Computation of epistemic uncertainty due to limited data samples in small field dosimetry using fuzzy set theory

Objective: To estimate the epistemic (or fuzzy) uncertainty, arising due to limited data samples in the measurement of the output factors (OF) of the small fields using Fuzzy Set Theory (FST). Methods: EBT3 film samples of size 50 × 50 mm were used for the measurement of the OF of stereotactic radiosurgery (SRS) cones of size 4, 6, 7.5, 10, 12.5 and 15 mm diameter, normalized with respect to the output of 100 × 100 mm open field size. Three measurements were done per cone/field size. Red color channel was chosen for the dosimetry purpose, net optical density (NOD) was converted to the dose using non-linear relation. To estimate the epistemic uncertainty associated with the measured OF due to limited number of data samples, a triangular fuzzy number (TFN) was assumed as the fuzziness in the dose delivered by the individual SRS cone/field. Uncertainty in the OF was estimated by applying the Fuzzy Vertex Method (FVM). The membership functions of the OF were constructed for each cone size and the nature of the uncertainty in the OF of the cones was expressed in the terms of its fuzziness. For the sake of completeness of the study, the statistical uncertainty involved in the procedure has also been calculated. Results: The statistical and fuzzy uncertainties in the measurement of OF of cones range from 3.28 to 6.25% and 2.58 to 5.44% respectively. The smallest cone of 4 mm has the largest values of statistical and fuzzy uncertainties. The membership functions of the OF for the studied cones were triangular in nature. Conclusions: The epistemic uncertainty arising due to limited number of data samples holds a significant fraction of the prescribed dose, and therefore, should not be ignored in the total uncertainty estimation. Advances in knowledge: This study highlights the significance of epistemic component of measurement uncertainty arising out due to the insufficient/limited number of measurements of a quantity.

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Uncertain Analysis of a Stationary Solar Compound Parabolic Concentrator PV Collector System Using Fuzzy Set Theory

Journal of Renewable Energy ◽

10.1155/2018/2915731 ◽

2018 ◽

Vol 2018 ◽

pp. 1-12

Author(s):

Hoe-Gil Lee ◽

Singiresu S. Rao

Keyword(s):

Solar Energy ◽

Set Theory ◽

Fuzzy Set ◽

Fuzzy Set Theory ◽

Uncertain Parameters ◽

Membership Functions ◽

Solar Pv ◽

Compound Parabolic Concentrator ◽

Collector System ◽

Analysis Methodology

The uncertain analysis of fixed solar compound parabolic concentrator (CPC) collector system is investigated for use in combination with solar PV cells. Within solar CPC PV collector systems, any radiation within the collector acceptance angle enters through the aperture and finds its way to the absorber surface by multiple internal reflections. It is essential that the design of any solar collector aims to maximize PV performance since this will elicit a higher collection of solar radiation. In order to analyze uncertainty of the solar CPC collector system in the optimization problem formulation, three objectives are outlined. Seasonal demands are considered for maximizing two of these objectives, the annual average incident solar energy and the lowest month incident solar energy during winter; the lowest cost of the CPC collector system is approached as a third objective. This study investigates uncertain analysis of a solar CPC PV collector system using fuzzy set theory. The fuzzy analysis methodology is suitable for ambiguous problems to predict variations. Uncertain parameters are treated as random variables or uncertain inputs to predict performance. The fuzzy membership functions are used for modeling uncertain or imprecise design parameters of a solar PV collector system. Triangular membership functions are used to represent the uncertain parameters as fuzzy quantities. A fuzzy set analysis methodology is used for analyzing the three objective constrained optimization problems.

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Mixed aleatory and epistemic uncertainty quantification using fuzzy set theory

International Journal of Approximate Reasoning ◽

10.1016/j.ijar.2015.07.002 ◽

2015 ◽

Vol 66 ◽

pp. 1-15 ◽

Cited By ~ 16

Author(s):

Yanyan He ◽

Mahsa Mirzargar ◽

Robert M. Kirby

Keyword(s):

Uncertainty Quantification ◽

Set Theory ◽

Fuzzy Set ◽

Fuzzy Set Theory ◽

Epistemic Uncertainty ◽

Aleatory And Epistemic Uncertainty

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Fuzzy Logic Applications for Performance-Based Design

Advances in Civil and Industrial Engineering - Performance-Based Seismic Design of Concrete Structures and Infrastructures ◽

10.4018/978-1-5225-2089-4.ch009 ◽

2017 ◽

pp. 239-260

Author(s):

Ferhat Pakdamar

Keyword(s):

Fuzzy Logic ◽

Set Theory ◽

Fuzzy Set ◽

Fuzzy Set Theory ◽

Fractal Geometry ◽

Performance Based Design ◽

Design Criteria ◽

Membership Functions ◽

Rule Based ◽

Multivariate Sample

In this chapter, it is expressed how performance based design criteria are modeled with fuzzy logic and why it needs to be modeled with fuzzy logic. Firstly, a brief information is given about current theories and techniques such as Fuzzy Logic, Chaos, Fractal Geometry, Artificial Neural Networks; and it is mentioned about advantages of applying these techniques to the problems. Then graphical inference deduction technique is expressed by giving a summary info about Fuzzy Set Theory, membership functions, clustering, rule-based systems and defuzzification. Then the divergence of performance based design criteria is set forth by making curvature evaluations for various regulations on a column section as a structure element. Finally, it is shown in detail how to use the fuzzy set theory for solution of this disharmony by using the clustering technique on a univariate sample first and then on a multivariate sample.

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Fuzzy Approaches and Analysis in Image Processing

Advanced Image Processing Techniques and Applications - Advances in Computational Intelligence and Robotics ◽

10.4018/978-1-5225-2053-5.ch001 ◽

2017 ◽

pp. 1-31 ◽

Cited By ~ 2

Author(s):

Ezhilmaran D ◽

Adhiyaman M

Keyword(s):

Neural Network ◽

Image Processing ◽

Set Theory ◽

Fuzzy Set ◽

Fuzzy Set Theory ◽

Membership Functions ◽

Significant Development ◽

Diverse Field ◽

Self Study

Fuzzy set theory originates to a great extent of interest among the researchers in past decades. It is a key tool to handle the imperfect of information in the diverse field. Typically, it plays a very important role in image processing and found the significant development in many active areas such as pattern recognition, neural network, medical imaging, etc. The use of fuzzy set theory is to tackle uncertainty in the form of membership functions when there is an image gray levels or information is lost. This chapter concerns the preliminaries of fuzzy, intuitionistic fuzzy, type-2 fuzzy and intuitionistic type-2 fuzzy set theory and its application in the fingerprint image; furthermore, the contrast enhancement and edge detection are carried out for that with the assistance of fuzzy set theory. It is useful to the students who want to self-study. This chapter composed just to address that issue.

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Fuzzy Approaches and Analysis in Image Processing

Computer Vision ◽

10.4018/978-1-5225-5204-8.ch020 ◽

2018 ◽

pp. 511-542

Author(s):

Ezhilmaran D ◽

Adhiyaman M

Keyword(s):

Neural Network ◽

Image Processing ◽

Set Theory ◽

Fuzzy Set ◽

Fuzzy Set Theory ◽

Membership Functions ◽

Significant Development ◽

Diverse Field ◽

Self Study

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Development of Highway Congestion Index with Fuzzy Set Models

Transportation Research Record Journal of the Transportation Research Board ◽

10.3141/1802-03 ◽

2002 ◽

Vol 1802 (1) ◽

pp. 16-22 ◽

Cited By ~ 12

Author(s):

Manouchehr Vaziri

Keyword(s):

Set Theory ◽

Fuzzy Set ◽

Fuzzy Set Theory ◽

Travel Speed ◽

Video Segment ◽

Membership Functions ◽

Highway Traffic ◽

Index Development ◽

Congestion Index ◽

Travel Rate

Development of a highway congestion index on the basis of expert and user opinions with fuzzy set theory was attempted. Forty 1-min videotape segments showing different highway traffic flow conditions were displayed to a group of highway experts and users. They were asked to complete the relevant questionnaires on the existence and acceptability of congestion for each video segment display. Five congestion-descriptive variables of travel speed, travel rate, delay rate, travel rate ratio, and delay ratio were determined for each video segment. Information about the values of congestion-descriptive variables for the displayed videos, questionnaire responses, and fuzzy set theory were used to develop congestion fuzzy set membership functions. The membership functions characterized the congestion intensity fuzzy values of “congested” and “unacceptably congested.” The membership functions were suggested as congestion indexes measured on a scale of 0 to 1. In the questionnaire, the surveyed group also provided opinions regarding the relative importance of the descriptive variables in explaining congestion. This information was used to determine average weighting values for the developed indexes. Using the average weighting values, overall indexes for “congested” and “unacceptably congested” were developed. The overall congestion indexes were also suggested for congestion intensity assessment and evaluation. The relationships between the Highway Capacity Manual levels of service and the developed congestion indexes were studied. The results were used to address some issues regarding normative index development. Although the study findings are based on a rather limited database and are location specific, the applied methodology can be used to capture congestion intensity perception in any future index development. The study index development was based on fuzzy set theory and is suggested as an alternative or complementary approach to past normative index development methods.

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