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Erratum to: A framework for assessing middle school students' thinking in conditional probability and independence

James E. Tarr, Graham A. Jones
1997 Mathematics Education Research Journal  
•Can quantify, albeit imprecisely, changing probabilities in a "without replacement" situation.  ...  •States the necessary conditions under which two events are related. •Can quantify, albeit imprecisely, changing probabilities in a "without replacement" situation.  ... 
doi:10.1007/bf03217316 fatcat:7j42xe7minbrxahvhy42ogwjge

Evidential Networks for Fault Tree Analysis with Imprecise Knowledge

Jianping Yang, Hong-Zhong Huang, Yu Liu, Yan-Feng Li
2012 International journal of turbo & jet-engines  
In this paper, the evidential networks (EN) are employed to quantify and propagate the aforementioned uncertainty and imprecision in fault tree analysis.  ...  The figures of the logic gates and the converted equivalent EN, together with the associated truth tables and the conditional belief mass tables, are also presented in this work.  ...  The results illustrate that the EN can quantify the imprecision and uncertainty and propagate this imprecision from the basic events to the top event.  ... 
doi:10.1515/tjj-2012-0015 fatcat:frxweofz7zci5k554bj7swisbm

Preliminary Interpretation Using Ambiguous Queries

Shivani Surana
2017 International Journal for Research in Applied Science and Engineering Technology  
The user interacts with it by specifying probability distributions over attributes, which then expresses imprecise conditions about the entities of interest.  ...  Preliminary interpretation helps the user on the right query conditions by addressing three key challenges: 1) Efficiently computing results for an imprecise query. 2) Gives out the result of the sensitivity  ...  This method is designed to accommodate uncertainty and imprecision in user-provided query conditions through two major technical contributions: A novel notion of sensitivity to quantify the impact of uncertainty  ... 
doi:10.22214/ijraset.2017.10158 fatcat:pp2bkjsxmzg3vl2achoczmcrz4

Scoring Imprecise Credences: A Mildly Immodest Proposal

Conor Mayo-Wilson, Gregory Wheeler
2016 Philosophy and Phenomenological Research  
To do so, we employ a (slightlygeneralized) impossibility theorem of Seidenfeld, Schervish, and Kadane (2012) , who show that there is no strictly proper scoring rule for imprecise probabilities.  ...  The second is a shift from a numerically precise model of belief to an imprecise model represented by a set of probability functions (2010).  ...  imprecise belief states, or (ii) abandon Quantifiability altogether.  ... 
doi:10.1111/phpr.12256 fatcat:g7udhm3pizd3fd4wwpdi4im34q

Reliability Analysis of Aircraft Servo-Actuation Systems Using Evidential Networks

Jianping Yang, Hong-Zhong Huang, Rui Sun, Hu Wan, Yu Liu
2012 International journal of turbo & jet-engines  
The EN manage and quantify the imprecision of the servo-actuation effectively, and propagate imprecision from the root nodes to the top nodes representing the system reliability.  ...  In the mean time, available data is insufficient and imprecise during its design stage. In this paper, evidential networks (EN) are used to handle imprecise probabilities.  ...  A conditional belief function quantifies the dependency between a node and its parents And it allows for computing its mass distribution according to other variables [17] .  ... 
doi:10.1515/tjj-2012-0011 fatcat:snapppktg5ezbbnmsdovnc4b5u

Towards a comprehensive uncertainty assessment in environmental research and decision support

Peter Reichert
2020 Water Science and Technology  
in addition to the uncertainty of predictions in decision support; and (vi) explicitly considering the ambiguity about prior distributions for predictions and preferences by using imprecise probabilities  ...  Bayesian probabilities.  ...  I would like to mention in particular Nele Schuwirth, Simon Lukas Rinderknecht, Johanna Mieleitner, Carlo Albert, Simone Langhans, Fridolin Haag, and Judit Lienert.  ... 
doi:10.2166/wst.2020.032 pmid:32644952 fatcat:pdqxsxyidveijm3z5eyx4mrjuy

Dispositional Logic

L.A. Zadeh
1988 Applied Mathematics Letters  
decisions in an environment of uncertainty and imprecision.  ...  The same applies to quantifiers, probabilities, possibilities and, more generally, to everything else.  ...  imprecision.  ... 
doi:10.1016/0893-9659(88)90185-1 fatcat:tsezuqhx45circa7sisymjsw7m

Decision Making with Imprecise Probabilities [chapter]

Frank P. A. Coolen
1994 Operations Research Proceedings 1993  
In this paper the use of imprecise probabilities is discussed, with emphasis on elicitation and combination of opinions and decision making, and some recent results are briefly mentioned.  ...  The theory of imprecise probabilities, a generalization of standard subjective probability, allows us to deal with such information.  ...  Acknowledgments The author is grateful to Martin Newby for useful cooperation, and to Paul van der Laan, Peter Sander and Emiel van Berkum for discussions and remarks during the research.  ... 
doi:10.1007/978-3-642-78910-6_145 fatcat:gr3osuk5tzae3fg2s2tar6hfqi

Reasoning and learning in probabilistic and possibilistic networks: An overview [chapter]

Jörg Gebhardt, Rudolf Kruse
1995 Lecture Notes in Computer Science  
of uncertain and imprecise knowledge.  ...  We give an overview on the semantical background and relevant properties of probabilistic and possibflistic networks, respectively, and consider knowledge representation and independence as well as evidence  ...  Equation (1) reads as follows: The marginal conditional probability on Y2AuB, given any instantiation of the variables in C, equals the product of the marginal conditional probabilities on ~A and 12B,  ... 
doi:10.1007/3-540-59286-5_45 fatcat:oaliua7gajdrbplqdfl3vowmie

A Restriction Level Approach for the Representation and Evaluation of Fuzzy Association Rules

Miguel Delgado, M. Dolores Ruiz, Daniel Sánchez
2009 European Society for Fuzzy Logic and Technology  
The second one is a new proposal for the representation of imprecise properties (in particular for fuzzy sets) by using restriction levels, which verifies all the crisp logic equivalences [1] .  ...  The first one is a model for the representation and evaluation of crisp association rules.  ...  Acknowledgment This work has been partially supported by the projects TIN2006-15041-C04-01 and TIN2006-07262.  ... 
dblp:conf/eusflat/DelgadoRS09 fatcat:z4ghmpeblvfqva2lvc7vhf2wim

Tolerance Analysis Approach based on the Classification of Uncertainty (Aleatory/Epistemic)

J.Y. Dantan, N. Gayton, A.J. Qureshi, M. Lemaire, A. Etienne
2013 Procedia CIRP  
It presents: a brief view of the uncertainty classification: Aleatory uncertainty comes from the inherent uncertain nature and phenomena, and epistemic uncertainty comes from the lack of knowledge, a formulation  ...  of the tolerance analysis problem based on this classification, its development: Aleatory uncertainty is modeled by probability distributions while epistemic uncertainty is modeled by intervals; Monte  ...  While information regarding variability is best conveyed using probability distributions, information regarding imprecision is more faithfully conveyed using families of probability distributions encoded  ... 
doi:10.1016/j.procir.2013.08.044 fatcat:77dbod3f5najxi7jri7pomtvh4

Probability Semantics for Aristotelian Syllogisms [article]

Niki Pfeifer, Giuseppe Sanfilippo
2021 arXiv   pre-print
For framing the Aristotelian syllogisms as probabilistic inferences, we interpret basic syllogistic sentence types A, E, I, O by suitable precise and imprecise conditional probability assessments.  ...  Based on a generalization of de Finetti's fundamental theorem to conditional probability, we investigate the coherent probability propagation rules of argument forms of the syllogistic Figures I, II, and  ...  Niki Pfeifer is supported by the German Federal Ministry of Education and Research (BMBF project 01UL1906X: "Logic and philosophy of science of reasoning under uncertainty").  ... 
arXiv:2008.10338v2 fatcat:vikkuejtv5fqlddknhp2wlwrjm

Imprecision in Machine Learning and AI

Cassio P. de Campos, Alessandro Antonucci
2015 The IEEE intelligent informatics bulletin  
Sharp (or, say, precise) values are typically used to quantify these probabilities.  ...  CONCLUSIONS We advocated the use of imprecise probability in AI and machine learning.  ... 
dblp:journals/cib/CamposA15 fatcat:vzo5b45mzzgbdkonzadqfkbhtq

Bayesian Network Based Imprecise Probability Estimation Method for Wind Power Ramp Events

Yuanchun Zhao, Wenli Zhu, Ming Yang, Mengxia Wang
2021 Journal of Modern Power Systems and Clean Energy  
In this paper, an imprecise conditional probability estimation method for WPREs is proposed based on the Bayesian network (BN) theory.  ...  Meanwhile, by using the extracted dependencies and Bayesian rules, the method can simplify the conditional probability estimation and perform reliable prediction even with scarce samples.  ...  An extended imprecise Dirichlet model (IDM) is then developed to quantify these unclear dependencies and establish the imprecise conditional probability table (CPT) at each node.  ... 
doi:10.35833/mpce.2019.000294 fatcat:bqi5topfbbfhdltbupmrlm6nqa

A Symbolic Approach to Reasoning with Linguistic Quantifiers [chapter]

Didier Dubois, Henri Prade, Lluis Godo, Ramon López de Màntaras
1992 Uncertainty in Artificial Intelligence  
This paper investigates the possibility of performing automated reasoning in probabilistic logic when probabilities are expressed by means of linguistic quantifiers.  ...  The quantified syllogism, modelling the chaining of probabilistic rules, is studied in this context.  ...  quantifiers or conditional probabilities.  ... 
doi:10.1016/b978-1-4832-8287-9.50015-3 fatcat:c4jhijfsyrhxjff5u2phn7fpym
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