Fundamentals of Possibilistic Measures
- Department of Cybernetics
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 non-numerical 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.
- Syllabus of lectures:
- Syllabus of tutorials:
- Study Objective:
- Study materials:
(1)G. De Cooman: Possibility theory I, II, III, International Journal of General Systems 25(1997), pp. 291-323, 325-351, 353-371.
(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.
- Further information:
- No time-table has been prepared for this course
- The course is a part of the following study plans: