Neyman–Pearson Lemma for Fuzzy Hypotheses Testing with Vague Data |
| |
Authors: | Hamzeh Torabi Javad Behboodian S. Mahmoud Taheri |
| |
Affiliation: | (1) Department of Statistics, Yazd University, Yazd, Iran;(2) Department of Statistics, Islamic Azad University of Shiraz, Shiraz, Iran;(3) School of Mathematical Sciences, Isfahan University of Technology, 84156 Isfahan, Iran |
| |
Abstract: | In hypotheses testing, such as other statistical problems, we may confront imprecise concepts. One case is a situation in which both hypotheses and observations are imprecise. This paper tries to develop a new approach for testing fuzzy hypothesis when the available data are fuzzy, too. First, some definitions are provided, such as: fuzzy sample space, fuzzy-valued random sample, and fuzzy-valued random variable. Then, the problem of fuzzy hypothesis testing with vague data is formulated. Finally, we state and prove a generalized Neyman–Pearson Lemma for such problem. The proposed approach is illustrated by some numerical examples. |
| |
Keywords: | Fuzzy hypothesis Vague data Fuzzy-valued random variable Fuzzy-valued random sample Probability of type I and type II errors Neyman– Pearson Lemma |
本文献已被 SpringerLink 等数据库收录! |
|