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Reformulating decision theory using fuzzy set theory and Shafer's theory of evidence

Robert F. Bordley
2003 Fuzzy sets and systems (Print)  
In addition, we use the Heisenberg Uncertainty Principle to argue for a change in one of the technical assumptions underlying decision theory.  ...  We argue that this formulation addresses many of the observed empirical deviations between decision theory and experiment. It also addresses the anomalies of quantum physics.  ...  For future reading The following articles could also be of interest to the reader, [3, 4, 6, 9, 14, 22, 23, 24, 26, 29, 30, 31, 37, 58] .  ... 
doi:10.1016/s0165-0114(02)00515-8 fatcat:7fm7ha2au5bozjszk6zqpl6sje

Death of Paradox: The Killer Logic Beneath the Standards of Proof

Kevin M. Clermont
2012 Social Science Research Network  
This modern logic suggests that factfinders view evidence of an imprecisely perceived and described reality to form a fuzzy degree of belief in a fact's existence; they then apply the standard of proof  ...  I contend that for understanding the standards of proof, the modern versions of logic-in particular, fuzzy logic and belief functions-work better than classical probability.  ...  Zadeh, Fuzzy Sets as a Basis for a Theory of Possibility, 1 Fuzzy Sets & Sys. 3 (1978). F .  ... 
doi:10.2139/ssrn.1986346 fatcat:kginrm5fpfgrfp4r3eoazzvmnq

Fusion of qualitative beliefs using DSmT [article]

Florentin Smarandache, Jean Dezert
2006 arXiv   pre-print
We show how qualitative beliefs can be efficiently combined using an extension of Dezert-Smarandache Theory (DSmT) of plausible and paradoxical quantitative reasoning to qualitative reasoning.  ...  This paper introduces the notion of qualitative belief assignment to model beliefs of human experts expressed in natural language (with linguistic labels).  ...  In [18, 19] , Parsons proposes a qualitative Dempster-Shafer Theory, called Qualitative Evidence Theory (QET), by using techniques from qualitative reasoning [2] .  ... 
arXiv:cs/0607147v2 fatcat:jgoaqzawtbc5xadryevghfxr2i

The Metaphysical Character of the Criticisms Raised Against the Use of Probability for Dealing with Uncertainty in Artificial Intelligence

Carlotta Piscopo, Mauro Birattari
2008 Minds and Machines  
In artificial intelligence (AI), a number of criticisms were raised against the use of probability for dealing with uncertainty.  ...  A lack of clarity and understanding of this claim had a major impact on AI.  ...  -FNRS of Belgium's French Community, of which he is a Research Associate.  ... 
doi:10.1007/s11023-008-9097-3 fatcat:2vruronlvbagzn6erzbyvmkmgi


2013 American Journal of Engineering and Applied Sciences  
Then a review is conducted of general topics such as the foundations and applications of possibility theory and evidence theory.  ...  Of the several optional treatments for epistemic uncertainty, possibility theory and evidence theory have proved to be the most computationally efficient and stable for reliability analysis and engineering  ...  This research was partially supported by the National Science Foundation of China under contract number 50775026.  ... 
doi:10.3844/ajeassp.2013.95.136 fatcat:7v6zcpeevndxzc3bii5uiufs5e

Common Sense on Standards of Proof

Kevin M. Clermont
2017 Social Science Research Network  
At the close of evidence, the standard of proof requires only comparing belief and disbelief For example, the civil standard, rather than asking whether a fact more likely than not happened according to  ...  First, in accordance with belieffunction theory, the factfinder should start at zero belief Given imperfect evidence, the factfinder will end up retaining a fair amount ofuncommitted belief As evidence  ...  Shafer's belief functions (see GLENN SHAFER, A MATHEMATICAL THEORY OF EVIDENCE (1976)).  ... 
doi:10.2139/ssrn.3007129 fatcat:tlqjmn2do5hwrobuhbf77mfq4q

Measures of uncertainty in expert systems

Peter Walley
1996 Artificial Intelligence  
The measures are additive probabilities (used in the Bayesian theory), coherent lower (or upper) previsions, belief functions (used in the Dempster-Shafer theory) and possibility measures (fuzzy logic)  ...  Each of the four measures seems to be useful in special kinds of problems, but only lower and upper previsions appear to be sufficiently general to model t.he most common types of uncertainty.  ...  In particular I must thank Terrence Fine, Frank Hampel and Philippe Smets for stimulating discussions, and Smets, Nit Wilson and George Klir for sending me copies of relevant papers.  ... 
doi:10.1016/0004-3702(95)00009-7 fatcat:td76tlmqfffsbbffmzywsei52a

On the relative belief transform

Fabio Cuzzolin
2012 International Journal of Approximate Reasoning  
We discuss its rationale in both the probability-bound and Shafer's interpretations of belief functions.  ...  Relative plausibility and belief of singletons Duality Dempster's combination Commutativity In this paper we discuss the semantics and properties of the relative belief transform, a probability transformation  ...  and Shafer's interpretations of the theory.  ... 
doi:10.1016/j.ijar.2011.12.009 fatcat:czkz6bzf7jaa5pe45ydpych7bm

The Role of Calculi in Uncertain Inference Systems [article]

Michael P. Wellman, David Heckerman
2013 arXiv   pre-print
Arguments against Bayesian decision theory are weakened when the calculus is relegated to this role.  ...  We broaden the debate by (1) exploring the constellation of secondary tasks surrounding any primary decision problem, and (2) identifying knowledge engineering concerns that present additional representational  ...  Acknowledgments Jack Breese and an anonymous referee provided valu able suggestions for this paper.  ... 
arXiv:1304.2747v1 fatcat:tgoms5yj45fexon7xpcz3y6kcy

Visions of a generalized probability theory [article]

Fabio Cuzzolin
2018 arXiv   pre-print
Finally, some initial steps towards a generalization of the notion of total probability to belief functions are taken, in the perspective of endowing the theory of evidence with a complete battery of estimation  ...  a focus on both a perspective 'geometric approach' to uncertainty and an algebraic solution to the issue of conflicting evidence.  ...  It contains as special cases both fuzzy set and possibility theory.  ... 
arXiv:1810.10341v1 fatcat:y2ljft5jqfatzp47tmxyo4papq

Formal approaches to rule-based systems in medicine: The case of CADIAG-2

Agata Ciabattoni, David Picado Muiño, Thomas Vetterlein, Moataz El-Zekey
2013 International Journal of Approximate Reasoning  
The three frameworks are based on fuzzy logics, probability theory and possibilistic logic, respectively. CADIAG-2 is used here as a case study to evaluate these frameworks.  ...  We point out their use, advantages and disadvantages. In addition, the described models provide insight into various aspects of CADIAG-2.  ...  Acknowledgement This research was supported by the Vienna Science and Technology Fund (WWTF) Grant MA07-016.  ... 
doi:10.1016/j.ijar.2012.09.002 fatcat:bwi6y47elvdmlauytabixh7zou

Combining stochastic uncertainty and linguistic inexactness: theory and experimental evaluation of four fuzzy probability models

Rami Zwick, Thomas S. Wallsten
1989 International Journal of Man-Machine Studies  
This study presents such a framework by combining concepts from probability and fuzzy set theories.  ...  These results and others suggest that subjects are unable to represent the full complexity of a problem.  ...  The views, opin ions and findings contained in this paper are those of the authors and should not be construed as an official Department of the Army position , policy, or decision .  ... 
doi:10.1016/s0020-7373(89)80021-5 fatcat:2vrat5o7ubdedm3vbzgocoaqmu

Relational structures for measures of ignorance

Camilo Franco De Los Rios, Javier Montero, J. Tinguaro Rodriguez
2011 Proceedings of the 7th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-2011)  
Different types of inexactness can be represented by fuzzy sets: vagueness, where there are no precise boundaries, ambiguity, when more than one distinguishable concept is described, generality, such that  ...  a word applies to a variety of situations, and ambivalence, where conflicting valuations can coexist.  ...  Such characterization A1-A3 of ambiguity has been proved useful with respect to some concepts of Dempster-Shafer's theory of evidence [12] , [15] , as in the following example.  ... 
doi:10.2991/eusflat.2011.77 dblp:conf/eusflat/RiosMR11 fatcat:pag2lxd2jvfhpjskictjw362di

A Formal Account of Effectiveness Evaluation and Ranking Fusion

Enrique Amigó, Fernando Giner, Stefano Mizzaro, Damiano Spina
2018 Proceedings of the 2018 ACM SIGIR International Conference on Theory of Information Retrieval - ICTIR '18  
This paper proposes a theoretical framework which models the information provided by retrieval systems in terms of Information Theory.  ...  The proposed framework allows to formalize: (i) system effectiveness as an information theoretic similarity between system outputs and human assessments, and (ii) ranking fusion as an information quantity  ...  ACKNOWLEDGEMENTS This research was partially supported by the Spanish Government (project Vemodalen TIN2015-71785-R) and the Australian Research Council (project LP150100242).  ... 
doi:10.1145/3234944.3234958 dblp:conf/ictir/AmigoGMS18 fatcat:2y7yyfkrdrhg7cdhpig6ajauxu

From Shallow to Deep Interactions Between Knowledge Representation, Reasoning and Machine Learning (Kay R. Amel group) [article]

Zied Bouraoui and Antoine Cornuéjols and Thierry Denœux and Sébastien Destercke and Didier Dubois and Romain Guillaume and João Marques-Silva and Jérôme Mengin and Henri Prade and Steven Schockaert and Mathieu Serrurier and Christel Vrain
2019 arXiv   pre-print
Some common concerns are identified and discussed such as the types of used representation, the roles of knowledge and data, the lack or the excess of information, or the need for explanations and causal  ...  This paper is the first step of a work in progress aiming at a better mutual understanding of research in KRR and ML, and how they could cooperate.  ...  The use of fuzzy sets to describe associations between data and decision trees may have some interest: extending the types of relations that may be represented, making easier the interpretation of rules  ... 
arXiv:1912.06612v1 fatcat:yfnx3pzs6jhxtggaylc76pwjc4
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