human judgements of species diversity


We are currently conducting a research project that looks at human perceptions of ecological diversity and how such perceptions feed into judgements regarding how people rank communities for conservation.

The survey is core to our investigation and involves participants making intuitive judgements about the relative diversity of different communities and using the available information to rank the same communities in terms of their conservation importance. The survey takes approximately 15 minutes to complete and it is not necessary for you to be an expert in this area to participate; we hope to have respondents from a range of backgrounds.

More information can be found in the plain language that precedes the survey. The following link will take you to the survey.


AudioSlides for Knowledge-based systems article

Elsevier now make AudioSlides available with the journal articles.  I thought I’d try this out and see how it goes.  Obviously it can be a bit odd to make a recording of your voice available and I don’t really see that this would increase the number of people that read your article but thought it was worthwhile to try anyway.


Use and perceptions of worked example videos for first-year students studying mathematics in a primary education degree

Conference paper accepted for upcoming DELTA in Kiama, NSW (Australia).  I really got a lot out of DELTA in Rotorua, NZ – so I’ll be looking forward to attending this conference.  This particular project was undertaken with the help of some 3rd year science students.

Title: Use and perceptions of worked example videos for first-year students studying mathematics in a primary education degree

Authors: S. James, J. Brown, T. Gilbee and C. Rees


Worked example videos have great potential to be 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 mathematics subject taught in the first year of a primary education degree and investigated student perceptions and their usage patterns.  An additional aspect of this undertaking was the inclusion of subtitles to make the videos accessible to hearing impaired and ESL students.  This report will reflect on the process of creating these videos, as well as some initial findings on their success.