Invited Lectures

Prioritized Aggregation Operators andtheir Application

Ronald Yager, Iona College, USA

Abstract: In this talk we shall look at a number of prioritized aggregationoperators and investigate some of the applications inwhich they can be used.

Ronald R. Yager has worked in the area of machine intelligence for over twenty-five years. He has published over 500 papers and fifteen books in areas related to fuzzy sets, decision making under uncertainty and the fusion of information. He is among the world's top 1% most highly cited researchers with over 7000 citations. He was the recipient of the IEEE Computational Intelligence Society Pioneer award in Fuzzy Systems. Dr. Yager is a fellow of the IEEE, the New York Academy of Sciences and the Fuzzy Systems Association. He was given a lifetime achievement award by the Polish Academy of Sciences for his contributions. He served at the National Science Foundation as program director in the Information Sciences program. He was a NASA/Stanford visiting fellow and a research associate at the University of California, Berkeley. He has been a lecturer at NATO Advanced Study Institutes. He is a distinguished honorary professor at the Aalborg University Denmark. He is an affiliated distinguished researcher at the European Centre for Soft Computing. He received his undergraduate degree from the City College of New York and his Ph. D. from the Polytechnic University of New York. Currently, he is Director of the Machine Intelligence Institute and Professor of Information Systems at Iona College. He is editor and chief of the International Journal of Intelligent Systems. He serves on the editorial board of numerous technology journals.

Copulas and Integrals in multicriteria decision support

Radko Mesiar, Slovak University of Technology (STU) Bratislava

Abstract: We give a short overview of basics of copula theory, modeling the stochastic dependence structure of
random vectors, including the statistical interpretation of some copulas, with several examples and construction methods. Basic classes of copulas are introduced and discussed, including two types of generated copulas, EV-copulas and Archimax copulas.

Universal integrals are shown to be an appropriate way how to extend boolean utility function into a graded (fuzzy) utility function.Based on the idea of copula modeling of dependence between function and measure values, copula-based integrals are introduced, covering the Choquet integral (based on product copula) and the Sugeno integral (based on the comonotonicity copula) among others. An axiomatic approach to these integrals based on the comonotone modularity will be also added.

Radko Mesiar, graduated at Comenius University, Faculty of Mathematics and Physics, in 1974, PhD at the same faculty obtained in 1979 with PhD thesis “Subadditive martingale processes”. Since 1978 member of the Department of Mathematics at Faculty of Civil Engineering, STU Bratislava. DSc since 1996 (in Czech Republic, Academy of Sciences). Associate professor since 1983, full professor since 1998.  He is fellow member of Czech Academy of Sciences, Institute of Information and Automation, Praha (Czech Republic, since 1995) and of IRAFM, University of Ostrava (Czech Republic, since 2006). He is co-author of two scientific monographs (Triangular Norms, Kluwer, 2000; Aggregation Functions, Cambridge University Press, 2009) and 5 edited volumes. Author of more than 200 papers in WOS in journals like Fuzzy Sets and Systems, Information Sciences, IEEE Trans. Fuzzy Systems, Int. J. General Systems, J. Math. Anal. Appl., Int. J. Uncertainty, Fuzziness and Knowledge-Based Systems, Kybernetika, EJOR, Appl. Math. Letters, Non-Linear Analysis, etc. His fields of interest include measure theory, uncertainty modelling, fuzzy sets and fuzzy logic, multicriteria decision support, copulas, triangular norms, aggregation operators and related operators, intelligent computing.

Fuzzy sets in evaluation methods: qualitative and bipolar approaches.

Didier Dubois, IRIT, CNRS and Université de Toulouse, France

Abstract: In decision applications, especially multicriteria decision-making, numerical approaches are often questionable because it is hard to elicit numerical values quantifying preference, criteria importance or uncertainty. More often than not, multicriteria decision-making methods, especially fuzzy set based ones, come down to number-crunching recipes with debatable foundations.

In the first part of the tutorial we provide a critical assessment of some evaluation techniques based on fuzzy sets. We discuss
- the meaning of scales for membership functions and its consequence on aggregation operations,
- the cognitive limitations of numerical approaches to evaluation
- the use of linguistic variables, and fuzzy intervals.

In contrast, qualitative approaches where only maximum and minimum are used, enjoy a property of scale invariance that insures their robustness. One of the most sophisticated aggregation operation making sense on qualitative scales is Sugeno integral. It is not purely ordinal as it assumes commensurability between preference intensity and criteria importance or similarly, utility and uncertainty. We shall provide an introduction to qualitative decision theory under uncertainty based on possibility theory.

However, since absolute qualitative value scales must have few levels so as to remain cognitively plausible, there are as not more classes of equivalent decisions than value levels. We shall present results on the use of qualitative aggregation techniques, and the way of overcoming their main defect: the lack of discrimination power.

Qualitative aggregations such as Sugeno integrals cannot be strictly increasing and violate the strict Pareto property. In this tutorial, we report results obtained when trying to increase the discrimination power of Sugeno integrals, generalizing such refinements of the minimum and maximum as leximin and leximax. The representation of leximin and leximax by sums of numbers of different orders of magnitude (forming a super-increasing sequence) can be generalized to weighted max and min (yielding a "big-stepped" weighted average) and Sugeno integral (yielding a "big-stepped" Choquet integral). This methodology also requires qualitative monotonic set-functions to be refined by numerical set-functions, and we show they can always be belief or plausibility functions in the sense of Shafer.

Finally the last part of the tutorial will present results on bipolar qualitative approaches to multifactorial evaluations. While many evaluation methods aim at providing a preference ranking of decisions, not so many of them deal with the fact that an option can be intrinsically good or bad. We review bipolar qualitative decision rules and show they bridge the gap between decision heuristics based on focalisation on the most important criteria, and numerical bipolar approaches like cumulative prospect theory, and bicapacity methods.

Didier Dubois is a Research Advisor at IRIT, the Computer Science Department of Paul Sabatier University in Toulouse, France and belongs to the French National Centre for Scientific Resarch (CNRS). His topics of interest range from Artificial Intelligence to Operations Research and Decision Sciences, with emphasis on the modelling, representation and processing of imprecise and uncertain information in reasoning, decision and risk analysis.
He is the co-author, with Henri Prade, of two monographs on fuzzy sets and possibility theory, and 15 edited volumes on uncertain reasoning, fuzzy sets, and decision analysis. Also with Henri Prade, he coordinated the HANDBOOK of FUZZY SETS series published by Kluwer (7 volumes, 1998-2000) including the book Fundamentals of Fuzzy Sets. He has contributed about 200 technical journal papers on uncertainty theories and applications. He is a Co-Editor-in -Chief of the journal Fuzzy Sets and Systems and a member of the Editorial Board of several technical journals dealing with uncertain reasoning. He is a former president of the International Fuzzy Systems Association (IFSA, 1995-1997) and an IFSA and an ECCAI fellow. He received the 2002 Pioneer Award of the IEEE Neural Network Society.

A primer on cycle-transitivity

Bernard De Baets, KERMIT, Ghent University

Abstract: The cycle-transitivity framework has been developed over the past years to provide a general setting for studying the transitivity of reciprocal relations. The latter can be seen as graded generalizations of classical complete relations and are suited for expressing graded preferences in a bipolar setting. An operational model naturally resulting in a reciprocal relation is that of computing winning probabilities between random variables (either (treated as) independent, artificially coupled by a same copula, or coupled by means of a multi-dimensional copula). This approach not only provides an interesting point of departure for developing alternative theories of stochastic dominance, it also sheds a new light on mutual rank probabilities in partially ordered sets and AUC values in multi-class classification or ordinal regression problems in machine learning. But above all, the cycle-transitivity framework turns out to be an endless playground for the researcher knowledgeable in aggregation functions.

Bernard De Baets (1966) holds an M.Sc. degree in Mathematics (1988), a Postgraduate degree in Knowledge Technology (1991) and a Ph.D. degree in Mathematics (1995), all summa cum laude from Ghent University (Belgium), and is a Government of Canada Award holder (1988). He is a Full Professor in Applied Mathematics (2008) at Ghent University, where he is leading KERMIT, the research unit Knowledge-Based Systems. He is an Honorary Professor of Budapest Tech (2006) and an IFSA Fellow (2011). His publications comprise more than 250 papers in international journals and about 50 book chapters. He serves on the Editorial Boards of various international journals, in particular as co-editor-in-chief of Fuzzy Sets and Systems. B. De Baets coordinates the EURO Working Group on Fuzzy Sets (EUROFUSE), and is member of the Board of Directors of EUSFLAT and of the Administrative Board of the Belgian OR Society.

Luigi Troiano,
9 Jul 2011, 07:04
Luigi Troiano,
9 Jul 2011, 07:04
Luigi Troiano,
9 Jul 2011, 06:59
Luigi Troiano,
9 Jul 2011, 06:59