Special issue: interfaces between fuzzy set theory and interval analysis

Lodwick, Weldon A.; Jamison, K. David

doi:10.1016/s0165-0114(02)00245-2

Cited by 42 publications

(11 citation statements)

References 12 publications

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“…While interval analysis arose out of a need to analyze error and uncertainty on digital computers [18], fuzzy set theory arose from a need of more complete and inclusive mathematical models of uncertainty [29]. Relationships between fuzzy set theory and interval mathematics have been reported by Lodwick [30].…”

Section: From Interval Analysis To Fuzzy Set Theorymentioning

confidence: 99%

A Review on Evolving Interval and Fuzzy Granular Systems

Leite¹,

Costa²,

Gomide³

2016

L&NLM

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This article provides definitions and principles of granular computing and discusses the generation and online adaptation of rule-based models from data streams. Essential notions of interval analysis and fuzzy sets are addressed from the granular computing point of view. The article also covers different types of aggregation operators which perform information fusion by gathering large volumes of dissimilar information into a more compact form. We briefly summarize the main historical landmarks of evolving intelligent systems leading to the state of the art. Evolving granular systems extend evolving intelligent systems allowing data, variables and parameters to be granules (intervals and fuzzy sets). The aim of the evolution of granular systems is to fit the information carried by data streams from time-varying processes into rule-based models and, at the same time, provide granular approximation of functions and linguistic description of the system behavior.

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Section: From Interval Analysis To Fuzzy Set Theorymentioning

confidence: 99%

A Review on Evolving Interval and Fuzzy Granular Systems

Leite¹,

Costa²,

Gomide³

2016

L&NLM

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“…(11)- (16) are nonlinear programming problems with bounded variables, the built-in optimization subroutine called ``fmincon'' provided in the commercial software Matlab is used to construct the interval values in Eqs. (11)- (16).…”

Section: Control Chartmentioning

confidence: 99%

“…Then these quantitative values can be manipulated to help decision-makers achieve greater insight into the meaning of the data and further examine specific hypotheses. Obviously, while assigning the qualitative variables to be meaningful numerical values, a certain degree of uncertainty called vagueness other than randomness is involved and thus yields coded data virtually interval-valued [15][16][17] .…”

Section: Introductionmentioning

confidence: 99%

Interval-valued process data monitoring and controlling

Hsu

Kung

Shu³

2013

AIR

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Statistical process control, a recognized technique for improving quality and productivity, has been widely employed throughout various industries. The conventional Shewhart control charts are applicable only when the collected sample data are real-valued data. For the purpose of controlling uncertain information when interval-valued data inevitably appear in the manufacturing or service processes, in this paper an interval-data analysis methodology is first applied. We construct Shewhart control charts whose control limits, consequently as interval numbers, are obtained by using the united extension principle, which is an effective method for dealing with closed interval data. Then, to identify the special causes of variation and alarm the requirement for corrective actions, we propose new rules for classifying current conditions of the manufacturing process based on an acceptability function of two interval numbers constructed from interval-valued sample data. Finally, the proposed methodologies are illustrated by practical examples to show their potential applications.

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“…However, they are all closely connected with interval analysis [12]. For example, the mathematical analysis associated with fuzzy set theory can be performed as interval analysis on different α levels [13] and [14]. Fuzzy arithmetic can be performed as interval arithmetic on α cuts.…”

Section: Introductionmentioning

confidence: 99%

Interval Based Finite Elements for Uncertainty Quantification in Engineering Mechanics

Muhanna

Mullen

2012

IFIP Advances in Information and Communication Technology

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This paper illustrates how interval analysis can be used as a basis for generalized models of uncertainty. When epistemic uncertainty is presented as a range and the aleatory is based on available information, or when random variables are assigned an interval probability, the uncertainty will have a Probability Bound (PB) structure. When Interval Monte Carlo (IMC) is used to sample random variables, interval random values are generated. Interval Finite Element Method (FEM) is used to propagate intervals through the system and sharp interval solutions are obtained. Interval solutions are sorted and PBs of the system response are constructed. All relevant statistics are calculated characterizing both aleatory and epistemic uncertainty. The above mentioned sequence is presented in this work and illustrative examples are solved.

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Special issue: interfaces between fuzzy set theory and interval analysis

Cited by 42 publications

References 12 publications

A Review on Evolving Interval and Fuzzy Granular Systems

A Review on Evolving Interval and Fuzzy Granular Systems

Interval-valued process data monitoring and controlling

Interval Based Finite Elements for Uncertainty Quantification in Engineering Mechanics

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