A fuzzy statistical test of fuzzy hypotheses

Watanabe, Norio; Imaizumi, Tadashi

doi:10.1016/0165-0114(93)90170-m

Cited by 67 publications

(23 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Their studies cannot be used in testing the parameters of two populations, especially when the population variances are unknown. Watanabe and Imaizumi [8] addressed testing the difference of two population means and the fuzzy hypothesis that two population means are almost equal. They focused only on two independent populations and fuzzy hypotheses with crisp observations, so their methods cannot be applied to test the difference of two population means using paired fuzzy data.…”

Section: Introductionmentioning

confidence: 99%

Tests of quality characteristics of two populations using paired fuzzy sample differences

Tsai

Chen

2005

Int J Adv Manuf Technol

View full text Add to dashboard Cite

Testing the parameters of two populations is important in inference statistics. This study extends this topic to fuzzy environments to widen the application, especially in manufacturing environments. The aim of this study is to implement tests of central tendency of two dependent populations with paired fuzzy sample differences. When the distribution of the population of differences is normal, the membership function of the fuzzy test statistic is constructed, and the fuzzy probability is calculated based on this membership function. Unlike classical tests, which provide only binary decisions, fuzzy probabilities can provide a degree of rejection of the null hypothesis. The proposed method reduces to the classical test method when crisp data are used. When the distribution is non-normal, a signed distance method is used to determine the distance between two fuzzy numbers and to define ranking. After the fuzzy problem is defuzzified, the classical sign test is applied to determine whether the medians of two populations are equal. Two examples are presented to elucidate the proposed methods. We can conclude that the proposed method can not only apply a randomized test to obtain the paired t test in the fuzzy sense, but can also use the signed distance ranking of fuzzy numbers to derive a sign test problem in the fuzzy sense.

show abstract

Section: Introductionmentioning

confidence: 99%

Tests of quality characteristics of two populations using paired fuzzy sample differences

Tsai

Chen

2005

Int J Adv Manuf Technol

View full text Add to dashboard Cite

show abstract

“…On the other hand, Casals et al [19] studied fuzzy decision problems by relating the concepts of hypothesis testing and fuzzy information nature. Saade and Schwarzlander [20] and Saade [21] proposed a characterization of fuzzy hypothesis testing while Watanabe and Imaizumi [22] related the concepts of hypothesis test statistics and fuzzy hypotheses. Arnold [23,24] related the concept of fuzzy hypothesis testing with conventional methods of real data analysis.…”

Section: A Brief Review Of Fuzzy Theorymentioning

confidence: 99%

A Confidence Set Analysis for Observed Samples: A Fuzzy Set Approach

González

Castro

Lachos

et al. 2016

Entropy

View full text Add to dashboard Cite

Abstract:Confidence sets are generally interpreted in terms of replications of an experiment. However, this interpretation is only valid before observing the sample. After observing the sample, any confidence sets have probability zero or one to contain the parameter value. In this paper, we provide a confidence set analysis for an observed sample based on fuzzy set theory by using the concept of membership functions. We show that the traditional ad hoc thresholds (the confidence and significance levels) can be attained from a general membership function. The applicability of the newly proposed theory is demonstrated by using well-known examples from the statistical literature and an application in the context of contingency tables.

show abstract

“…Son et al (1992), using a generalized Neyman-Pearson lemma, present a locally most powerful fuzzy test and study its application in signal detection. Watanabe and Imaizumi (1993) introduce a testing method of a fuzzy hypothesis for random data. They didn't precisely define the probabilities of type I and type II errors.…”

Section: Hypothesis Testingmentioning

confidence: 99%