Testing hypotheses for multivariate normal distribution with fuzzy random variables

Gholamreza Hesamian and Mohamad Ghasem Akbari

International Journal of Systems Science, 2022, vol. 53, issue 1, 14-24

Abstract: There are several studies on fuzzy univariate hypothesis tests corresponding to a normal distribution. A fuzzy statistical test was proposed in this study for mean and variance–covariance matrix of a multivariate normal with fuzzy random variables. For this purpose, a notion of fuzzy multivariate normal random variable with fuzzy mean and non-fuzzy variance–covariance matrix was first developed. Then, the concepts of the fuzzy type-I error, fuzzy type-II error, fuzzy power, non-fuzzy significance level and fuzzy p-value were extended. A degree-based criterion was also suggested to compare the fuzzy p-values as well as a specific significance level to decide whether accepting or rejecting the underlying hypotheses. The effectiveness of the proposed fuzzy hypothesis test was also examined through some numerical examples.

Date: 2022
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DOI: 10.1080/00207721.2021.1936274

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