انجمن سیستم های فازی ایران سیستم های فازی و کاربردها 2717-4409 4 2 2022 02 20 Bootstrap approach in hypothesis testing of variance for fuzzy random variables رویکرد بوت استرپ در آزمون فرضیه برای واریانس متغیر تصادفی فازی 187 204 146084 10.22034/jfsa.2022.310120.1093 FA اعظم شهرکی داﻧﺸﮑﺪه رﯾﺎﺿﯽ آﻣﺎر و ﻋﻠﻮم ﮐﺎﻣﭙﯿﻮﺗﺮ، داﻧﺸﮕﺎه ﺳﯿﺴﺘﺎن و ﺑﻠﻮﭼﺴﺘﺎن، زاﻫﺪان، اﯾﺮان محمد حسین دهقان داﻧﺸﮑﺪه رﯾﺎﺿﯽ آﻣﺎر و ﻋﻠﻮم ﮐﺎﻣﭙﯿﻮﺗﺮ، داﻧﺸﮕﺎه ﺳﯿﺴﺘﺎن و ﺑﻠﻮﭼﺴﺘﺎن، زاﻫﺪان، اﯾﺮان حامد احمدزاده داﻧﺸﮑﺪه رﯾﺎﺿﯽ آﻣﺎر و ﻋﻠﻮم ﮐﺎﻣﭙﯿﻮﺗﺮ، داﻧﺸﮕﺎه ﺳﯿﺴﺘﺎن و ﺑﻠﻮﭼﺴﺘﺎن، زاﻫﺪان، اﯾﺮان Journal Article 2021 10 12 The purpose of this paper is to express and calculate the variance confidence interval with the Chachi method of data conversion and without converting the initial data with the bootstrap method. Because the data conversion depends on the amount of variance in the denominator of the conversion expression, it fluctuates and as a result, estimating the confidence intervals and testing the hypothesis is challenged. The results of both methods are compared and their advantages and disadvantages are examined. For this purpose, they first deal with concepts such as the fuzzy random variable and the distance between fuzzy data based on the concept of α-shak as well as α -cut. The hypothesis testing process is then performed for the variance of a sample fuzzy data. The bootstrap method was used to test the hypothesis and the mentioned confidence intervals were compared with the confidence intervals obtained by α -bresh method. ﻫﺪف اﯾﻦ ﻣﻘﺎﻟﻪ ﺑﯿﺎن و ﻣﺤ ﺎﺳﺒﻪ ﻓﺎﺻﻠ ﻪ اﻃﻤﯿﻨﺎن وارﯾﺎﻧﺲ ﺑﺎ روش ﭼﺎﭼﯽ )ﺗﺒﺪﯾﻞ دادهﻫﺎ( و ﺑﺪون ﺗﺒﺪﯾﻞ )دادهﻫﺎی اوﻟﯿﻪ( ﺑﺎ روش ﺑﻮتاﺳﺘﺮپ اﺳﺖ. ﺑﻪ دﻟﯿﻞ اﯾﻨﮑﻪ ﺗﺒﺪﯾﻞ دادهﻫﺎ ﺑﻪ ﻣﻘﺪار وارﯾﺎﻧﺲ در ﻣﺨﺮج ﻋﺒﺎرت ﺗﺒﺪﯾﻞ ﺑﺴﺘﮕﯽ دارد، دﭼﺎر ﻧﻮﺳﺎﻧﺎت ﺷﺪه و در ﻧﺘﯿﺠﻪ ﺑﺮآورد ﻓﺎﺻﻠﻪﻫﺎی اﻃﻤﯿﻨﺎن و آزﻣﻮن ﻓﺮﺿﯿﻪ ﺑﻪ ﭼﺎﻟﺶ ﮐﺸﯿﺪه ﻣﯽﺷﻮد. ﻧﺘﺎﯾﺞ ﻫﺮدو روش را ﻣﻘﺎﯾﺴﻪ و ﻣﺰاﯾﺎ و ﻣﻌﺎﯾﺐ آﻧﻬﺎ ﺑﺮرﺳﯽ ﻣﯽﺷﻮﻧﺪ. ﺑﺮای اﯾﻦ ﻣﻨﻈﻮر، در اﺑﺘﺪا ﺑﺎ ﻣﻔﺎﻫﯿﻤﯽ ﻣﺜﻞ ﻣﺘﻐﯿﺮ ﺗﺼﺎدﻓﯽ ﻓ ﺎزی و ﻓﺎﺻﻠ ﻪ ﺑﯿﻦ دادهﻫﺎی ﻓﺎزی ﺑﺮ اﺳﺎس ﻣﻔﻬﻮم -αﺷﮏ و ﻧﯿﺰ -αﺑﺮش ﭘﺮداﺧﺘﻪ ﻣﯽﺷﻮﻧﺪ. ﺳﭙﺲ ﻓﺮآﯾﻨﺪ آزﻣﻮن ﻓﺮﺿﯿﻪ را ﺑﺮای وارﯾﺎﻧﺲ دادهﻫﺎی ﻓﺎزی ﯾﮏ ﻧﻤﻮﻧﻪای اﻧﺠﺎم ﻣﯽﺷﻮد. در اﻧﺠﺎم آزﻣﻮن ﻓﺮﺿﯿﻪ از روش ﺑﻮتاﺳﺘﺮپ اﺳﺘﻔﺎده ﺷﺪه اﺳﺖ و ﻓﺎﺻﻠﻪﻫﺎی اﻃﻤﯿﻨﺎن ﻣﺬﮐﻮر را ﺑﺎ ﻓﺎﺻﻠﻪﻫﺎی اﻃﻤﯿﻨﺎن ﺣﺎﺻﻞ از روش -αﺑﺮش ﻣﻘﺎﯾﺴﻪ ﺷﺪه اﺳﺖ. https://jfsa.fuzzy.ir/article_146084_0a45f919f21eb0d967bbf76b0a7ac54c.pdf