### Abstract

In the crisp case, it is well known that the sample mean converges in probability to the population mean. This fact is generally known as the weak law of large numbers and is a direct consquence of the Chebyshev's inequality. If we substitute the fuzzy measure for the probability measure and fuzzy integral for the Lebesgue integral, then what can we say about the Chebyshev's inequality and weak law of large numbers? This is the focal point of this article.

Original language | English |
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Title of host publication | Proceedings of the Fifth Joint Conference on Information Sciences, JCIS 2000, Volume 1 |

Editors | P.P. Wang, P.P. Wang |

Pages | 80-83 |

Number of pages | 4 |

Volume | 5 |

Edition | 1 |

State | Published - 2000 |

Event | Proceedings of the Fifth Joint Conference on Information Sciences, JCIS 2000 - Atlantic City, NJ, United States Duration: Feb 27 2000 → Mar 3 2000 |

### Other

Other | Proceedings of the Fifth Joint Conference on Information Sciences, JCIS 2000 |
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Country | United States |

City | Atlantic City, NJ |

Period | 2/27/00 → 3/3/00 |

### All Science Journal Classification (ASJC) codes

- Computer Science(all)

### Cite this

*Proceedings of the Fifth Joint Conference on Information Sciences, JCIS 2000, Volume 1*(1 ed., Vol. 5, pp. 80-83)

**Fuzzy Weak Law of Large Numbers.** / Cheng, Shih-Chuan; Mordeson, John N.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the Fifth Joint Conference on Information Sciences, JCIS 2000, Volume 1.*1 edn, vol. 5, pp. 80-83, Proceedings of the Fifth Joint Conference on Information Sciences, JCIS 2000, Atlantic City, NJ, United States, 2/27/00.

}

TY - GEN

T1 - Fuzzy Weak Law of Large Numbers

AU - Cheng, Shih-Chuan

AU - Mordeson, John N.

PY - 2000

Y1 - 2000

N2 - In the crisp case, it is well known that the sample mean converges in probability to the population mean. This fact is generally known as the weak law of large numbers and is a direct consquence of the Chebyshev's inequality. If we substitute the fuzzy measure for the probability measure and fuzzy integral for the Lebesgue integral, then what can we say about the Chebyshev's inequality and weak law of large numbers? This is the focal point of this article.

AB - In the crisp case, it is well known that the sample mean converges in probability to the population mean. This fact is generally known as the weak law of large numbers and is a direct consquence of the Chebyshev's inequality. If we substitute the fuzzy measure for the probability measure and fuzzy integral for the Lebesgue integral, then what can we say about the Chebyshev's inequality and weak law of large numbers? This is the focal point of this article.

UR - http://www.scopus.com/inward/record.url?scp=1642396695&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=1642396695&partnerID=8YFLogxK

M3 - Conference contribution

SN - 0964345692

SN - 9780964345690

VL - 5

SP - 80

EP - 83

BT - Proceedings of the Fifth Joint Conference on Information Sciences, JCIS 2000, Volume 1

A2 - Wang, P.P.

A2 - Wang, P.P.

ER -