Strong limit theorems for random sets and fuzzy random sets with slowly varying weights

Fu, Ke-Ang; Zhang, Li Xin

doi:10.1016/j.ins.2008.01.005

Cited by 13 publications

(6 citation statements)

References 35 publications

(48 reference statements)

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“…Hence it would be valuable to integrate the probability theory with the fuzzy set theory [30,31]. Therefore, a few ideas and techniques are proposed, for example, probability measures of fuzzy events [32], fuzzy random set [33], fuzzy random variable [34,35], nonstationary fuzzy sets [36], and fuzzy model with probability-based rule weights [37]. In a general sense, two sorts of combination standard caused these strategies.…”

Section: Introductionmentioning

confidence: 99%

Multiple Criteria Decision Making Based on Probabilistic Interval-Valued Hesitant Fuzzy Sets by Using LP Methodology

Sindhu

Rashid

Kashif

et al. 2019

Discrete Dynamics in Nature and Society

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Probabilistic interval-valued hesitant fuzzy sets (PIVHFSs) are an extension of interval-valued hesitant fuzzy sets (IVHFSs) in which each hesitant interval value is considered along with its occurrence probability. These assigned probabilities give more details about the level of agreeness or disagreeness. PIVHFSs describe the belonging degrees in the form of interval along with probabilities and thereby provide more information and can help the decision makers (DMs) to obtain precise, rational, and consistent decision consequences than IVHFSs, as the correspondence of unpredictability and inaccuracy broadly presents in real life problems due to which experts are confused to assign the weights to the criteria. In order to cope with this problem, we construct the linear programming (LP) methodology to find the exact values of the weights for the criteria. Furthermore these weights are employed in the aggregation operators of PIVHFSs recently developed. Finally, the LP methodology and the actions are then applied on a certain multiple criteria decision making (MCDM) problem and a comparative analysis is given at the end.

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Section: Introductionmentioning

confidence: 99%

Multiple Criteria Decision Making Based on Probabilistic Interval-Valued Hesitant Fuzzy Sets by Using LP Methodology

Sindhu

Rashid

Kashif

et al. 2019

Discrete Dynamics in Nature and Society

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“…Hong and Kim [18] established a weak law of large number of independent and identically distributed fuzzy random variables. Fu and Zhang [13] obtained some strong limit theorems for fuzzy random variables with slowly varying weight. It should be mentioned that, although the concept of variance has been found very convenient in studying limit theorems, but, as the authors know, it has not been developed the limit theorems for fuzzy random variables based on the concept of variance, except the works by Korner [22] and Feng [10].…”

Section: Introductionmentioning

confidence: 99%

“…They studied the strong convergence for weighted sums of linearly negative quadrant dependent arrays. Fu and Wu [12] studied the almost sure central limit theorem for linearly negative quadrant dependent sequences. In this article, for the first time, we investigate some well known maximal inequalities for quadratic form of independent fuzzy random variables.…”

Section: Introductionmentioning

confidence: 99%

Maximal inequalities and some convergence theorems for fuzzy random variable

Ahmadzade¹,

Amini²,

Taheri³

et al. 2016

Kybernetika

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“…Based on the strong law of large numbers for fuzzy random variables with respect to the uniform metric, Wang [36] established some asymptotical properties of point estimation with fuzzy random samples. Fu and Zhang [8] obtained some strong limit theorems for fuzzy random variables with slowly varying weight. Li and Zhung [18] and Hong [10] obtained a general method for certain convergence theorems of fuzzy random variables based on Hausdorff metric.…”

Section: Introductionmentioning

confidence: 99%

Negative dependence for fuzzy random variables: Basic definitions and some limit theorems

Ahmadzade

Amini

Taheri

et al. 2016

Filomat

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The concept of negative dependence for fuzzy random variables is introduced. The basic properties of such random variables are investigated. Some results on weak and strong convergence for sums and weighted sums of pairwise negatively dependent fuzzy random variables are derived. As a direct extension of classical methods, some limit theorems are established based on the concept of variance and covariance.

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Strong limit theorems for random sets and fuzzy random sets with slowly varying weights

Cited by 13 publications

References 35 publications

Multiple Criteria Decision Making Based on Probabilistic Interval-Valued Hesitant Fuzzy Sets by Using LP Methodology

Multiple Criteria Decision Making Based on Probabilistic Interval-Valued Hesitant Fuzzy Sets by Using LP Methodology

Maximal inequalities and some convergence theorems for fuzzy random variable

Negative dependence for fuzzy random variables: Basic definitions and some limit theorems

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