Title: Probabilistic Analysis of Belief Functions (IFSR International Series in Systems Science and Systems Engineering, 16)
Publisher: Kluwer Academic / Plenum
Publication Date: 2001
Language: English
ISBN 10: 030646702X
ISBN 13: 9780306467028
Binding: Hardcover
Condition: New

About this title

Synopsis

Inspired by the eternal beauty and truth of the laws governing the run of stars on heavens over his head, and spurred by the idea to catch, perhaps for the smallest fraction of the shortest instant, the Eternity itself, man created such masterpieces of human intellect like the Platon's world of ideas manifesting eternal truths, like the Euclidean geometry, or like the Newtonian celestial me� chanics. However, turning his look to the sub-lunar world of our everyday efforts, troubles, sorrows and, from time to time but very, very seldom, also our successes, he saw nothing else than a world full of uncertainty and tem� porariness. One remedy or rather consolation was that of the deep and sage resignation offered by Socrates: I know, that I know nothing. But, happy or unhappy enough, the temptation to see and to touch at least a very small por� tion of eternal truth also under these circumstances and behind phenomena charged by uncertainty was too strong. Probability theory in its most sim� ple elementary setting entered the scene. It happened in the same, 17th and 18th centuries, when celestial mechanics with its classical Platonist paradigma achieved its greatest triumphs. The origins of probability theory were inspired by games of chance like roulettes, lotteries, dices, urn schemata, etc. and probability values were simply defined by the ratio of successful or winning results relative to the total number of possible outcomes.

Synopsis

This volume is a highly theoretical and mathematical study analyzing the notion and theory of belief functions, also known as the Dempster-Shafer theory, from the point of view of the classical Kolmogorov axiomatic probability theory. In other terms, the theory of belief functions is taken as an interesting, non-traditional application of probability theory, and the standard methodology of probability theory, and measure theory in general, is applied in order to arrive at some new and perhaps interesting generalizations and results not accessible within the classical combinatorial framework of the theory of belief functions (Dempster-Shafer theory) over finite spaces. The relation to great systems and their theory seems to be very close and should become clear from the first two chapters of the book.

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