Interval analysis and fuzzy set theory

Moore, Ramon E.; Lodwick, Weldon A.

doi:10.1016/s0165-0114(02)00246-4

Cited by 259 publications

(102 citation statements)

References 18 publications

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“…As for the probabilistic structural reliability, different methods are available, although the related literature is by far more limited than the previous case. One of the most common approach consists of treating epistemic uncertainty using set of descriptor values, such as in the case of intervals [10], convex models [2], random sets [20] and fuzzy sets [22].…”

Section: Structural Reliability Methodsmentioning

confidence: 99%

A Computational Tool for Bayesian Networks Enhanced With Reliability Methods

Tolo¹,

Patelli²,

Beer³

et al. 2015

Proceedings of the 1st International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECO

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Abstract. A computational framework for the reduction and computation of Bayesian Networks enhanced with structural reliability methods is presented. During the last decades, the inner flexibility of the Bayesian Network method, its intuitive graphical structure and the strong mathematical background have attracted increasing interest in a large variety of applications involving joint probability of complex events and dependencies. Furthermore, the fast growing availability of computational power on the one side and the implementation of robust inference algorithms on the other, have additionally promoted the success of this method. Inference in Bayesian Networks is limited to only discrete variables (with the only exception of Gaussian distributions) in case of exact algorithms, whereas approximate approach allows to handle continuous distributions but can either result computationally inefficient or have unknown rates of convergence.This work provides a valid alternative to the traditional approach without renouncing to the reliability and robustness of exact inference computation. The methodology adopted is based on the combination of Bayesian Networks with structural reliability methods and allows to integrate random and interval variables within the Bayesian Network framework in the so called Enhanced Bayesian Networks. In the following, the computational algorithms developed are described and a simple structural application is proposed in order to fully show the capability of the tool developed.

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Section: Structural Reliability Methodsmentioning

confidence: 99%

A Computational Tool for Bayesian Networks Enhanced With Reliability Methods

Tolo¹,

Patelli²,

Beer³

et al. 2015

Proceedings of the 1st International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECO

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“…"Intervals on the real line have a dual nature, as set (of real numbers) with the usual set operations, and as a new kind of number represented by pairs of real numbers with an arithmetic" [8].…”

Section: General Intervalmentioning

confidence: 99%

Distributed Intervals: A Formal Framework for Information Granulation

Tahayori

Pedrycz

Antoni

2007

2007 Canadian Conference on Electrical and Computer Engineering

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Abstract-The notion of distributed interval, as a formal framework for information granulation, represented by the collection of finite number of general-intervals is introduced. Operations on distributed intervals are defined based on the corresponding general-intervals'. Distributed intervals provide a bi-criteria framework for information granulation that can be used as a conceptually rich structure in granular computing.

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“…The above range estimation problem is a specific problem related to a combination of interval and probabilistic uncertainty. Such problems -and their potential applications -have been described, in a general context, in the monographs [27,45]; for further developments, see, e.g., [2,3,4,5,7,11,28,30,40,41,48] and references therein.…”

Section: Formulation Of the Problemmentioning

confidence: 99%

Towards Combining Probabilistic and Interval Uncertainty in Engineering Calculations: Algorithms for Computing Statistics under Interval Uncertainty, and Their Computational Complexity

et al. 2006

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Abstract. In many engineering applications, we have to combine probabilistic and interval uncertainty. For example, in environmental analysis, we observe a pollution level x(t) in a lake at different moments of time t, and we would like to estimate standard statistical characteristics such as mean, variance, autocorrelation, correlation with other measurements. In environmental measurements, we often only measure the values with interval uncertainty. We must therefore modify the existing statistical algorithms to process such interval data.In this paper, we provide a survey of algorithms for computing various statistics under interval uncertainty and their computational complexity. The survey includes both known and new algorithms.

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Interval analysis and fuzzy set theory

Cited by 259 publications

References 18 publications

A Computational Tool for Bayesian Networks Enhanced With Reliability Methods

A Computational Tool for Bayesian Networks Enhanced With Reliability Methods

Distributed Intervals: A Formal Framework for Information Granulation

Towards Combining Probabilistic and Interval Uncertainty in Engineering Calculations: Algorithms for Computing Statistics under Interval Uncertainty, and Their Computational Complexity

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