Gleb Beliakov and Gang Li from Deakin University chaired the two aggregation operators special sessions run on the first day of the World Congress on Computational Intelligence 2012 of which FUZZIEEE is a part. The sessions were attended by well known researchers in the Fuzzy Sets community including Bernard de Baets, Bernadette Bouchon-Meunier, Vladik Kreinovich, Jozo Dujmovic and Michio Sugeno.
Some thought about the 6 talks that were presented at these sessions:
1. Defining Bonferroni means over lattices – Gleb Beliakov and Simon James
One of the interesting questions arising from this talk was about whether one could compare the generalized Bonferroni mean with mandatory inputs with the step-wise aggregation proposed by Dujmovic with soft and hard partial conjunction. It could be something worth investigating: the advantage of a more analytical function usually lies in interpretability of the behaviour (e.g. analysis of the derivatives) however something else that’s interesting here (although it doesn’t relate to the lattice representation) is the overall impact of each of the weights with such constructions – there’s a little bit of an absorption effect.
2. A fuzzy decision support method for customer preference analysis based on Choquet integral – Huy Quan Vu, Gang Li and Gleb Beliakov
Gang presented this talk. His TULIP group is currently looking at the modeling of online hotel evaluations. A number of feature extraction methods from data mining are integrated with fitting approaches for fuzzy measures in order to evaluate the preferences of different types of users, e.g. how does a couple travelling for vacation differ to a business-person when they provide an overall evaluation of a hotel? I think this is one of the more promising application areas of aggregation functions, well-supported by the fact that Gang and his team are publishing a number of papers in high quality tourism management journals at the moment.
3. Andness and Orness as a mean of overall importance – Jozo Dujmovic
The andness of an aggregation operator gives an overall impression of how important it is for the criteria to by simultaneously satisfied. In this research, Dujmovic has showed that relative importance and andness are independent of one another, while sensitivity and tradeoff result directly from the former parameters. An interesting survey was conducted with both experts and non-experts, leading one to say that when the relative importance hits about 0.75-0.8 on the scale of importance, the criteria becomes more mandatory. A nice formula (i1+i2+i3…)/(nL) approximates the andness, where i1, i2 are the relative importances, n is the number of criteria and L is the number of levels. So if both importances are 10/10, then we would have an andness of 1 (they’re both mandatory), while we would have something inbetween if the importances were 7/10 and 8/10. Dujmovic’s work is strongly geared towards real applications and usability by non-experts – the examples in this case related to people searching for houses with some specified preferences.
4. A speculative algorithm to extract fuzzy measures from sample data – Xiaojing Wang, Angel Garcia Contreras, Martine Ceberio, Christian Del Hoyo and Luis Gutierrez
This talk was presented by Vladik Kreinovich from University of Texas. The authors are investigating some various methods for approximating a fuzzy measure from data (in this case, experiments were conducted on samples generated by a function, with and without noise for n=4,5,6). The minimization is with respect to least squares residuals. The speculative algorithm involves dividing the search area into intervals and eliminating regions of the domain that will not lead to a global optimum.
5. Color image reduction by minimizing penalty functions – Daniel Paternain, Aranzazu Jurio, Javier Fernandez, Humberto Bustince and Gleb Beliakov
This talk was presented by Gleb. Bustince and his team at GIARA at University of Navarra look at the problem of image reduction using aggregation functions defined over lattices. Of particular interest here is the difference between penalties over a Cartesian product of lattices, and the Cartesian product of penalties – sometimes (if the median is used) they are the same, however sometimes the optimisation of the penatly becomes very difficult. This particular project looked at approximating the optimal solution by taking a discrete number of aggregation functions and minimizing over the space. The median performs the best in cases of impulse noise, while mean operators can perform well for Gaussian noise.
6. Admissibility of preferences and modeling capabilities of fuzzy integrals – Takehiko Nakama and Michio Sugeno
This was one of the more theoretical of the sessions, presented by Takehiko Nakama. Sugeno integrals (and their variations) are looked at for modeling preferences, and tested against whether they are able to generate ALL the rational preference relations that a user could provide, and whether they can generate irrational preference relations. Intuitively – I would think the monotonicity of the Sugeno integrals should ensure that dominance is not violated, however Takehiko did note that sometimes x dominating y on all sub-criteria could result in an indifference between x and y. A new type of hierarchical Sugeno integral is of interest here, as for 3 items it can generate all possible rational preference relations (although it does lead to some inadmissible preferences).
I’m looking forward to the rest of the FUZZIEEE conference – nice to have my talk out of the way!