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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.

Copyright of Contaduría y Administración is the property of Facultad de Contaduria y Administracion-Universidad Nacional Autonoma de Mexico 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.)

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]

Nonparametric tests do not rely on data belonging to any particular parametric family of probability distributions, which makes them preferable in case of doubt about the underlying population. Although the two‐tailed sign test is likely the most common nonparametric test for location problems, practitioners face serious drawbacks, such as its lack of statistical power and its inapplicability when information regarding data and hypotheses is uncertain or imprecise. In this paper, we generalize the two‐tailed sign test by embedding fuzzy hypotheses caused by uncertainty/imprecision regarding linguistic statements on fractions of underlying quantiles. By achieving this objective, (1) crucial limitations of the common two‐tailed sign test are mitigated/overcome, (2) various further strengths are incorporated into the sign test (e.g., meeting the trade‐off between point‐ and interval‐valued hypotheses, facilitated formulation of fuzzy hypotheses, standardization of membership functions), and (3) shortcomings that often come along with fuzzy hypothesis testing are avoided (e.g., higher complexity, fuzzy test decision, possibilistic interpretation of test results). In addition, we conduct a comprehensive case study using a real data set on the psychosocial status during the COVID‐19 pandemic. The results of the case study clearly indicate that the generalized two‐tailed sign test is preferable to the two‐tailed sign test with point‐ or interval‐valued hypotheses. [ABSTRACT FROM AUTHOR]

The failure criterion of structural serviceability is often fuzzy, which has a direct impact on the results of structural reliability analysis. Membership function is a basic mathematical tool to describe the fuzziness of failure criteria. At present, the fuzzy statistical method for generating the fuzzy set membership function is to take the numerical interval of the fuzzy set as a sample, and directly generate the membership function through statistics. However, this kind of sample will cover the uncertainty of the individual's understanding of fuzzy boundaries to a certain extent, and its statistical results are difficult to truly reflect the characteristics of fuzzy sets. The fuzzy boundary is described by the membership density function, and the numerical interval covering the fuzzy boundary is taken as the sample. The fuzzy statistical method for generating the membership density function is proposed, and the indirect statistical method for generating the membership function is established. The comparative analysis results show that the membership functions generated by the two statistical methods are different. The membership function generated by indirect statistical method can fully reflect the uncertainty of the individual's understanding of the fuzzy boundary, more truly reflect the characteristics of the fuzzy set, and provide a more solid foundation for the fuzzy probability analysis of structural serviceability. [ABSTRACT FROM AUTHOR]

The sign test is one of the most popular nonparametric tests for location problems and allows testing for any quantile of a population. However, the common sign test has serious drawbacks such as loss of information by considering solely signs of observations but not their magnitudes, various problems related to handling of ties in the data, and the lack of embedding uncertainty regarding the fraction of underlying quantile. To address these issues, we present an extended sign test based on fuzzy categories and fuzzy formulated hypotheses that improves the generality, versatility, and practicability of the common sign test. This generalized test procedure is neat in theory and practice and avoids disadvantages that are often associated with fuzzy tests (e.g., a considerably higher complexity of the underlying model, a fuzzy test decision, and a possibilistic instead of a probabilistic interpretation of test results). In addition, we perform a comprehensive case study on COVID‐19 in HIV‐infected individuals with a focus on human body temperature and related measurement problems. The results of the study clearly indicate that fuzzy categories and fuzzy hypotheses improve the performance of the sign test. [ABSTRACT FROM AUTHOR]

Although control charts can notify the state of out-of-control in a process by generating a signal, the indication is usually followed by a considerable amount of delay. Identifying the real time of the change in a process would provide a starting point for further investigation of an assignable cause. This paper addresses the problem of detecting the change point in different processes when the quality characteristics drift steadily away from an in-control state. For this purpose, a fuzzy statistical clustering (FSC) method is used to estimate the drift time in different processes. Since the application of an FSC method requires both in- and out-of-control values of the process parameter, a linear regression model is utilised to estimate the trend rate and then calculate the out-of-control process parameter. Through extensive simulations, the performance of the proposed change point estimation method is analysed and compared with the most recent estimators for several control charts. The results demonstrate that the proposed method is more effective in detecting the drift time through a wide range of trend rates. Furthermore, it is shown that the proposed method offers a higher estimation precision compared to conventional statistical methods. [ABSTRACT FROM AUTHOR]

In order to reduce the risk of slope stability evaluation due to the fuzziness of calculation parameters, a finite element analysis method of slope stability based on fuzzy statistics is proposed. Based on the principle of quasi-static method and with the help of the finite element software COMSOL multiphysics, this paper studies the stability of the gravel soil accumulation rock slope under the action of different seismic acceleration. By analyzing the displacement, plastic zone and safety factor of the rock soil slope, the stability of the rock soil slope is analyzed. The research results show that the fuzziness of mechanical parameters of rock and soil slope will lead to the fuzziness of position displacement and stress analysis results of rock and soil slope, and the analysis of rock and soil slope with the method of fuzzy finite element analysis can strengthen the comprehensive understanding of position displacement, stress and safety of rock and soil slope by engineers and technicians, and reduce the stability of rock and soil slope due to the fuzziness of calculation parameters to a certain extent Evaluate the risk qualitatively. [ABSTRACT FROM AUTHOR]

This paper is concerned with fuzzy hypothesis testing in the framework of the randomized and non-randomized hypergeometric test for a proportion. Moreover, we differentiate between a test of significance and an alternative test to control the type I error or both error types simultaneously. In contrast to classical (non-)randomized hypothesis testing, fuzzy hypothesis testing provides an additional gradual consideration of the indifference zone in compliance with expert opinion or user priorities. In particular, various types of hypotheses with user-specified membership functions can be formulated. Additionally, the proposed test methods are compared via a comprehensive case study, which demonstrates the high flexibility of fuzzy hypothesis testing in practical applications. [ABSTRACT FROM AUTHOR]

Copyright of Tunnel Construction / Suidao Jianshe (Zhong-Yingwen Ban) is the property of Tunnel Construction Editorial Office 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.)

In this paper we propose fuzzy hypothesis testing for a proportion with crisp data as the exact generalized one-tailed hypergeometric test with fuzzy (non-)complementary hypotheses, and incorporate the conventional hypergeometric test with crisp hypotheses into its framework. In particular, we formulate hypotheses as ontic or epistemic (fuzzy) sets, since we assume that presumptions regarding the true population proportion can be expressed in the conjunctive or disjunctive reading. Further, we suggest modeling of membership functions in terms of cost or frequency due to considerations of user's priorities or incomplete knowledge in relation to hypotheses formulation. Considering a hypothesis as union of its crisp and fuzzy areas, we illustrate via real-life examples that in contrast to classical test theory, fuzzy hypothesis testing provides an additional partial and gradual consideration of the indifference zone for both complementary and non-complementary hypotheses. The test concept is introduced for both test methods, a test of significance and an alternative test, and leads to a crisp test decision considering further cost aspects like the sample size. The generalized error criteria are derived and interpreted in relation to both hypotheses. Additionally, a corresponding sensitivity analysis is presented for one of the most promising test types. [ABSTRACT FROM AUTHOR]

Industrial robots, which enable manufacturing firms to produce high-quality products in a cost-effective manner, are important components of advanced manufacturing technologies. The performance of industrial robots is determined by multiple and conflicting criteria that have to be simultaneously considered in a robust selection study. In this study, a decision model based on fuzzy linear regression is presented for industrial robot selection. Fuzzy linear regression provides an alternative approach to statistical regression for modelling situations where the relationships are vague or the data set cannot satisfy the assumptions of statistical regression. The results obtained by employing fuzzy linear regression are compared with those of earlier studies applying different analytical methods to a previously reported robot selection problem. [ABSTRACT FROM PUBLISHER]

Agility is the performance measure of agile manufacturing (AM) practices and with the increasing adoption of AM systems its assessment has gained in importance. This study has been undertaken to fill the observed research gap that no research has been attempted to validate an agility assessment result using an alternative effective method. The agility assessment of an Indian electric automotive car manufacturing organisation has been done using a scoring approach and validated using an effective multi-grade fuzzy method. The result indicates that the organisation was agile to an extent of 84.1% using the scoring approach and 7.05 using the multi-grade fuzzy method, which implies the organisation is agile. The gap analysis results indicate that the largest gap is observed in the case of ‘nature of management’ criterion followed by ‘devolution of authority’, ‘customer response adoption’ and ‘employee involvement’. Necessary actions were taken for the improvement of these agility gaps. The improvement in agile performance measures is 7.7 to 9.7 (on a Likert scale of range 0–10) after the implementation of the suggested proposals. The statistical validation study indicates the feasibility of improvement in agility after the assessment exercise with a practical success rate of 90%. [ABSTRACT FROM PUBLISHER]

In marketing, qualitative data are used in theory development to investigate marketing phenomena in more depth. After qualitative data are collected, the judgment-based classification of items into categories is routinely used to summarize and communicate the information contained in the data. In this article, the authors provide marketing researchers with a method that (1) provides useful substantive information about the proportion and degree to which items belong to several categories and (2) measures the classification accuracy of the judges. The model is called the fuzzy latent class model (FLCM), because it extends Dillon and Mulani's (1984) latent class model by freeing it from the restrictive assumption that all items are crisp for a given categorization. Instead, FLCM allows for items to be either crisp or fuzzy. Crisp items belong exclusively to one category, whereas fuzzy items belong--in varying degree--to multiple categories. This relaxation in the assumption about the nature of qualitative data makes FLCM more widely applicable: Qualitative data in marketing research are often fuzzy, because they involve open-ended descriptions of complex phenomena. The authors also propose a moment-based measure of overall data fuzziness that is bounded by 0 (completely crisp) and 1 (completely fuzzy). [ABSTRACT FROM AUTHOR]

Classifiers based on Gamma statistical distribution can be found in the scientific literature, but they assume the collected data doesn't present any errors. However, in some cases, information precision can not be guaranteed, then the fuzzy approach is convenient. Several methods found in the literature are not able to ponder the specific contribution of each class and/or feature for the classification tasks. This paper presents a proposal of a new classifier named Doubled Weighted Fuzzy Gamma Naive Bayes network (DW-FGamNB). This new classifier uses two types of weights in order to allow users to ponder the real contribution of each class and feature in the classification task. The theoretical development is presented, as well as results of its application on simulated multidimensional data using Gamma statistical distribution. A comparison among DW-FGamNB, Fuzzy Gamma Naive Bayes classifier, classical Gamma Naive Bayes classifier, Naive Bayes classifier, DecionTree-Naive Bayes, Decision Tree C4.5, Logistic Regression, Multilayer Perceptron Neural Network, Adaboost-M1, Radial Basis Function Network and Random Forest was performed. The results obtained showed that the DW-FGamNB produced the best performance, according to the Overall Accuracy Index, Kappa and Tau Coefficients, and diagnostic tests. [ABSTRACT FROM AUTHOR]

The phenomena treated in this paper are classified into the following three cases: (I) Phenomena whose objective variable is quantitative, where such quantitative changes of the objective variable are referred to as quantitative external criterion. (II) Phenomena whose objective variable is qualitative, where the qualitative changes of the objective variable are referred to as qualitative external criterion. (III) Phenomena which are specified without any objective variables. This paper has consisted of three parts corresponding to the above classification of phenomena. The methods for analyzing phenomena with quantitative external criterion are presented in Section 3 as fuzzy time-series analysis and in Section 4 as fuzzy regression qualitative analysis. The methods for analyzing phenomena with qualitative external criterion are described in Section 5 as fuzzy discriminant qualitative analysis and in Section 7 as fuzzy discriminant analysis. In Section 6 the fuzzy discriminant qualification analysis is successively applied to the analysis of purchasing factors in consumer's behavior. The methods for analyzing phenomena without any external criteria are treated in Sections 8 to 11. In Section 8 the heuristic method is proposed in order to find a fuzzy transitive relation. This heuristic method is applied to the hierarchical clustering problem in Section 9 and to the identifying problem of preference ordering in Section 10. In Section 11 the evaluation of alternatives with multiple attributes is analytically discussed in view of the concept of fuzzy sets. In Section 1 the survey of the fuzzy set theory and the into-introductory description of fuzzy multivariate analysis are given. Section 2 briefly describes concepts and definitions of fuzzy sets in preparation for the main parts of this paper. At the end Section 12 summarizes the results of this paper. [ABSTRACT FROM AUTHOR]

In view of the problems existing in the evaluation index selection and whether the evaluation method is too simple to evaluate the coordinated development of regional economy. Based on the comprehensive analysis of the definition of the coordinated development of regional economy, this paper discusses the definition of the scientific connotation of the coordinated development of regional economy and puts forward three evaluation indexes for coordinated development of regional economy (the degree of regional economic integration, the degree of regional economic development gap, and the speed of regional economic development). In view of the diversity of evaluation factors and the fuzziness of the relationship between evaluation indexes, this paper uses the fuzzy classification statistical model to evaluate the coordinated development of regional economy and established a regional economic development coordination management system based on fuzzy hierarchical statistical model to evaluate the degree of regional economic coordinated development. Finally, the eastern region and the central and western regions are taken as the object of study. The analysis results show that the conclusion drawn from the model is basically consistent with the actual situation in China. This model can effectively manage the coordinated development of regional economy in China. [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of defining statistical parameters when the uncertainty is expressed using a fuzzy measure. We extend the concept of monotone expectation in order to define a monotone variance and monotone moments. We also study parameters that allow the joint analysis of two functions defined over the same reference set. Finally, we propose some parameters over product spaces, considering the case in which a function over the product space is available and also the case in which such function is obtained by combining those in the marginal spaces.

The aim of the paper is to examine procedures of descriptive statistics in the case when the values of relevant attribute in a sample are set in the form of fuzzy categories. The paper provides alternative definitions of a fuzzy random variable, and describes corresponding procedures for calculating the analogues of location and spread parameters. The paper also presents some illustrative examples and analyses the results obtained. Based on the result analysis, practical recommendations are given on how to use procedures of fuzzy statistics. [ABSTRACT FROM AUTHOR]