Formal Representations of Uncertainty

Dubois, Didier; Prade, Henri

doi:10.1002/9780470611876.ch3

Cited by 101 publications

(62 citation statements)

References 137 publications

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“…Therefore, this paper presents a new methodology for the determination of a real option value under these uncertainties, also with the objective to reduce the computational time. The methodology is based on: fuzzy numbers [29,30], to represent these uncertainties; and Monte Carlo simulation to obtain a good approximation of the real option value. The fuzzy number allows dealing with the technical uncertainty as a whole, avoiding the need to sample it, as it would be the case for the triangular probability distribution; this method greatly speeds up the process of the Monte Carlo simulation.…”

Section: Proposed Methodologymentioning

confidence: 99%

Hybrid fuzzy Monte Carlo technique for reliability assessment in transmission power systems

Canizes

Soares

Vale

et al. 2012

Energy

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a b s t r a c tThis paper proposes a new methodology to reduce the probability of occurring states that cause load curtailment, while minimizing the involved costs to achieve that reduction. The methodology is supported by a hybrid method based on Fuzzy Set and Monte Carlo Simulation to catch both randomness and fuzziness of component outage parameters of transmission power system.The novelty of this research work consists in proposing two fundamentals approaches: 1) a global steady approach which deals with building the model of a faulted transmission power system aiming at minimizing the unavailability corresponding to each faulted component in transmission power system. This, results in the minimal global cost investment for the faulted components in a system states sample of the transmission network; 2) a dynamic iterative approach that checks individually the investment's effect on the transmission network.A case study using the Reliability Test System (RTS) 1996 IEEE 24 Buses is presented to illustrate in detail the application of the proposed methodology.

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Section: Proposed Methodologymentioning

confidence: 99%

Hybrid fuzzy Monte Carlo technique for reliability assessment in transmission power systems

Canizes

Soares

Vale

et al. 2012

Energy

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“…However clever it may be, this view is debatable (see [32] for a summary of critiques). Especially, this representation is unstable: if P b x is uniform on E, then P b f (x) may fail to be so if E is finite and the image f (E) does not contain the same number of elements as E, or if E is an interval and f is not a linear transformation.…”

Section: Ontic Vs Epistemic Setsmentioning

confidence: 99%

“…Contrary to the numerical modeling tradition, such knowledge-based models are most of the time tainted with incompleteness: a set of logical formulae, representing an agent's beliefs is seldom complete, that is, cannot establish the truth or falsity of any proposition. This concern for incomplete information in Artificial Intelligence has strongly affected the development of new uncertainty theories [32], and has led to a critique of the Bayesian stance viewing probability theory as a unique framework for the representation of belief that mimics the probabilistic account of variability.…”

Section: Introductionmentioning

confidence: 99%

Statistical reasoning with set-valued information: Ontic vs. epistemic views

Couso

Dubois

2014

International Journal of Approximate Reasoning

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155

106

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OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. In information processing tasks, sets may have a conjunctive or a disjunctive reading. In the conjunctive reading, a set represents an object of interest and its elements are subparts of the object, forming a composite description. In the disjunctive reading, a set contains mutually exclusive elements and refers to the representation of incomplete knowledge. It does not model an actual object or quantity, but partial information about an underlying object or a precise quantity. This distinction between what we call ontic vs. epistemic sets remains valid for fuzzy sets, whose membership functions, in the disjunctive reading are possibility distributions, over deterministic or random values. This paper examines the impact of this distinction in statistics. We show its importance because there is a risk of misusing basic notions and tools, such as conditioning, distance between sets, variance, regression, etc. when data are set-valued. We discuss several examples where the ontic and epistemic points of view yield different approaches to these concepts.

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“…A wide comprehensive historical coverage on this topic has been performed by the work of Dubois and Prade (Dubois & Prade, 2009). The authors consider that an agent believes a piece of information to be uncertain when it is not able to state if the piece of information is true of false.…”

Section: Modern Approachesmentioning

confidence: 99%