M.R. Roubens - Böcker

This volume contains the proceedings of the Second Joint IFSA-EC and EURO-WGFS Workshop on Progress in Fuzzy Sets in Europe held on April 6 -8, 1989 in Vienna, Austria. The workshop was organized by Prof. Dr. Wolfgang H. Janko from the University of Economics in Vienna under the auspices of IFSA-EC, the European chapter of the International Fuzzy Systems Association, and EURO-WGFS, the working group on Fuzzy Sets of the Association of Eu­ ropean Operational Research Societies. The workshop gathered more than 30 participants coming from Western European countries (Austria, Bel­ gium, England, Germany, Finland, France, Hungary, Italy, Scotland and Spain) Eastern European countries (Bulgaria, the German Federal Repu­ blic, Hungary and Poland) and non-European countries such as China and Japan. The 15 selected and refereed papers included in the volume are in prin­ ciple the author's own versions, with limited editorial changes and small corrections. They are arranged in alphabetical order. I wish to thank all the contributors for their valuable papers and an outstan­ ding cooperation in the editorial project. I also would like to express my sincere thanks to Professor Dr. H. J. Zimmermann for the cooperation in the refereeing procedure.

Fuzzy Logic: State of the Art covers a wide range of both theory and applications of fuzzy sets, ranging from mathematical basics, through artificial intelligence, computer management and systems science to engineering applications.Fuzzy Logic will be of interest to researchers working in fuzzy set theory and its applications.

The encounter, in the late seventies, between the theory of triangular norms, issuing frorn stochastic geornetry, especially the works of Menger, Schweizer and Sklar, on the one band, and the theory of fuzzy sets due to Zadeh, 10n the other band has been very fruitful. Triangular norms have proved to be ready-rnade mathematical rnodels of fuzzy set intersections and have shed light on the algebraic foundations of fuzzy sets. One basic idea behind the study of triangular norms is to solve functional equations that stern frorn prescribed axioms describing algebraic properties such as associativity. Alternative operations such as rneans have been characterized in a similar way by Kolmogorov, for instance, and the rnethods for solving functional equations are now weil established thanks to the efforts of Aczel, among others. One can say without overstaternent that the introduction of triangular norms in fuzzy sets has strongly influenced further developrnents in fuzzy set theory, and has significantly contributed to its better acceptance in pure and applied rnathematics circles.The book by Fodor and Roubens systematically exploits the benefits of this encounter in the- analysis of fuzzy relations. The authors apply functional equation rnethods to notions such as equivalence relations, and various kinds of orderings, for the purpose of preference rnodelling. Centtal to this book is the rnultivalued extension of the well-known result claiming that any relation expressing weak preference can be separated into three cornponents respectively describing strict preference, indifference and incomparability.

This book provides a select collection of papers written by experts on multiple criteria decision aid and presented at the International Conference on Methods and Applications of Multiple Criteria Decision Making in May 1997 at Mons in Belgium. It covers methodological aspects of decision theory and comparisons between theoretical approaches to multiple criteria decision making. The material includes choice procedures, Multiple Attribute Utility Theory (MAUT), outranking methods like ELECTRE and PROMETHEE, verbal decision analysis and Data Envelopment Analysis (DEA).

The encounter, in the late seventies, between the theory of triangular norms, issuing frorn stochastic geornetry, especially the works of Menger, Schweizer and Sklar, on the one band, and the theory of fuzzy sets due to Zadeh, 10n the other band has been very fruitful. Triangular norms have proved to be ready-rnade mathematical rnodels of fuzzy set intersections and have shed light on the algebraic foundations of fuzzy sets. One basic idea behind the study of triangular norms is to solve functional equations that stern frorn prescribed axioms describing algebraic properties such as associativity. Alternative operations such as rneans have been characterized in a similar way by Kolmogorov, for instance, and the rnethods for solving functional equations are now weil established thanks to the efforts of Aczel, among others. One can say without overstaternent that the introduction of triangular norms in fuzzy sets has strongly influenced further developrnents in fuzzy set theory, and has significantly contributed to its better acceptance in pure and applied rnathematics circles.The book by Fodor and Roubens systematically exploits the benefits of this encounter in the- analysis of fuzzy relations. The authors apply functional equation rnethods to notions such as equivalence relations, and various kinds of orderings, for the purpose of preference rnodelling. Centtal to this book is the rnultivalued extension of the well-known result claiming that any relation expressing weak preference can be separated into three cornponents respectively describing strict preference, indifference and incomparability.

This book provides a select collection of papers written by experts on multiple criteria decision aid and presented at the International Conference on Methods and Applications of Multiple Criteria Decision Making (May 1997, Mons, Belgium). It covers methodological aspects of decision theory and comparisons between theoretical approaches to multiple criteria decision making. The material includes choice procedures, Multiple Attribute Utility Theory (MAUT), outranking methods like ELECTRE and PROMETHEE, verbal decision analysis and Data Envelopment Analysis (DEA). Audience: This book is mathematically oriented but the results are also of great interest to engineers and economists who design and implement decision support systems in practice. It also contains a sufficient number of examples to make it attractive to non-specialists.

Fuzzy Logic: State of the Art covers a wide range of both theory and applications of fuzzy sets, ranging from mathematical basics, through artificial intelligence, computer management and systems science to engineering applications.Fuzzy Logic will be of interest to researchers working in fuzzy set theory and its applications.