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Soft Methods in Probability, Statistics and Data Analysis pp 27–61Cite as

Toward a Perception-Based Theory of Probabilistic Reasoning with Imprecise Probabilities

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Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 16))

Abstract

The perception-based theory of probabilistic reasoning which is outlined in this paper is not in the traditional spirit. Its principal aim is to lay the groundwork for a radical enlargement of the role of natural languages in probability theory and its applications, especially in the realm of decision analysis. To this end, probability theory is generalized by adding to the theory the capability to operate on perception-based information, e.g., “Usually Robert returns from work at about 6 p.m”, or “It is very unlikely that there will be a significant increase in the price of oil in the near future”. A key idea on which perception-based theory is based is that the meaning of a proposition, p, which describes a perception, may be expressed as a generalized constraint of the form X isγ R, where X is the constrained variable, R is the constraining relation and isγ is a copula in which γ is a discrete variable whose value defines the way in which R constrains X. In the theory, generalized constraints serve to define imprecise probabilities, utilities and other constructs, and generalized constraint propagation is employed as a mechanism for reasoning with imprecise probabilities as well as for computation with perception-based information.

Reprinted from Journal of Statistical Planning and Inference 105 (2002), 233–264, with kind permission from Elsevier Science

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Author information

Authors and Affiliations

  1. Computer Science Division and the Electronics Research Laboratory, Department of EECS, University of California, Berkeley, CA, 94720-1776, USA

    Lotfi A. Zadeh

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  1. Lotfi A. Zadeh
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Editors and Affiliations

  1. Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01-447, Warsaw, Poland

    Przemysław Grzegorzewski  & Olgierd Hryniewicz  & 

  2. Facultad de Ciencias, Departamento de Estadística e I.O. y D.M., Universidad de Oviedo, C/Calvo Sotelo, s/n, 33007, Oviedo, Spain

    María Ángeles Gil

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Zadeh, L.A. (2002). Toward a Perception-Based Theory of Probabilistic Reasoning with Imprecise Probabilities. In: Grzegorzewski, P., Hryniewicz, O., Gil, M.Á. (eds) Soft Methods in Probability, Statistics and Data Analysis. Advances in Intelligent and Soft Computing, vol 16. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1773-7_2

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  • DOI: https://doi.org/10.1007/978-3-7908-1773-7_2

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-7908-1526-9

  • Online ISBN: 978-3-7908-1773-7

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