Fuzzy Statistics Research Articles

Estimating neutrosophic finite median employing robust measures of the auxiliary variable

Our study explores neutrosophic statistics, an extension of classical and fuzzy statistics, to address the challenges of data uncertainty. By leveraging accurate measurements of an auxiliary variable, we can derive precise estimates for the unknown population median. The estimators introduced in this research are particularly useful for analysing unclear, vague data or within the neutrosophic realm. Unlike traditional methods that yield single-valued outcomes, our estimators produce ranges, suggesting where the population parameter is likely to be. We present the suggested generalised estimator's bias and mean square error within a first-order approximation framework. The practicality and efficiency of these proposed neutrosophic estimators are demonstrated through real-world data applications and the simulated data set.

Picture hesitant fuzzy grey compromise relational bidirectional projection method with application in multi-attribute recommendation

In view of the technical defects of the existing grey relational projection method, a new grey compromise relational bidirectional projection method is proposed. By incorporating the information expression advantage of picture hesitant fuzzy number, the distance formula of picture hesitant fuzzy statistics is constructed based on the centralized trend measurement and discrete trend measurement in descriptive statistics. On this basis, a multi-attribute recommendation method of picture hesitant fuzzy grey compromise relational bidirectional projection is proposed by combining compromise idea and bidirectional projection technology. The validity and advantage of this method are verified by numerical analysis, which also suggested the rationality of the picture hesitant fuzzy statistical distance and the grey compromise relational bidirectional projection method.

Statistical inference on quantiles of two independent populations under uncertainty

Statistical inference is the process of drawing conclusions about underlying population(s) using sample data to either confirm or falsify hypotheses. However, the complexity of real-life problems often makes the underlying statistical models inadequate, as information is often imprecise in many respects. To address this common problem, some papers have been published on modifications and extensions of test concepts by employing tools of fuzzy statistics. In this paper, we present a non-parametric test for the difference between quantiles of two independent populations based on fuzzy random variables. For this purpose, we consider the fuzzy quantile function and its estimation based on alpha -values of fuzzy random variables. We then provide a fuzzy test based on the fuzzy empirical distribution function for the difference of fuzzy order statistics from these independent populations. We also suggest a specific degree-based criterion to compare the fuzzy test statistics at a specific significance level to decide whether the underlying fuzzy null hypothesis can be rejected or not. The effectiveness of the proposed two-sample test on quantiles is investigated via numerical examples.

Ratio-Type Estimator for Estimating the Neutrosophic Population Mean in Simple Random Sampling under Intuitionistic Fuzzy Cost Function

Survey sampling has a wide range of applications in biomedical, meteorological, stock exchange, marketing, and agricultural research based on data collected through sample surveys or experimentation. The collected set of information may have a fuzzy nature, be indeterminate, and be summarized by a fuzzy number rather than a crisp value. The neutrosophic statistics, a generalization of fuzzy statistics and classical statistics, deals with the data that have some degree of indeterminacy, imprecision, and fuzziness. In this article, we introduce a fuzzy decision-making approach for deciding a sample size under a fuzzy measurement cost modeled by an intuitionistic fuzzy cost function. Our research introduces neutrosophic ratio-type estimators for estimating the population mean of the neutrosophic study variable YN∈[YL,YU] utilizing all the indeterminate values of the neutrosophic auxiliary variable XN∈[XL,XU] rather than only the extreme values XL and XU. Three simulation studies are carried out to explain the proposed methods of parameter estimation, sample size determination, and efficiency comparison. The results reveal that the proposed neutrosophic class of estimators produces more accurate and precise estimates of the neutrosophic population mean than the existing neutrosophic estimators in simple random sampling, which is the ultimate goal of inferential statistics.

Optimizing construction parameters for fractured horizontal wells in shale oil

Shale oil is mainly extracted by fracturing. However, it is difficult to determine the optimum construction parameters to obtain maximum productivity. In this paper, a fuzzy comprehensive production evaluation model for fractured shale oil horizontal wells based on random forest algorithm and coordinated principal component analysis is proposed. The fracturing parameters of the target wells are optimized by combining this model with an orthogonal experimental design. The random forest algorithm was used to calculate the importance of data sample factors. The main controlling factors of the production of fractured horizontal wells in shale oil were obtained. To reduce the noise of the sample data, principal component analysis was used to reduce the dimensions of the main control factors. Furthermore, the random forest algorithm was used to determine the weight of the principal components after reducing the dimensionality. The membership function of the main control factors after reducing dimensionality was established by combining the fuzzy statistics and assignment methods. In addition, the membership matrix of the effect prediction of fractured horizontal wells in shale oil was determined. The fuzzy comprehensive evaluation method is used to score and evaluate the effect of fractured horizontal wells. Combined with the orthogonal experimental design method, the optimized parameter design of a fractured horizontal well considering the comprehensive action of multiple parameters is realized. After construction according to the optimized parameters, production following fracturing increases significantly. This verifies the rationality of the optimization method that is proposed in this paper.

Web Log Analysis and Security Assessment Method Based on Data Mining.

Web content mining describes the classification, clustering, and attribute analysis of a large number of text documents and multimedia files on the web. Special tasks include retrieval of data from the Internet search engine tool W; structured processing and analysis of web data. Today's blog analysis has security concerns. We do experiments to investigate its safety. Through experiments, we draw the following conclusions: (1) Web log extraction can use efficient data mining algorithms to systematically extract logs from web servers, then determine the main access types or interests of users, and then to a certain extent, based on the discovered user patterns, analyze the user's access settings and behavior. (2) No matter in the test set or the mixed test set, the curve value of deep mining is very stable, the curve value has been kept at 0.95, and the curve value of fuzzy statistics method and quantitative statistics method is stable within the interval of 0.90-095. The results also show that the data mining method has the highest identification accuracy and the best security performance. (3) Web usage analysis requires data abstraction for pattern discovery. This data abstraction can be achieved through data preprocessing, which introduces different formats of web server log files and how web server log data is preprocessed for web usage analysis. One of the most critical parts of the web mining field is web log mining. Web log mining can use powerful data mining algorithms to systematically mine the logs in the web server and then learn the user's access or preferred interests and then conduct a certain degree of user preferences and behavior patterns according to the discovered user patterns. Based on the above analysis, the current web log analysis is faced with security problems. We conduct experiments to study to verify the security performance of web logs and draw conclusions through experiments.

Fuzzy acceptance sampling plan for transmuted Weibull distribution

In conventional sampling plans, the rate of the fraction of faulty items is supposed and fixed, but in some practical situations, this value is not fixed but fuzzy. To attain real and flexible value, we used transmuted Weibull distribution in a fuzzy environment. Fuzzy transmuted Weibull distribution is based on fuzzy set theory. According to our investigation, transmuted Weibull is not used in acceptance sampling in a fuzzy environment. The improvement of this research is to evaluate the vague portion of malfunctioning items (tilde{p }) based on the probability distribution function of transmuted Weibull model and attain a fuzzy operating characteristic curve. First-time transmuted Weibull distribution is applied in acceptance sampling plan for cases where the quality of the product is imprecise. Therefore, fuzzy statistics has been used in this design instead of classical statistics. The results are described by numerical examples and an application of real data is considered for illustration.

Unbiased Fuzzy Estimators in Fuzzy Hypothesis Testing

In this paper, we develop fuzzy, possibilistic hypothesis tests for testing crisp hypotheses for a distribution parameter from crisp data. In these tests, fuzzy statistics are used, which are produced by the possibility distribution of the estimated parameter, constructed by the known from crisp statistics confidence intervals. The results of these tests are in much better agreement with crisp statistics than the ones produced by the respective tests of a popular book on fuzzy statistics, which uses fuzzy critical values. We also present an error that we found in the implementation of the unbiased fuzzy estimator of the variance in this book, due to a poor interpretation of its mathematical content, which leads to disagreement of some fuzzy hypotheses tests with their respective crisp ones. Implementing correctly this estimator, we produce test statistics that achieve results in hypotheses tests that are in much better agreement with the results of the respective crisp ones.

Finite Element Analysis Method of Slope Stability based on Fuzzy Statistics

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.

Fuzzy Xbar and S Control Charts Based on Confidence Intervals

There have been changes since the companies have realized the important role of quality improvement in their success. If they are able to produce high quality products and satisfy demands, then they can survive in competitive global markets. Quality improvement applications aim to decrease variability, which leads to less cost, production time, number of defects, scrap, rework and more customer satisfaction. Quality can be improved by reducing product variability. On the other hand, uncertainty or subjectivity is a part of many engineering and real life problems. However, these problems cannot be solved by traditional methods. This study focuses on constructing Xbar and S control charts in fuzzy environment. The approach is developed by considering the theoretical structure of the Shewhart control charts. The core of the approach depends on the combination of parametric interval estimation and fuzzy statistics. Control limits and samples are presented by fuzzy numbers which ensures to maintain fuzziness in control charts. An important property of the approach is that the fuzzy charts can be reduced to Shewhart control charts. A simulation study was conducted for the performance evaluation of fuzzy Xbar and S control charts. The proposed fuzzy control chart is sensitive to process mean shifts and variance changes, and outperforms the traditional control charts under the changes of variance. In addition, an example from the literature shows that the approach is an effective way of presenting fuzziness in the quality characteristics, which enables the approach to have high applicability to the real life problems.

Applying fuzzy statistics to evaluate and allocate resources in seven star grotto national park area

The purpose of this study is to use an objective function algorithm to establish the fuzzy number parameters of the fuzzy semantic scale, and then find the way to improve and the development and management of tourist attractions. This paper divides the development of the Seven Star Grotto National Park into three periods: 2001-2005, 2006-2010 and 2011-2015. Using expert scoring and field interviews, combined with the Seven Star Grotto National Park resource profile and Zhaoqing development profile, we quantitatively measured the overall resource level, resource value, scenic conditions and regional conditions of different time period.

State Evaluation Model of High voltage Switchgear Based on Fuzzy Set-valued Statistical Method and Kernel Vector Space Model

The traditional high voltage switchgear (HVS) state evaluation model mostly adopts electrical test, live detection and historical data, neglecting the influence of real-time operation data of HVS composition equipment on the state evaluation results. This paper proposes a HVS operation state evaluation model based on fuzzy set-valued statistics method and kernel vector space model based on electrical test data and on-line monitoring data. First of all, according to the components of high voltage switchgear, the operation state of HVS is described and the evaluation index system is established. Secondly, the fuzzy set-valued statistics method is used to construct the mathematical model of evaluation index weight. Then, the kernel vector space model is introduced, and the Gaussian kernel function is used to map the sample to the features of the high-dimensional feature space. The indicator vector of the sample data and the ideal indicator vector of the high-voltage switchgear operation status level standard are defined in the high-dimensional feature space, and the angle-weighted cosine between the two vectors is calculated as the closeness of the sample to the standard status level, and then the high-voltage switchgear operation status level is obtained. Finally, the real data of a power supply company in western China are simulated. The results show that the greater the closeness degree is, the closer the HVS corresponding to the sample is to the normal state, on the contrary, the smaller the closeness degree is, the closer the HVS is to the fault state.

Value for money evaluation for conversion of highway stock project from BT model to PPP model based on improved risk quantification method

With the accelerated urbanization progress, the governmental financial funds fail to satisfy the needs of highway project construction in some areas. The building-transfer (BT) model and public-private partnership (PPP) model have been carried out in succession in China to solve the shortage of financial funds. However, the emotion analysis method in Guide of Value for Money Evaluation for PPP Project (trial) enacted by the Ministry of Finance is of great subjectivity when applied to the calculation of risk quantification, which is the key to quantitative evaluation, so it is in urgent need of perfection through scientific methods to promote the implementation of PPP projects. On this basis, under the research background of conversion of a highway stock project from BT model to PPP model in city Z, the fuzzy analytic hierarchy process (HAHP) and set-valued statistics method were applied to the method improvement for the risk quantification part of value for money (VFM) evaluation cases in this project. The results show that the VFM (calculated based on the improved risk quantification method) of the BT-to-PPP model for the highway stock project in city Z is elevated from the original 248,240,000 RMB to 271,643,500 RMB. The conclusions can provide a certain reference basis for further improving China’s VFM evaluation system, and boosting the development of PPP model in China.

Decision Making for Project Appraisal in Uncertain Environments: A Fuzzy-Possibilistic Approach of the Expanded NPV Method

The major drawback of the classic approaches for project appraisal is the lack of the possibility to handle change requests during the project’s life cycle. This fact incorporates the concept of uncertainty in the estimation of this investment’s worth. To resolve this issue, the authors use fuzzy numbers, possibilistic moments of fuzzy numbers and the hybrid (fuzzy statistic) fuzzy estimators’ method in order to introduce a fuzzy possibilistic version of the expanded net present value method (FPeNPV). This approach consists of two factors: the fuzzy possibilistic NPV and the fuzzy option premium. For the estimation of the fuzzy NPV, some basic assumptions are taken into consideration: (1) the opportunity cost of capital, used as the present value interest factor calculated through the weighted average cost of capital (WACC), (2) the equity cost, determined through the possibilistic set-up of the capital asset pricing model CAPM, and (3) the inflation factor, also included in the estimation of the NPV. The fuzzy estimators’ method is used for the computation of the fuzzy option premium. An algorithm of nine major steps leads to the computation of the FPeNPV. This gives the administration the opportunity to adapt to potential changes in the company’s internal and external environments. In this way, the symmetry between the planning and execution phase of a project can be reinstated. The results validate the statement that fuzzy and intelligent methods remain valuable tools to express uncertainty in various scientific areas. Finally, an illustrative example aims at a thorough comprehension of this new approach of the expanded NPV method.

Possibility Measure of Accepting Statistical Hypothesis

Taking advantage of the possibility of fuzzy test statistic falling in the rejection region, a statistical hypothesis testing approach for fuzzy data is proposed in this study. In contrast to classical statistical testing, which yields a binary decision to reject or to accept a null hypothesis, the proposed approach is to determine the possibility of accepting a null hypothesis (or alternative hypothesis). When data are crisp, the proposed approach reduces to the classical hypothesis testing approach.

Achievements analysis of mooc English course based on fuzzy statistics and neural network clustering

At present, the field of natural language will also introduce in-depth learning, using the concept of word vector, so that the neural network can also complete the work in the field of statistics. It can be said that the neural network has begun to show its advantages in the field of natural language processing. In this paper, the author analyzes the multimedia English course based on fuzzy statistics and neural network clustering. Different factors were classified, and scores were classified according to the number of characteristics of different categories. It can be seen that with the popularization of the Internet, MOOC teaching meets the requirements of the current college English curriculum, is a breakthrough in the traditional teaching mode, improves students’ participation, and enables students to learn independently. It not only conforms to the characteristics of College students, but also improves their learning effect. In the automatic scoring stage, the quantitative text features are extracted by the feature extractor in the pre-processing stage, and then the weights of network connections obtained in the training stage are used to score the weights comprehensively. This model can better reflect students’ autonomous learning ability and language application ability.

Quality function deployment model using fuzzy programming with optimisation technique for customer satisfaction

Quality function deployment (QFD) is a customer-driven superiority organisation and product expansion scheme for attaining advanced consumer approval. This document is to inspect the execution of QFD at fuzzy surroundings and to expand equivalent events to contract by the fuzzy data. At this time, regard as the consumer approval limitations are ease, refund and safeness in FQFD (Fuzzy QFD) study using fuzzy logic controller (FLC) by optimisation method. This optimisation method to develop the accurateness values of FLC in QFD procedure, now PSO is utilised for optimisation method. For hard data production, dissimilar relationship utility is employed to the comparative inclination association on fuzzy statistics, it is not essential to develop two fuzzy statistics to obtain standard masses in FQFD. Since, the outcome of fuzzy to recognising the precedence stage of the consumer approval and utmost accurateness stage of the FQFD procedure.

An Alternative Method for GIS Insulation Performance Evaluation

The continuous improvement of system capacity and voltage level is somewhat accompanied by insulation fault as one of the main faults of GIS device. In this paper, an alternative method for identifying the GIS insulation performance based on fuzzy evidence theory is proposed by way of judging the four main features of GIS insulation level. Firstly, the fuzzy statistic test was used to obtain the normalized values of the four feature quantities of GIS insulation level. Four methods were used to calculate their respective expectations and deviations. The membership degree value was determined by the membership function, and the difference between the membership degrees was also considered. The degree of fusion was used to determine the weight of each feature quantity, so that the membership degree of the same kind of feature information fusion was obtained. Finally, the merged membership degree was transformed into the basic trust distribution function. The evidence theory then took the job to realize the pairwise fusion of the trust distribution functions between different feature quantities. The experimental results showed that this alternative way was proven to make effective judgment on the GIS insulation performance.

An abrasion damage evaluation method of metal mechanical material for automotive chassis based on wavelet transform

In order to overcome the problems of low accuracy and low fitting rate of traditional methods for evaluating abrasion damage of metal mechanical materials, a new method for evaluating abrasion damage of metal mechanical materials of automobile chassis based on wavelet transform is proposed in this paper. This method utilises the time-frequency joint wavelet feature extraction algorithm and the correlation coefficient algorithm to realise the extraction and selection of damage features. The membership function is constructed by the method of fuzzy statistics to evaluate the abrasion damage of metal mechanical materials in automobile chassis. The experimental results show that the evaluation accuracy of the proposed method is higher than 75%, and the fitting rate is higher than 56%, which proves that the proposed method has better evaluation effect.

Exponentially Weighted Moving Average Control Chart Based on Normal Fuzzy Random Variables

Exponentially weighted moving average (EWMA) chart is an alternative to Shewhart control charts and can serve as an effective tool for detection of shifts in small persistent process. Notably, existing methods rely on induced imprecise observations of a normal distribution with fuzzy mean and variance. Such techniques did not investigate the statistical properties relevant to a fuzzy EWMA. To overcome this shortcoming, employing a common notion of normal fuzzy random variable with fuzzy mean and non-fuzzy variance could be helpful. This paper first developed a notion of fuzzy EWMA statistic as a natural extension to the classical counterpart. Then, the concept of fuzzy EWMA control limit was introduced and discussed in cases where fuzzy mean and/or non-fuzzy variance was unknown parameters. A degree of violence was also employed to monitor the proposed fuzzy EWMA control chart. Potential applications of the proposed fuzzy EWMA chart were also demonstrated based on a real-life example. The advantages of the proposed method were also discussed in comparison with other existing fuzzy EWMA methods.