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Uncertain inference using interval probability theory

James W. Hall, David I. Blockley, John P. Davis
1998 International Journal of Approximate Reasoning  
The use of interval probability theory (IPT) for uncertain inference is demonstrated. The general inference rule adopted is the theorem of total probability.  ...  Uncertain inference using IPT is compared with Bayesian inference.  ...  A review of interval probability theory IPT is founded on the axioms of probability theory but allows support for a conjecture to be separated from support for the negation of the conjecture.  ... 
doi:10.1016/s0888-613x(98)10010-5 fatcat:5tamsy2zobbadmrydsq24dnk64

Page 468 of American Society of Civil Engineers. Collected Journals Vol. 113, Issue 4 [page]

1987 American Society of Civil Engineers. Collected Journals  
The method combines features of the theory of fuzzy sets, Shafer’s theory of evidence (Shafer 1976) and probability theory to form a suitable framework for uncertain logical rea- soning.  ...  Probability and fuzzy logic are examples of two such choices. The modeling of uncertain inference is, however, rather different from the traditional problems of modeling physical systems.  ... 

Uncertain deduction and conditional reasoning

Jonathan St. B. T. Evans, Valerie A. Thompson, David E. Over
2015 Frontiers in Psychology  
We argue that the study of "uncertain deduction" should directly ask people to assign probabilities to both premises and conclusions, and report an experiment using this method.  ...  Most every day and scientific inference is made from more or less confidently held beliefs and not assumptions, and the relevant normative standard is Bayesian probability theory.  ...  ofTable 3are derived using the total probability theorem of probability theory.  ... 
doi:10.3389/fpsyg.2015.00398 pmid:25904888 pmcid:PMC4389288 fatcat:bb37aks43bauzfn4qclakbtdye

Subject index to volume 2

1988 International Journal of Approximate Reasoning  
and, 330 Bayesian approach, heuristic, to knowledge acquisition, application to analysis of tissuetype plasminogen activator, 342 Bayesian belief networks, 337 stochastic stimulation of, 331 Bayesian inference  ...  model-based machine vision, 327-328 Bayesian prediction, for artificial intelligence, 342 Bayesian scheme, implementing of, for revising belief commitments, 329 Belief prior, representation of, 261-263 probability  ...  , in automatic object classification, comparison with fuzzy set theory, 105-106 Rule base, using numerical uncertainty repre- sentations, 330-331 Rule-based inference system, combination of uncertain  ... 
doi:10.1016/0888-613x(88)90114-4 fatcat:rj373wy2pzff3d3otqdhxs2gca


Oļegs Uzhga-Rebrov, Galina Kuleshova
2019 Environment Technology Resources Proceedings of the International Scientific and Practical Conference  
The present paper considers one approach to Bayes' formula based probabilistic inference under interval values of relevant probabilities; the necessity of it is caused by the impossibility to obtain reliable  ...  For visualisation purposes, the state of initial and target information is modelled using probability trees.  ...  That interpretation underlies the theory of uncertain probabilities of P. Walley. The theory can be regarded as a specific extension of the traditional subjective probability theory.  ... 
doi:10.17770/etr2019vol2.4112 fatcat:uxzqzydnvfervl2oiio45xvb3q


2011 International journal on artificial intelligence tools  
Interval data are widely used in real applications to represent the values of quantities in uncertain situations.  ...  However, the implied probabilistic causal relationships among interval-valued variables with interval data cannot be represented and inferred by general Bayesian networks with point-based probability parameters  ...  As well, the rule-based methods, D-S evidence theory, fuzzy set and rough set theories are frequently used mechanisms for representing and inferring uncertain knowledge. 19 Among these methods, the D-S  ... 
doi:10.1142/s0218213011000449 fatcat:64purxkyq5c6bai4jozmksspsy

Engineering Cost Evaluation Model Based on Multi Dimension Entropy and Intelligent Algorithm

Yanan Li, Anders Nilsson
2016 TELKOMNIKA (Telecommunication Computing Electronics and Control)  
Rough set theory is utilized to analyze the fuzzy, random and uncertain factors and upper and lower approximation set relation is used to calculate the value taking interval of reliability index to make  ...  interval reliability analysis method is that it is not necessary to make interval standardization calculation for uncertain parameters and reliability analysis is made in direct utilization of objective  ...  Traditional uncertain information processing method includes fuzzy set theory, evidence theory and probability statistics theory etc.  ... 
doi:10.12928/telkomnika.v14i2a.4347 fatcat:kbmy52rgwvf3lidfqt4vgvi3ty

Foundations of probabilistic inference with uncertain evidence

Frank J. Groen, Ali Mosleh
2005 International Journal of Approximate Reasoning  
Uncertain evidence is defined as the class of observations for which this statement cannot take place in certain terms.  ...  It is a significant class of evidence, since it cannot be treated using Bayes Theorem in its conventional form [G. Shafer, A Math-  ...  Alternative theories, such as Fuzzy Logic [2] , Possibility Theory [3] and Evidence Theory [4] have been advocated as theories that should be used where Probability Theory allegedly fails to apply  ... 
doi:10.1016/j.ijar.2004.09.001 fatcat:dacz7evwwfhyblwee3mfy5de2e

Representing knowledge and evidence for decision [chapter]

Henry E. Kyburg
1987 Lecture Notes in Computer Science  
We argue that pointvalued probabilities are a poor representation of uncertainty; that we need not be concerned with uncertain evidence; that interval-valued probabilities that result from knowledge of  ...  inference, inductive inference, statistical inference); and finally that this framework provides a very nearly classical decision theory --so far as it goes.  ...  (Kyburg, 1983) In what follows, I will sketch the properties of interval-valued epistemic probability, and exhibit a structure for knowledge representation that allows for both uncertain inference from  ... 
doi:10.1007/3-540-18579-8_2 fatcat:6vhh7fuukfhi3fphibaas77ncm

Bayesian inference in physics

Udo von Toussaint
2011 Reviews of Modern Physics  
Bayes: 1) Assign prior: 2) Assign likelihood: 3) Compute posterior using Bayes' theorem: posterior : contains complete information: summarizing quantities: mode: m=0 mean: <m 0 >=0.06 95%interval  ...  causes Calculus: Cox (1946): Basic requirements (i.e. transitivity,consistency) single out usual rules of probability theory to handle uncertainty Please note: probability here not restricted to  ... 
doi:10.1103/revmodphys.83.943 fatcat:l5v3msodj5a3je2xb6c63mszdq

Nonparametric predictive utility inference

B. Houlding, F.P.A. Coolen
2012 European Journal of Operational Research  
., that of decision making with uncertain utility and that of Nonparametric Predictive Inference (NPI).  ...  An example of the use of NPUI within a motivating sequential decision problem is also considered for two extreme selection criteria, i.e., a rule that is based on an attitude of extreme pessimism and a  ...  the resulting NPI to the theory of interval or imprecise probability.  ... 
doi:10.1016/j.ejor.2012.03.024 fatcat:ycfslgqeinbhxmsinwfg3rmghq

The conditional in mental probability logic [chapter]

Niki Pfeifer, Gernot D. Kleiter
2010 Cognition and ConditionalsProbability and Logic in Human Thinking  
This work is supported by the Austrian Research Fonds, FWF (project P20209 "Mental probability logic").  ...  It combines logic and subjective probability theory. Probability logic tells us how to infer deductively the coherent (lower and upper) probability of the conclusion from the premises.  ...  Therefore the heavy use of probability theory. In the traditional psychology of reasoning, however, the tasks were associated with deductive reasoning. Therefore the heavy use of classical logic.  ... 
doi:10.1093/acprof:oso/9780199233298.003.0009 fatcat:a73l3lopobdphompfw5jncukoi

Some varieties of qualitative probability [chapter]

Michael P. Wellman
1995 Lecture Notes in Computer Science  
In this essay I present a general characterization of qualitative probability, including a partial taxonomy of possible approaches.  ...  Acknowledgment This work was supported in part by grant F49620-94-1-0027 from the US Air Force Office of Scientific Research.  ...  Introduction In the standard theory of probability, degrees of belief for events or propositions take values in the real interval [0, 1] .  ... 
doi:10.1007/bfb0035948 fatcat:kwmscel3mzai3cfmugki3ehthy

Page 1467 of Mathematical Reviews Vol. , Issue 2001C [page]

2001 Mathematical Reviews  
Fuzziness Knowledge-Based Systems 6 (1998), no.6, 551-562; MR 2000d:68149] put forward a theory of incomplete interval prob- abilities, which is meant to give a common framework to both interval probabilities  ...  Fuhrmann and Levi then argue that if 7 has statistical as- sumptions that can be employed to license inductive inferences on probability judgments, both tests can be used (but sometimes they will generate  ... 

Uncertainty Management for Fuzzy Decision Support Systems [article]

Christoph F. Eick
2013 arXiv   pre-print
The certainty of propositions is represented using intervals [a, b] expressing that the proposition's probability is at least a and at most b.  ...  Different inference schemas for applying fuzzy rules by using modus ponens are discussed.  ...  then H [c d] else H [0 d] case2: assumes conventional probability theory is used9: Using: if E then H [c d] E [a b] • mscomb is used for combining evidence. • the modus ponens generating function  ... 
arXiv:1304.2351v1 fatcat:4lpezyv365d3nmklxg3vvgqnfi
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