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This paper presents a comprehensive study of the signed distance metric for fuzzy numbers. Due to the property of directionality, this measure has been widely used. However, it has a main drawback in handling asymmetry and irregular shapes in fuzzy numbers. To overcome this rather bad feature, we introduce two new distances, the balanced signed distance (BSGD) and the generalised signed distance (GSGD), seen as generalisations of the classical signed distance. The developed distances successfully and effectively take into account the shape, the asymmetry and the overlap of fuzzy numbers. The GSGD is additionally directional, while the BSGD satisfies the requirements for being a metric of fuzzy quantities. Analytical simplifications of both distances in the case of often-used particular types of fuzzy numbers are provided to simplify the computation process, making them as simple as the classical signed distance but more realistic and precise. We empirically analyse the sensitivity of these distances. Considering several scenarios of fuzzy numbers, we also numerically compare these distances against established metrics, highlighting the advantages of the BSGD and the GSGD in capturing the shape properties of fuzzy numbers. One main finding of this research is that the defended distances capture with great precision the distance between fuzzy numbers; additionally, they are theoretically appealing and are computationally easy for traditional fuzzy numbers such as triangular, trapezoidal, Gaussian, etc., making these metrics promising. [ABSTRACT FROM AUTHOR]

Risk-neutral fuzzy probability measures play a crucial role in evaluating American fuzzy put option and fuzzy call option pricing models that depend on the amount of increase or decrease of the equity prices. Volatility and risk-free interest rate are the two significant parameters that are affecting the financial market frequently. In 2008, Muzzioli et al [9] and Xcaojian Yu [17] used non-overlapping triangular/trapezoidal and non-overlapping fuzzy trapezoidal numbers respectively to describe the same to study American put option model. In this study, we recommend fuzzy measures involving non-overlapping fuzzy octagonal numbers using which we demonstrate American Put Fuzzy Option Model (APFOM) by incorporating the uncertain values to real in the volatile series. [ABSTRACT FROM AUTHOR]

Machine learning applied to regression models offers powerful mathematical tools for predicting responses based on one or more predictor variables. This paper extends the concept of multiple linear regression by implementing a learning system and incorporating both fuzzy predictors and fuzzy responses. To estimate the unknown parameters of this soft regression model, the approach involves minimizing the absolute distance between two lines under three constraints related to the absolute error distance between observed data and their respective predicted lines. A thorough comparative analysis is conducted, showcasing the practical applicability and superiority of the proposed soft multiple linear regression model. The effectiveness of the model is demonstrated through a comprehensive examination involving simulation studies and real-life application examples.

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Copyright of International Journal of Engineering Research & Development (IJERAD) is the property of International Journal of Engineering Research & Development and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The EM algorithm is a powerful tool and generic useful device in a variety of problems for maximum likelihood estimation with incomplete data which usually appears in practice. Here, the term ``incomplete" means a general state and in different situations it can mean different meanings, such as lost data, open source data, censored observations, etc. This paper introduces an application of the EM algorithm in which the meaning of ``incomplete" data is non-precise or fuzzy observations. The proposed approach in this paper for estimating an unknown parameter in the parametric statistical model by maximizing the likelihood function based on fuzzy observations. Meanwhile, this article presents a case study in the electronics industry, which is an extension of a well-known example used in introductions to the EM algorithm and focuses on the applicability of the algorithm in a fuzzy environment. This paper can be useful for graduate students to understand the subject in fuzzy environment and moreover to use the EM algorithm in more complex examples.

The EM algorithm is a powerful tool and generic useful device in a variety of problems for maximum likelihood estimation with incomplete data which usually appears in practice. Here, the term "incomplete" means a general state and in different situations it can mean different meanings, such as lost data, open source data, censored observations, etc. This paper introduces an application of the EM algorithm in which the meaning of "incomplete" data is non-precise or fuzzy observations. The proposed approach in this paper for estimating an unknown parameter in the parametric statistical model by maximizing the likelihood function based on fuzzy observations. Meanwhile, this article presents a case study in the electronics industry, which is an extension of a well-known example used in introductions to the EM algorithm and focuses on the applicability of the algorithm in a fuzzy environment. This paper can be useful for graduate students to understand the subject in fuzzy environment and moreover to use the EM algorithm in more complex examples. [ABSTRACT FROM AUTHOR]

The logistic distribution is widely used to model various types of applied data. The modified logistic distribution under neutrosophic statistics is introduced in this work. The neutrosophic logistic distribution (NLD) and its engineering applications are mainly emphasized. An appealing characteristic of the suggested NLD is that it is useful to many widely utilized survival assessment metrics, including the reliability function, hazard function, and survival function. Applications of some mathematical and statistical properties of the suggested model are discussed. Numerical investigations on simulated data are used to validate the theoretical findings experimentally. From an application point of view, it is inferred that the proposed distribution fits data with imprecise, hazy, and fuzzy information better than the usual model. In addition, the maximum likelihood (ML) technique for the proposed model is discussed under the neutrosophic inference framework. Eventually, some illustrative examples related to system reliability are provided to clarify further the implementation of the neutrosophic probabilistic model in real-world problems. [ABSTRACT FROM AUTHOR]

Purpose: Predicted the explanatory power of core through the application of autoregressive functions and fuzzy time series by archery performance. Can the archery performance of different athletes (high-score group and low-score group) be predicated and evaluated? In this study, purposive sampling was used to recruit the research participants by Chinese Taipei Archery Association (CTAA) were data collected in this study. Method: This study applied fuzzy statistics to the analysis of quadratic regression, autoregressive functions, and transfer functions. Subsequently, these statistics and relevant data were analyzed using Minitab 16.0 and Microsoft Office Excel 2013. Results: The findings of this study are listed as follows: Using autoregressive functions and fuzzy time series can truly reflect the explanatory power of athletes' performance in archery and effectively predict the archery performance of male athletes in the high-score group during the 2013 Asian Games. Suggestion: Fuzzy mode could be used to investigate the academic performance and learning environment of universities because it enhances the authenticity of students learn skill. Further academic learn training programs for student could be planned according to contest goals and contents, and the proportion of male to female student can be determined according to current situations. Contribution: The performance of student predicted using fuzzy time series should be used to design training programs for athletes and to assess students' ability to participate in learn environment. [ABSTRACT FROM AUTHOR]

An approach is proposed to construct fuzzy confidence intervals for unknown parameters in statistical models. In this approach, a family of confidence intervals of the unknown crisp parameters is considered. Such confidence intervals are used to obtain a fuzzy confidence interval for the parameter of interest. The proposed approach enjoys a wide range of confidence intervals to obtain a trapezoidal shaped fuzzy set of the parameter space as the fuzzy confidence interval for the parameter of interest. By using the resolution identity, it is shown that the constructed fuzzy confidence intervals are really fuzzy sets of the parameter space. Some numerical examples are provided to explain the functionality of the approach at one-sided and two-sided fuzzy confidence intervals. Moreover, the application of this proposed approach in health sciences is provided for the case of the recovery time of olfactory and gustatory dysfunctions for COVID-19 patients. [ABSTRACT FROM AUTHOR]

In several research areas, ratings data and response times have been successfully used to unfold the stagewise process through which human raters provide their responses to questionnaires and social surveys. A limitation of the standard approach to analyze this type of data is that it requires the use of independent statistical models. Although this provides an effective way to simplify the data analysis, it could potentially involve difficulties with regard to statistical inference and interpretation. In this sense, a joint analysis could be more effective. In this research article, we describe a way to jointly analyze ratings and response times by means of fuzzy numbers. A probabilistic tree model framework has been adopted to fuzzify ratings data and four-parameters triangular fuzzy numbers have been used in order to integrate crisp responses and times. Finally, a real case study on psychometric data is discussed in order to illustrate the proposed methodology. Overall, we provide initial findings to the problem of using fuzzy numbers as abstract models for representing ratings data with additional information (i.e., response times). The results indicate that using fuzzy numbers leads to theoretically sound and more parsimonious data analysis methods, which limit some statistical issues that may occur with standard data analysis procedures. [ABSTRACT FROM AUTHOR]