Pre-Aggregation Functions: Theory and Applications in Classification and Image Processing

Prof. Humberto Bustince

Public University of Navarra, Spain

In recent times, there has been a huge interest in the study of generalized forms of monotonicity which allows to define and/or cover many functions which, not being aggregation functions because they are not monotone in an usual sense, are of great interest for applications in fields such as image processing, classification or decision making. One important step in this direction has been the introduction of the notion of pre-aggregation function, which is a function with the same boundary conditions as an usual aggregation function, but for which only monotonicity along some fixed direction is required. This notion has shown itself very useful for classification problems, and it has also allowed to include in a common framework some relevant operators outside from the scope of aggregation functions, as it is the case, in particular, of the mode. The requirement of monotonicity along a fixed direction which is the same for every considered point in the unit hypercube is, however, still too strict for application in fields such as image processing, for instance. When dealing with edge detection in an image, for instance ,relevant directions to be considered may change from one pixel (point) to another one. Taking into account this consideration, among others, in this talk we speak about directional monotone functions and ordered directionally monotone functions, and we introduce the idea of pre-aggregation function. We also discuss the applications of these concepts in image processing and classification problems.


Prof. Bustince

Humberto Bustince is full professor of Computer Science and Artificial Intelligence in the Public University of Navarra. He is the main researcher of the Artificial Intelligence and Approximate Reasoning group of this University, whose main research lines are both theoretical (aggregation functions, information and comparison measures,fuzzy sets and extensions) and applied (image processing,classification, machine learning, data mining and big data). He has led 11 I+D public-funded research projects, at a national and at a regional level. Now he is the main researcher of a project in the Spanish Science Program and of scientific network about fuzzy logic and soft computing. He has been in charge of research projects collaborating with private companies such as Caja de Ahorros de navarra, INCITA, Gamesa or Tracasa. He has taken part in two international research projects. He has authored more than 200 works, according to Web of Science, in conferences and international journals, with around 100 of them in journals of the first quartile of JCR. Moreover, five of these works are also among the highly cited papers of the last ten years, according to Science Essential Indicators of Web of Science. He has regular collaborations with leading international research groups from countries such as the United Kingdom, Belgium, Australia, Germany, Portugal the Czech Republic, Slovakia, Canada, the United States or Brasil. He is editor-in-chief of the online magazine Mathware&Soft Computing of the European Society for Fuzzy Logic and technologies, EUSFLAT) and of the Axioms journal. He is associated editor of the IEEE Transactions on Fuzzy Systems journal and member of the editorial board of the journals Fuzzy Sets and Systems, Information Fusion, International Journal of Computational Intelligence Systems and Journal of Intelligent & Fuzzy Systems. He is co-author of a monography about avergaing functions and co-editor of several books. He has organized some reknowned international conferences such as EUROFUSE 2009 and AGOP 2013. He is Senior member of the IEEE Association and Fellow of the International Fuzzy Systems Association (IFSA).

Statistical Decision-Making in Mixed Models of Uncertainty

Prof. Dan Ralescu

University of Cincinnati, USA

Many statistical data are imprecise due to factors such as measurement errors, computation errors, and lack of information. In such cases, data are better represented by intervals-or fuzzy sets- rather than by single numbers. Existing methods for analyzing interval-valued data include regressions in the metric space of intervals and symbolic data analysis, the latter being proposed in a more general setting. However, there has been a lack of literature on the parametric modeling and distribution-based inferences for interval-valued, and fuzzy-valued data. We propose a normal hierarchical model for random sets-in particular for random intervals. In addition, we develop a minimum contrast estimator (MCE) for the model parameters, which is both consistent and asymptotically normal. Simulation studies support our theoretical findings and show promising results. Finally, we successfully apply our model and MCE to a real data set.


Dr. Ralescu

Dan Ralescu is the coauthor of the first comprehensive monograph on fuzzy sets and systems, published in the early 1970s. He has authored and coauthored more than 80 papers in scientific journals. In the late 1970s he has initiated the theory of fuzzy random variables and mixed models of uncertainty. His recent interests are in statistical decision making under various kinds of uncertainty. He was awarded the IFSA Fuzzy Pioneer in 2003. His international collaborations include lectures in Brazil, China, France, Japan, and Spain, among others.

Knowing Sensitivity and Intelligence from the Viewpoint of System and Design

Prof. Hisao Shiizuka

Kogakuin University, Japan

When we make decisions in everyday life, we infer some form. It is known that there are three reasoning methods: deduction, induction, and abduction. Inference is closely related to sensitivity and intelligence. First of all, in this keynote I will confirm the following. Intelligence is a general ability including ability to infer, plan, solve problems, think abstractly, understand complex ideas, and learn quickly. It also includes the ability to learn from experience. Intelligence is not simply for learning from books, for narrow academic skills or for good grades in the exam. It rather represents a broader capability to understand our environment, "understanding" things and "giving meaning" and finding out what to do.

The following items are three key elements of intelligence that intelligence experts are reaching agreement:

  1. Abstract thinking or reasoning (which is agreed by 99.3% of researchers)
  2. Problem solving ability (This is agreed by 97.7% of researchers)
  3. Ability to gain knowledge (this is agreed by 96.0% of researchers)

Well, here I first propose "Innovation Tetra" which constitutes the basis of reasoning. Furthermore, I apply this "Innovation Tetra" to show the possibility of developing new reasoning. The fuzzy inference method so far is based on deduction. In order to develop a new way of fuzzy reasoning, it would be to establish an inference method that can be applied to new artificial intelligence by leaving deductive reasoning.

In this keynote I would like to describe some related matters from the above viewpoint.


Dr. Shiizuka

Dr. Hisao Shiizuka received his B.S. and M.S. degrees in the Electrical Engineering from Kogakuin University, Tokyo Japan, in 1971 and 1973, respectively, and Doctor of Engineering (Ph D) on "Properties of Three Terminal RC Networks and Their Application to Synthesis Problems" from Kogakuin University, Tokyo Japan, in 1983.

He had been a Professor of Kansei Engineering, Information Design and Soft Computing at Faculty of Informatics, Kogakuin University since 2006, Tokyo Japan, after having contributed for 11 years as a Professor of Artificial Intelligence System, Linear System Theory and Electric Circuits, to the Department of Computer Science and Communication Engineering at Kogakuin University since 1995, Tokyo Japan.

He was a visiting researcher at The University of Illinois at Chicago (UIC) in 1993. He is engaged in the circuit theory, the graph theory, the Petri net, and the application of the system simulation and the fuzzy theory and the researches on a soft computing and Kansei engineering, etc. Currently, his research interests are Kansei Engineering, Soft Computing, Information Design and Artificial Intelligence. He was a director of Japan Society for Fuzzy Theory in 1995-1997, and was a director of Japan Society of Kansei Engineering in 1999-2001. He was the President of Japan Society of Kansei Engineering, from 2007 to 2013. He holds a lot of the chair of the academic society successively.

Now he is a Professor emeritus, Kogakuin University, Senior Research Scientist of Fuzzy Logic Systems Institute, and Chair of International Society of Affective Science and Engineering, and also he is the president of Shiizuka Kansei Engineering Laboratory, Co., Ltd.