Generalized Theory of Uncertainty: Principal Concepts and Ideas

Lotfi A. Zadeh

Chapter 6 in Fundamental Uncertainty, 2011, pp 104-150 from Palgrave Macmillan

Abstract: Abstract It is a deep-seated tradition in science to turn to probability theory when one is faced with a problem in which uncertainty plays a significant role. Underlying this tradition is the assumption that there is just one kind of uncertainty—probabilistic uncertainty. The generalized theory of uncertainty (GTU) challenges this assumption. The principal thesis of GTU is that there are many different kinds of uncertainty. Principally, there are two kinds: probabilistic uncertainty and possibilistic uncertainty. In addition, there are various combinations of these uncertainties, principally probabilistic/possibilistic uncertainty and possibilistic/probabilistic uncertainty. In relation to probabilistic/possibilistic uncertainty, a case in point is the Dempster–Shafer theory of evidence. Basically, the Dempster–Shafer theory is a theory of random sets. A random set is a probability distribution of possibility distributions.

Keywords: Fuzzy Logic; Generalize Constraint; Possibility Distribution; Fuzzy Random Variable; Extension Principle (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1057/9780230305687_6

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