|March 27 – 29, 2019 - Nara, Japan|
Choquet integrals are an effective tool for aggregation of numerical data. From a mathematical point of view they generalize the Lebesgue integral when the measure is not additive. Non-additivity permits us to represent interactions that cannot be represented by additive measures. Choquet integrals have been used in a large variety of contexts that include decision making, computer vision, and economy.
In this talk we will illustrate their use in decision making. We will review some results on Choquet integral based probability-density functions, which can be used to model decision making and classification problems. This will lead us to consider distances based on the Choquet integral, and the problem of measure identification. This last problem corresponds to metric learning. We will show its use in risk assessment in data privacy.
Vicenc Torra is a professor at the Hamilton Institute at Maynooth University (Ireland). He is an IEEE and EurAI Fellow. He has written six books. They include "Modeling decisions" (with Y. Narukawa, Springer, 2007) and "Data Privacy" (Springer, 2017). His fields of interests include data privacy, approximate reasoning and decision making. He is editor of the Transactions on Data Privacy (http://www.tdp.cat) and founder of the conference series Modeling Decisions for Artificial Intelligence (MDAI). He regularly participates in program committees in the areas of approximate reasoning and data privacy, and is member of the editorial board of Information Sciences, Fuzzy Sets and Systems, and Progress in Artificial Intelligence. a His web page is: http://www.mdai.cat/vtorra
We see outer world with language and also think in inner world with language. Thinking is something different from imagining or dreaming; it is viewed as 'a logical act' associated with language.
In this talk, we first characterize 'thinking' on the semantic level from the perspectives of Systemic Functional Linguistics and then investigate logic for thinking imbedded in language on the grammatical level. Conventional logic with relations such as AND, OR and IF-THEN was born from language; in fact, these are grammatical relations between clauses (sentences). Next we explore primary and higher-order logic for thinking. As a result, there are a variety of grammatical relations found between clauses.
In addition, we consider when infants begin to think, reviewing their language development studied by Halliday and point out that grammar is a driving force for thinking as higher-order consciousness developed together with language. In this sense, resources necessary for thinking are all prepared in language.
After graduating from the Department of Physics, the University of Tokyo, Michio Sugeno worked at a company for three years. Then, he served the Tokyo Institute of Technology as Research Associate, Associate Professor and Professor from 1965 to 2000. After retiring from the Tokyo Institute of Technology, he worked as Laboratory Head at the Brain Science Institute, RIKEN from 2000 to 2005 and, then as Distinguished Visiting Professor at Doshisha University from 2005 to 2010. Finally, he worked as Emeritus Researcher at the European Centre for Soft Computing in Spain from 2010 to 2015. He is Emeritus Professor at the Tokyo Institute of Technology. He was President of the Japan Society for Fuzzy Theory and Systems from 1991 to 1993, and also President of the International Fuzzy Systems Association from 1997 to 1999. He is the first recipient of the IEEE Pioneer Award in Fuzzy Systems with Zadeh in 2000. He also received the 2010 IEEE Frank Rosenblatt Award and Kampé de Feriét Award in 2012.
Decision under uncertainty concerns acts characterized by outcomes that can be achieved with some probabilities. Recommending the best decisions is challenging because aggregation of the outcomes over probabilistic states of the world needs to respect preferences of decision makers (DMs). The method used to assist the DMs has to: rely on realistically available preference information, handle a possible inconsistency of this information, aggregate the outcomes in an intelligible and non-compensatory way. To respond satisfactorily to these requirements, we propose a methodology that relies on preference information in the form of decision examples provided by DMs on a subset of reference acts. As this information may be inconsistent with respect to stochastic dominance, it is structured using Dominance-based Rough Set Approach, and then used for inducing a preference model composed of "if..., then..." decision rules. Decision rules constitute an intelligible and non-compensatory aggregation model able to represent complex interactions. We induce all different minimal-cover sets of rules, each one being compatible with the consistent part of the preference information. Applying such compatible instances of the preference model on all considered acts, we get robust recommendations. We also present some indicators for judging the spaces of consensus and disagreement between DMs.
Roman Slowinski is a Professor and Founding Chair of the Laboratory of Intelligent Decision Support Systems at the Institute of Computing Science, Poznan University of Technology, Poland. Full member of the Polish Academy of Sciences, elected president of the Poznan Branch of the Academy (2011-2018) and chairman of the Committee on Informatics (2016-2019). Member of Academia Europaea, Past President and Fellow of the International Rough Set Society, and IEEE. He is coordinator of the EURO Working Group on Multiple Criteria Decision Aiding. In his research, he combines Operational Research and Artificial Intelligence for Decision Aiding. Recipient of the EURO Gold Medal (1991), and Doctor Honoris Causa of Polytechnic Faculty of Mons (2000), University Paris Dauphine (2001), and Technical University of Crete (2008). In 2005 he received the Annual Prize of the Foundation for Polish Science - the highest scientific honor awarded in Poland. Since 1999, he is the principal editor of the European Journal of Operational Research, a premier journal in Operational Research.
There are many variations and generalizations of the method of fuzzy c-means. In this talk some of them are overviewed from three viewpoints:
(1) relations between fuzzy model and statistical model are discussed;
(2) introduction of size variables and covariance variables are considered;
(3) theoretical properties of fuzzy classifiers are shown and contrasted with those in statistical model.
Specifically, generalizations of fuzzy c-means include (i) generalized entropy methods, (ii) Yang's fuzzified maximum likelihoods, and (iii) Generalized Gustafson-Kessel method. Variations encompass the noise cluster model, and also rough c-means model.
When we consider the properties of fuzzy classifiers of generalized fuzzy c-means, a fuzzy classifier is obtained by substituting an object symbol $x_k$ by the generic variable symbol $x$ in the solution of the belongingness, which is defined on the whole space instead of the set of objects. The behaviors of fuzzy classifiers when $x$ goes to an infinity point are studied. In addition to the above generalizations, a more abstract form of generalizations is studied. Simple illustrative examples are shown.
Dr. Sadaaki Miyamoto was born in Osaka, Japan, in 1950. He received the B.S.,M.S. and the Dr. Eng. degrees in Applied Mathematics and Physics Engineering from Kyoto University, Japan, in 1973, 1975, and 1978, respectively. After joined the University of Tsukuba as a Research Associate, he was an Assistant Professor and Associate Professor at the same university. He became a Professor at the Faculty of Engineering of the University of Tokushima in 1990. He then moved to the University of Tsukuba as a Professor with the Institute of Information Sciences and Electronics in 1994. He retired from the University of Tsukuba at the end of March, 2016, and is now a Professor Emeritus of the University of Tsukuba. His research interest includes the theory of uncertainty using rough sets and multisets, and the theory and algorithms of data clustering. He published over 100 journal papers and about 300 conference proceeding papers. He wrote 4 monographs on fuzzy clustering. He received several awards from Japan Society of Fuzzy Theory and Applications. He is a Fellow of the International Fuzzy System Association.