Intuitionistic fuzzy random variable and testing hypothesis about its variance

Zainali, Z.; Akbari, Mohammad Ghasem; Noughabi, Hadi Alizadeh

doi:10.1007/s00500-014-1437-z

Cited by 9 publications

(5 citation statements)

References 22 publications

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“…[6,15,29,30,37]). In analyzing fuzzy data two main types of summary measures/parameters may be distinguished:…”

Section: Remarkmentioning

confidence: 99%

Bootstrap Approach to the One-Sample and Two- Sample Test of Variances of a Fuzzy Random Variable

Chachi

2017

Stat., optim. inf. comput.

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The aim of this paper is to present in a concise and integrated way of the bootstrap approach to statistical testing of hypotheses about the variance of fuzzy random variable. In this approach, first a notion of fuzzy random variables is recalled. Then, we will consider hypothesis-tests for the (crisp-valued) variance of fuzzy data in a population. For this purpose, the α-pessimistic values of the imprecise observations are used for defining a new notion of distance measure between fuzzy data, which is then used to make a procedure for testing the statistical hypotheses. Based on this argument, the application of bootstrap techniques in dealing with these testing problems will be introduced. The procedure develops a non-parametric approach to testing statistical hypotheses based on one-sample and two-sample fuzzy data.

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“…[6,15,29,30,37]). In analyzing fuzzy data two main types of summary measures/parameters may be distinguished:…”

Section: Remarkmentioning

confidence: 99%

Bootstrap Approach to the One-Sample and Two- Sample Test of Variances of a Fuzzy Random Variable

Chachi

2017

Stat., optim. inf. comput.

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“…Thus a decision-maker could utilize the value to make a decision. Therefore, in intuitionistic fuzzy random environments, we introduce a scalar expected value operator of intuitionistic fuzzy random variable, which is different from the notion of expectation proposed by Zainali et al [34].…”

Section: A Scalar Expected Value Operator Of Intuitionistic Fuzzy Ranmentioning

confidence: 99%

“…Suppose 1 and 2 are two fuzzy variables defined in the credibility space (Θ, ℘(Θ), Cr), and the membership functions of the two fuzzy variables are In this paper, we will denote Definition 9 (see [34]). An intuitionistic fuzzy random variable is a Borel measurable functioñ:…”

Section: Preliminariesmentioning

confidence: 99%

“…Recently, Definition 9 [34] has introduced an intuitionistic fuzzy random variable as a Borel measurable function from a probability space to a collection of intuitionistic fuzzy sets. In this paper, for our purpose, we impose a new measurability from a probability space to a collection of intuitionistic fuzzy variables and thus propose a new definition of intuitionistic fuzzy random variable.…”

Section: Intuitionistic Fuzzy Random Variablesmentioning

confidence: 99%

“…In order to extend uncertain theory and develop its applications, Pei [33] introduced intuitionistic fuzzy variables and developed outranking methods for evaluating intuitionistic fuzzy variables. Zainali et al [34] introduced the notion of intuitionistic fuzzy random variable based on probability space and defined the expectation value of an intuitionistic fuzzy random variable as a fuzzy number in the basis of credibility measure. Moreover, they investigated the method of testing statistical hypothesis concerning the variance of intuitionistic fuzzy random variables.…”

Section: Introductionmentioning

confidence: 99%

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A Scalar Expected Value of Intuitionistic Fuzzy Random Individuals and Its Application to Risk Evaluation in Insurance Companies

Jin

2018

Mathematical Problems in Engineering

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Randomness and uncertainty always coexist in complex systems such as decision-making and risk evaluation systems in the real world. Intuitionistic fuzzy random variables, as a natural extension of fuzzy and random variables, may be a useful tool to characterize some high-uncertainty phenomena. This paper presents a scalar expected value operator of intuitionistic fuzzy random variables and then discusses some properties concerning the measurability of intuitionistic fuzzy random variables. In addition, a risk model based on intuitionistic fuzzy random individual claim amount in insurance companies is established, in which the claim number process is regarded as a Poisson process. The mean chance of the ultimate ruin is investigated in detail. In particular, the expressions of the mean chance of the ultimate ruin are presented in the cases of zero initial surplus and arbitrary initial surplus, respectively, if individual claim amount is an exponentially distributed intuitionistic fuzzy random variable. Finally, two illustrated examples are provided.

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Testing statistical hypotheses for intuitionistic fuzzy data

Akbari

Hesamian

2018

Soft Comput

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Intuitionistic fuzzy random variable and testing hypothesis about its variance

Cited by 9 publications

References 22 publications

Bootstrap Approach to the One-Sample and Two- Sample Test of Variances of a Fuzzy Random Variable

Bootstrap Approach to the One-Sample and Two- Sample Test of Variances of a Fuzzy Random Variable

A Scalar Expected Value of Intuitionistic Fuzzy Random Individuals and Its Application to Risk Evaluation in Insurance Companies

Testing statistical hypotheses for intuitionistic fuzzy data

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