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Design and implementation of the fuzzy expert system in Monte Carlo methods for fuzzy linear regression

机译：模糊Carlo模糊线性回归模糊专家系统的设计与实现

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In this study, fuzzy expert system (FES) in Monte Carlo (MC) method, which is used for estimating fuzzy linear regression model (FLRM) parameters, is applied to determine the parameter intervals, for the first time in the literature. MC method in estimating FLRM parameters is a new field of study that is very useful and time saving. However a major problem might occur in determining the parameter intervals from which the regression model parameters are supposed to come. If the intervals are calculated too large, FLRM error will be very large. Accordingly, the actual model parameters will not be obtained if the intervals are calculated too narrow. This drawback has not been addressed in the literature before and only optimization methods have been applied to achieve the best interval values. In this article, the FES is used for the first time in order to solve the problem in parameter estimation process for the FLRM in the field of statistics. For this purpose, the difference between the fuzzy observation value and fuzzy estimation value's support set (W) is taken into account. The most appropriate intervals calculated for the parameters are those that make W as small as possible. Thus, FES is designed to determine the best intervals for the model parameters. The system knowledge base is composed of 7 fuzzy rules. As a result, it is deduced that the FLRM parameter estimates obtained from the MC method using FES are very close to the real values. The real impact of this paper will be in showing the applicability of FESs in order to solve problems that we encounter in the field of statistics by the help of linguistic expressions. Moreover, these outcomes will be useful for enriching the studies that have already focused on FLRMs and will encourage researchers to use FES to solve problems in statistics. To sum up, this study demonstrates that FESs which is used in technological devices and makes our lives easier can also be used in solving problems that we confront in the field of statistics efficiently with using linguistic expressions like human inference system. (C) 2019 Elsevier B.V. All rights reserved.
机译：在本研究中，应用用于估计模糊线性回归模型（FLRM）参数的Monte Carlo（MC）方法的模糊专家系统（FES）以确定参数间隔，首次在文献中。 MC方法估计FLRM参数是一个新的研究领域，非常有用和节省时间。然而，在确定应该发生回归型参数的参数间隔时可能会出现一个主要问题。如果计算过大的间隔，FLRM误差将非常大。因此，如果计算过窄的间隔，则不会获得实际模型参数。在文献之前尚未解决此缺点，并且仅应用优化方法来实现最佳间隔值。在本文中，第一次使用FES以解决统计领域FLRM参数估计过程中的问题。为此目的，考虑模糊观察值和模糊估计值的支持集（W）之间的差异。为参数计算的最合适的间隔是那些尽可能小的那些。因此，FES旨在确定模型参数的最佳间隔。系统知识库由7个模糊规则组成。结果，推导出从使用FES获得的MC方法获得的FLRM参数估计非常接近真实值。本文的实际影响将展示驻友的适用性，以解决我们在语言表达式的帮助下解决我们在统计领域遇到的问题。此外，这些结果将有助于丰富已经专注于FLRMS的研究，并鼓励研究人员使用FE解决统计问题的问题。总而言之，这项研究表明，在技术设备中使用的居民，使我们的生活更容易，也可以用于解决我们使用人类推理系统等语言表达式有效地在统计领域面对的问题。 （c）2019年Elsevier B.V.保留所有权利。

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