Fundamentals of Possibilistic Measures
Code  Completion  Credits  Range  Language 

XP33POS  ZK  4  2P+0S  Czech 
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 Department of Cybernetics
 Synopsis:

Possibilistic measures present a mathematical tool for uncertainty (randomness) quantification and processing applying the notions and apparatus of the so called fuzzy sets. They are alternative to probabilistic measures in the sense that they are based on the maxitivity priciple in spite to the additivity principle applied in the standard measure and probability theory. Because of the fact that the operation of maximum (supremum) can be defined also in certain nonnumerical structures, possibilistic measures taking their values in partially ordered sets and, in particular, in complete lattices, are worth being investigated. The lecture will not suppose any preliminary knowledge in fuzzy set theory, lattice theory or the standard measure and probability theory.
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 Study materials:

(1)G. De Cooman: Possibility theory I, II, III, International Journal of General Systems 25(1997), pp. 291323, 325351, 353371.
(2) D.Dubois, H.Prade: Possibility theory  an approach to computerized processing of uncertainty. Plenum Press, New York, 1988.
(3) D.Dubois et al. : Possibility theory, probability theory and fuzzy sets  misunderstandings, bridges and gaps. In: The Handbook of Fuzzy Sets Series  Fundamentals of Fuzzy Sets. D.Dubois and H.Prade, Eds., Kluwer Academic Publishers, 2000, pp. 343  438.
(4)J.A.Goguen: L  fuzzy sets. Journal of Mathematical Analysis and Applications 18(1967), pp. 145  174.
 Note:
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 No timetable has been prepared for this course
 The course is a part of the following study plans:

 Doctoral studies, daily studies (compulsory elective course)
 Doctoral studies, combined studies (compulsory elective course)