Fuzzy Random Variables

Puri, Madan L.; Ralescu, Dan A.; Zadeh, Lotfi A.

doi:10.1016/b978-1-4832-1450-4.50029-8

Cited by 134 publications

(159 citation statements)

References 13 publications

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“…If = 2, then the exact solution of (40) (2,2)-solution, then the corresponding (2,2)-system will be To demonstrate the agreement between the exact and approximate solution, Table 1 shows the absolute error of the 10 th PRS approximate solution for FFIVPs (30) and (31) obtained for different values of -cut representations and nodes with fractional order = 1.9. Some graphical results are also presented in Figures 1 and 2.…”

Section: Numerical Simulation and Discussionmentioning

confidence: 99%

Computational Optimization of Residual Power Series Algorithm for Certain Classes of Fuzzy Fractional Differential Equations

Alaroud

Al‐Smadi

Ahmad

et al. 2018

International Journal of Differential Equations

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This paper aims to present a novel optimization technique, the residual power series (RPS), for handling certain classes of fuzzy fractional differential equations of order 1 < ≤ 2 under strongly generalized differentiability. The proposed technique relies on generalized Taylor formula under Caputo sense aiming at extracting a supportive analytical solution in convergent series form. The RPS algorithm is significant and straightforward tool for creating a fractional power series solution without linearization, limitation on the problem's nature, sort of classification, or perturbation. Some illustrative examples are provided to demonstrate the feasibility of the RPS scheme. The results obtained show that the scheme is simple and reliable and there is good agreement with exact solution.

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Section: Numerical Simulation and Discussionmentioning

confidence: 99%

Computational Optimization of Residual Power Series Algorithm for Certain Classes of Fuzzy Fractional Differential Equations

Alaroud

Al‐Smadi

Ahmad

et al. 2018

International Journal of Differential Equations

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“…Definition 1 (Puri and Ralescu, 1986). For a probability space ( , , ) F P  , a fuzzy random variable is a function  :…”

Section: Fuzzy Random Variablementioning

confidence: 99%

Inexact Fuzzy Stochastic Chance Constraint Programming for Emergency Evacuation in Qinshan Nuclear Power Plant under Uncertainty

Huang¹,

Nie²,

Guo³

et al. 2017

J ENVIRON INFORM

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ABSTRACT. Nuclear power accidents are one of the most dangerous disasters posing a lethal threat to human health and have detrimental effects lasting for decades. Therefore, emergency evacuation is important to minimize injuries and prevent lethal consequences resulting from a nuclear power accident. An inexact fuzzy stochastic chance constrained programming (IFSCCP) method is developed to address various uncertainties in evacuation management problems. It integrates the interval-parameter programming (IPP) and fuzzy stochastic chance constrained programming (FSCCP) methods into a general framework, in which the IPP method addresses the uncertainties presented as intervals defined by crisp lower and upper bounds, and the FCCP treat the dual-uncertainties expressed as fuzzy random variables. The measures of possibility and necessity were employed to convert the fuzzy random variables into crisp values to reflect the decision maker's pessimistic and optimistic preferences. The IFSCCP model is applied to support nuclear emergency evacuation management in the Qinshan Nuclear Power Site, which is one of the largest nuclear plants in China. The results provide stable intervals for the objective function and decision variables with different fuzzy and probability confidence levels regarding the local residents' distribution. Nine scenarios are analyzed to reflect the impacts of the imprecision (fuzziness and randomness) associated with the size of the population in a plume emergency planning zone. The results are valuable for supporting local decision makers to generate effective emergency evacuation strategies.

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“…In addition, ϕ is associated with a bounded density measure with support (0,1] which allows us to weigh the importance given to each α-level. Given a probability space (Ω, A, P ), a random fuzzy set X (RFS for short) is a Borel measurable mapping with respect to D ϕ θ [21]. If…”

Section: Preliminariesmentioning

confidence: 99%

Analysis of the reliability of the fuzzy scale for assessing the students’ learning styles in Mathematics

Guajardo¹,

López²,

Ruiz³

2015

Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and

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The reliability of the fuzzy scale for assessing the responses of a person in an opinion questionnaire (which is usually treated as a Likert-type questionnaire) is analyzed. Thus, a comparison between a classical Likert scale-based questionnaire and its fuzzy rating scale-based version in terms of their reliability is established. For this purpose, some questions of the Grasha-Riechmann student learning style scales have been answered by a group of students using both scales. Considering that the Likert version of this questionnaire is reliable, the aim is to check the reliability of its fuzzy version by comparing the corresponding Cronbach's alpha coefficients.

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Fuzzy Random Variables

Cited by 134 publications

References 13 publications

Computational Optimization of Residual Power Series Algorithm for Certain Classes of Fuzzy Fractional Differential Equations

Computational Optimization of Residual Power Series Algorithm for Certain Classes of Fuzzy Fractional Differential Equations

Inexact Fuzzy Stochastic Chance Constraint Programming for Emergency Evacuation in Qinshan Nuclear Power Plant under Uncertainty

Analysis of the reliability of the fuzzy scale for assessing the students’ learning styles in Mathematics

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