Fuzzy Sets Theory and Applications / Edition 1

by Andrï Jones, Arnold Kaufmann, Hans-Jïrgen Zimmermann

Overview

Problems in decision making and in other areas such as pattern recognition, 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 shastic (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 domain 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.

Product Details

ISBN-13:	9789027722621
Publisher:	Springer Netherlands
Publication date:	06/30/1986
Series:	Nato Science Series C: , #177
Edition description:	1986
Pages:	403
Product dimensions:	8.27(w) x 11.69(h) x 0.05(d)

Table of Contents

1: Some theoretical Aspects.- 1.1 Mathematics and fuzziness.- 1.2 Radon—Nikodym Theorem for fuzzy set—valued measures.- 1.3 Construction of a probability distribution from a fuzzy information.- 1.4 Convolution of fuzzyness and probability.- 1.5 Fuzzy sets and subobjects.- 2: From theory to applications.- 2.1 Outline of a theory of usuality based on fuzzy logic.- 2.2 Fuzzy sets theory and mathematical programming.- 2.3 Decisions with usual values.- 2.4 Support logic programming.- 2.5 Hybrid data — various associations between fuzzy subsets and random variables.- 2.6 Fuzzy relation equations : methodology and applications.- 3: Various particular applications.- 3.1 Multi criteria decision making in crisp and fuzzy environments.- 3.2 Fuzzy subsets applications in O.R. and management.- 3.3 Character recognition by means of fuzzy set reasoning.- 3.4 Computerized electrocardiography and fuzzy sets.- 3.5 Medical applications with fuzzy sets.- 3.6 Fuzzy subsets in didactic processes.