Fuzzy empirical distribution function: properties and application

Title:

Fuzzy empirical distribution function: properties and application

Creator:

Hesamian, Gholamreza and Taheri, S. M.

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:b509fa72-30c0-4055-9827-2e9285c814bb
uuid:b509fa72-30c0-4055-9827-2e9285c814bb

Subject:

fuzzy cummulative distribution function, fuzzy empirical distribution function, Kolmogorov-Smirnov test, fuzzy p-value, convergence with probability one, degree of accept, degree of reject, and Glivenko-Cantelli theorem

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

The concepts of cumulative distribution function and empirical distribution function are investigated for fuzzy random variables. Some limit theorems related to such functions are established. As an application of the obtained results, a method of handling fuzziness upon the usual method of Kolmogorov-Smirnov one-sample test is proposed. We transact the α-level set of imprecise observations in order to extend the usual method of Kolmogorov-Smirnov one-sample test. To do this, the concepts of fuzzy Kolmogorov-Smirnov one-sample test statistic and p-value are extended to the fuzzy Kolmogorov-Smirnov one-sample test statistic and fuzzy p-value, respectively. Finally, a preference degree between two fuzzy numbers is employed for comparing the observed fuzzy p-value and the given fuzzy significance level, in order to accept or reject the null hypothesis of interest. Some numerical examples are provided to clarify the discussions in this paper.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

[962]-982

Source:

Kybernetika | 2013 Volume:49 | Number:6

Harvested from:

CDK

Metadata only:

false