Fuzzy Sets Theory and Applications

1. Front Matter

   Pages i-xii

   PDF

2. Some theoretical aspects

   1. Front Matter

      Pages 1-1

      PDF

   2. Mathematics and Fuzziness

      • R. Lowen

      Pages 3-38

   3. Radon-Nikodym Theorem for Fuzzy Set-Valued Measures*

      • D. A. Ralescu

      Pages 39-50

   4. Construction of a Probability Distribution from a Fuzzy Information

      • S. Moral

      Pages 51-60

   5. Convolution of Fuzzyness and Probability

      • Anio O. Arigoni

      Pages 61-68

   6. Fuzzy Sets and Subobjects

      • Ulrich Höhle

      Pages 69-76

3. From theory to applications

   1. Front Matter

      Pages 77-77

      PDF

   2. Outline of a Theory of Usuality Based on Fuzzy Logic

      • L. A. Zadeh

      Pages 79-97

   3. Fuzzy Set Theory and Mathematical Programming

      • H.-J. Zimmermann

      Pages 99-114

   4. Decisions with Usual Values

      • R. R. Yager

      Pages 115-131

   5. Support Logic Programming

      • J. F. Baldwin

      Pages 133-170

   6. Hybrid Data – Various Associations Between Fuzzy Subsets and Random Variables

      • A. Kaufmann

      Pages 171-211

   7. Fuzzy Relation Equations : Methodology and Applications

      • Elie Sanchez

      Pages 213-229

4. Various particular applications

   1. Front Matter

      Pages 231-231

      PDF

   2. Multi Criteria Decision Making in Crisp and Fuzzy Environments

      • H.-J. Zimmermann

      Pages 233-256

   3. Fuzzy Subsets Applications in O.R. and Management

      • A. Kaufmann

      Pages 257-300

   4. Character Recognition by Means of Fuzzy Set Reasoning

      • J. Mantas

      Pages 301-316

   5. Computerized Electrocardiography and Fuzzy Sets

      • R. Degani, G. Bortolan

      Pages 317-329

   6. Medical Applications with Fuzzy Sets

      • Elie Sanchez

      Pages 331-347

Problems in decision making and in other areas such as pattern recogni­ tion, control, structural engineering etc. involve numerous aspects of uncertainty. Additional vagueness is introduced as models become more complex but not necessarily more meaningful by the added details. During the last two decades one has become more and more aware of the fact that not all this uncertainty is of stochastic (random) cha­ racter and that, therefore, it can not be modelled appropriately by probability theory. This becomes the more obvious the more we want to represent formally human knowledge. As far as uncertain data are concerned, we have neither instru­ ments nor reasoning at our disposal as well defined and unquestionable as those used in the probability theory. This almost infallible do­ main is the result of a tremendous work by the whole scientific world. But when measures are dubious, bad or no longer possible and when we really have to make use of the richness of human reasoning in its variety, then the theories dealing with the treatment of uncertainty, some quite new and other ones older, provide the required complement, and fill in the gap left in the field of knowledge representation. Nowadays, various theories are widely used: fuzzy sets, belief function, the convenient associations between probability and fuzzines~ etc ••• We are more and more in need of a wide range of instruments and theories to build models that are more and more adapted to the most complex systems.

• Mathematica
• addition
• equation
• function
• logic
• mathematics
• probability theory
• theorem
• variable

• Université Catholique de Louvain, Louvain-la-Neuve, Belgium

  André Jones

• O.R. and M.S Consultant, Grenoble, France

  Arnold Kaufmann

• Institute of Technology, Aachen, Germany

  Hans-Jürgen Zimmermann

Policies and ethics