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.

Einstein exponential operation laws of spherical fuzzy sets and aggregation operators in decision making

The spherical fuzzy set (SFS) model is one of the newly developed extensions of fuzzy sets (FS) for the purpose of dealing with uncertainty or vagueness in decision making. The aim of this paper is to define new exponential and Einstein exponential operational laws for spherical fuzzy sets and their corresponding aggregation operators. We introduce the operational laws for exponential and Einstein exponential SFSs in which the base values are crisp numbers and the exponents (weights) are spherical fuzzy numbers. Some of the properties and characteristics of the proposed operations are then discussed. Based on these operational laws, some new aggregation operators for the SFS model, namely Spherical Fuzzy Weighted Exponential Averaging (SFWEA) and Spherical Fuzzy Einstein Weighted Exponential Averaging (SFEWEA) operators are introduced. Finally, a decision-making algorithm based on these newly introduced aggregation operators is proposed and applied to a multi-criteria decision making (MCDM) problem related to ranking different types of psychotherapy.

Comparative study between GRA and MEREC technique on an agricultural-based MCGDM problem in pentagonal neutrosophic environment

In this research article, an improved Multi-criteria group decision-making (MCGDM) strategy has been developed in pentagonal neutrosophic environment incorporating grey relational analysis and method on the removal effects of criteria (MEREC) techniques to address the relative advantages and disadvantages of these aspects in MCGDM. The aim of the study is to improve MCGDM technique which can capture the underlying uncertainties in robust way and can produce consistent results in a more rigorous way. Here, the conception of Hamming distance between two pentagonal neutrosophic number (PNN)s is introduced and the weighted arithmetic and geometric averaging operators in PNN arena are deployed to craft our computational technique more progressive and robust. An agriculture-based numerical problem is illustrated to demonstrate the ranking results of the alternatives by both of the techniques. After evaluating the problem by two aggregation operators, it is found that "plantation crop" is the best alternative under certain circumstances. Lastly, the sensitivity investigation is performed which reveals that with the appliance of arithmetic and geometric aggregation operators the best ranked alternative preserves its position by both of the ranking methods, which definitely exhibit the consistency and robustness of our executed methodology.

Selection of most effective COVID-19 virus protector using a novel MCGDM technique under linguistic generalised spherical fuzzy environment

In this article, we have introduced a new linguistic generalized spherical fuzzy set by combining the idea of generalized spherical fuzzy set and linguistic fuzzy set. Linguistic generalized spherical fuzzy set is described by linguistic positive, linguistic neutral and linguistic negative membership degrees with the condition that the square sum of its linguistic membership degrees is less than or equal to 3 which deal with the uncertain and imprecise information in decision making in a much more suitable way. We have discussed some basic operations of linguistic generalized spherical fuzzy sets and introduced new score and accuracy functions to compare any two linguistic generalized spherical fuzzy numbers. We have developed various types of aggregation operators based on the newly defined linguistic generalized spherical fuzzy set, which have been manifested to construct a new multi-criteria group decision-making technique. Numerical example has been presented to demonstrate the proposed model. Finally, sensitivity and comparative analysis is performed to show the reliability and efficiency of the new multi-criteria group decision-making technique.

A state-of-the-art survey on spherical fuzzy sets1

In addition to the well-known fuzzy sets, a novel type of fuzzy set called spherical fuzzy set (SFS) is recently introduced in the literature. SFS is the generalized structure over existing structures of fuzzy sets (intuitionistic fuzzy sets-IFS, Pythagorean fuzzy sets-PFS, and neutrosophic fuzzy sets-NFS) based on three dimensions (truth, falsehood, and indeterminacy) to provide a wider choice for decision-makers (DMs). Although the SFS has been introduced recently, the topic attracts the attention of academicians at a remarkable rate. This study is the expanded version of the authors’ earlier study by Ozceylan et al. [1]. A comprehensive literature review of recent and state-of-the-art papers is studied to draw a framework of the past and to shed light on future directions. Therefore, a systematic review methodology that contains bibliometric and descriptive analysis is followed in this study. 104 scientific papers including SFS in their titles, abstracts and keywords are reviewed. The papers are then analyzed and categorized based on titles, abstracts, and keywords to construct a useful foundation of past research. Finally, trends and gaps in the literature are identified to clarify and to suggest future research opportunities in the fuzzy logic area.

Neutrosophic ratio-type estimators for estimating the population mean

All researches, under classical statistics, are based on determinate, crisp data to estimate the mean of the population when auxiliary information is available. Such estimates often are biased. The goal is to find the best estimates for the unknown value of the population mean with minimum mean square error (MSE). The neutrosophic statistics, generalization of classical statistics tackles vague, indeterminate, uncertain information. Thus, for the first time under neutrosophic statistics, to overcome the issues of estimation of the population mean of neutrosophic data, we have developed the neutrosophic ratio-type estimators for estimating the mean of the finite population utilizing auxiliary information. The neutrosophic observation is of the form $${Z}_{N}={Z}_{L}+{Z}_{U}{I}_{N}\, {\rm where}\, {I}_{N}\in \left[{I}_{L}, {I}_{U}\right], {Z}_{N}\in [{Z}_{l}, {Z}_{u}]$$ Z N = Z L + Z U I N where I N ∈ I L , I U , Z N ∈ [ Z l , Z u ] . The proposed estimators are very helpful to compute results when dealing with ambiguous, vague, and neutrosophic-type data. The results of these estimators are not single-valued but provide an interval form in which our population parameter may have more chance to lie. It increases the efficiency of the estimators, since we have an estimated interval that contains the unknown value of the population mean provided a minimum MSE. The efficiency of the proposed neutrosophic ratio-type estimators is also discussed using neutrosophic data of temperature and also by using simulation. A comparison is also conducted to illustrate the usefulness of Neutrosophic Ratio-type estimators over the classical estimators.

Optimized Application of Sustainable Development Strategy in International Engineering Project Management

The aim of this paper is to establish an international framework for sustainable project management in engineering, to make up the lack of research in this field, and to propose a scientific theoretical basis for the establishment of a new project management system. The article adopts literature review, mathematical programming algorithm and case study as the research method. The literature review applied the visual clustering research method and analyzed the results of 21-year research in this field. As a result, the project management system was found to have defects and deficiencies. A mathematical model was established to analyze the composition and elements of the optimized international project management system. The case study research selected large bridges for analysis and verified the superiority and practicability of the theoretical system. Thus, the goal of sustainable development of bridges was achieved. The value of this re-search lies in establishing a comprehensive international project management system model; truly integrating sustainable development with project management; providing new research frames and management models to promote the sustainable development of the construction industry.

Corpus translation system based on Web Services and its application

In order to construct an efficient translation system, this paper constructs a corpus translation system based on Web Services. Moreover, this paper builds a network term detection system based on machine learning algorithms, expands the corpus data with the support of the crawler system, and uses WEB retrieval translation technology. At the same time, in response to the problem of sentence length changes in English abstracts, this paper proposes a method to obtain standard sentence length changes based on edit distance and SVM sorting. Based on requirements, this paper designs the architecture and data integration process of the data integration system. In addition, this paper outlines the detailed design and implementation process of each module of the system, and proposes a system performance optimization plan, and combines translation requirements to construct a corpus translation system based on Web Services. Finally, this paper designs experiments to verify the performance of the model. The research results show that the system constructed in this paper has a good application effect.

Research on political text metaphor translation system based on web data mining technology

In order to improve the translation effect of political text metaphors, based on Web data mining technology, this paper constructs a political text metaphor translation system based on Web data mining technology. Aiming at the two shortcomings of the selection of the initial center point of the K-Means algorithm and the isolated points, this paper gives a solution to the ICKM algorithm that combines the density parameter and the coordinate rotation algorithm. The algorithm uses the object with the largest density parameter as the first center point, and uses the KCR algorithm to find the next center point, which avoids the influence of isolated points on the data sample to a certain extent. The constructed political text metaphor translation system based on Web data mining technology needs to accurately translate political texts and also needs to meet the requirements of metaphor translation. Finally, this paper designs experiments to verify the system performance. The research results show that the system constructed in this paper can meet the needs of political text metaphor translation.

Ideological and political teaching information management based on artificial intelligence and data security model

In order to solve the security problems of the ideological and political teaching system itself, the ideological and political teaching information management technology needs to be further improved. According to actual needs, based on artificial intelligence and data security models, this paper studies and implements a network security information management system based on artificial intelligence and security models. The system can effectively manage the contents of safe work and increase the ability of information sharing and collaborative work. According to the actual needs of most current systems, with data mining, data recognition, and security management as the goals, this paper builds the structure of the functional modules and adopts the function cascade to finally realize the safety information management of this system. In addition, this article designs experiments to verify the performance of the model constructed in this article. The research results show that the model has good performance and meets actual needs.

Shanxi merchant economic history education system based on fuzzy control and quantum evolution algorithm

In order to improve the economic history education effect of Shanxi merchants, this paper combines fuzzy control and quantum evolution algorithm to construct Shanxi merchant economic history education system. The purpose of this paper to construct the Shanxi merchant economic history education system is to establish a learning platform on the Internet or local area network that allows students to learn outside the classroom. This system will consist of multiple sub-modules, and it will provide knowledge points and networks, problem sets, student assignments, teacher-student interaction links, and teaching resource management for Shanxi merchant economic history teaching. Moreover, this system will be designed as an open network-assisted teaching system. In addition, this paper designs experiments to verify the performance of the algorithm constructed in this paper. The research shows that the Shanxi merchant economic history education system based on fuzzy control and quantum evolution algorithm constructed in this paper performs well in data mining and also has good performance in practical education.

Studys on the laws of Gauss projection for area distortion

In the regions which has high altitude and is far from central meridian, Gauss projection has bigger area distortion and becomes main factors which influences the accuracy of area measurement. Through researching in detail the area distortion in the three respects that from ground to reference ellipsoid surface from reference ellipsoid surface to Gauss plane and from Gauss plane to compensating level surface, this paper finds the laws of Gauss projection for area distortion, and draws one computation model on 2000 coordinates system. This has contributed to restrict the influence of Gauss projection and choose suitable central meridian and compensating level surface.

Research on music teaching practice based on fuzzy intelligent interactive tablet

With the development of economy and the progress of science and technology, China, as a powerful country in science and technology and education, has been constantly improving the level of educational informatization and perfecting the basic teaching equipment, which has realized informatization and modernization to a certain extent. This research takes intelligent interactive tablet as interactive means and combines the theories of aesthetics, psychology, pedagogy and fuzzy teaching to research the appreciation, singing and creation aspects of music teaching practice. After three months of teaching practice, the students are evaluated and construct fuzzy cluster evaluation model, investigation and analysis and other methods, which verified that the fuzzy intelligent interactive tablet can provide rich content for music teaching, improve the teaching efficiency of students’ participation, and prove that the fuzzy intelligent interactive tablet has a great auxiliary effect on music teaching.

Fuzzy logic neural network based growth enterprise market analysis for registration-based IPO system

In real life, the stock price is always easy to be mispriced after listing, too high or too low. There are numerous reasons behind mispricing. Many scholars believe that the information asymmetry is one of them. In an inefficient market, the information asymmetry is bound to exist and be very high. In order to investigate the impact of registration-based IPO system reforms in mispricing, this paper takes the GEM market as an example to analyze the impact of the GEM market on mispricing. And we proposed a method with fuzzy logic neural network for Growth Enterprise Market analysis for IPO system. After processing data, we use ARIMA and EGARCH model to find the results. The immaturity will result in the negative impact caused by reformation, which will deviate from the goal that makes Chinese stock market become better.

Improved extended Gaussian image and its application on 3D point clouds registration

To solve the problem of lacking geometric and topological information for conventional 3D point clouds registration algorithm, this paper proposed a novel 3D point clouds registration algorithm based on improved extended Gaussian image. The proposed registration algorithm first estimates a normal vector and curvature of every point by least square method. Then, according to the normal vector to calculate extended Gaussian image (EGI) and complex extended Gaussian image (CEGI). By using the calculated EGI/CEGI and spherical harmonic function, a correlated function is constructed to calculate 3D rotation space to obtain initial positions coarse registration result. At last, by using the Fourier transform to estimate translation vector and coarse registration, the iterative closest point algorithm is used to obtain the fine registration results. Experiments on three groups of different 3D point clouds are performed to validate the proposed registration algorithm. Experimental results have shown that the proposed algorithm has good performances on registration of different forms of 3D point clouds. The robustness and efficiency of our proposed algorithm can effectively solve the problem that it is difficult to find the target or the homonymic feature points in the registration process of 3D point clouds.

The music psychology that uses fuzzy models to promote mental health

Through the analysis of design psychology, this paper first sorts out the development context of design psychology, and then elaborates the definition of design psychology. Moreover, this paper combines the actual demands of music psychology to construct a model, applies the fuzzy model to this model, and systematically studies the basic concepts of design psychology. Simultaneously, this paper combines its concept with examples of interface interaction design of mobile Internet product to study and observe the application of design psychology in this field. In addition, this paper summarizes a set of scientific and reasonable specific methods for interface interaction design, and then uses this method to guide the practice of system model interaction design, constructs the model structure based on demand analysis, and optimizes the system structure. Finally, this paper designs experiments to verify the performance of the model. The research results show that the model constructed in this paper has certain practical effects.

Hybrid fuzzy interface model of sports rehabilitation activities

At present, the relevant test data and training indicators of athletes during rehabilitation training lack screening and analysis, so it is impossible to establish a long-term longitudinal tracking research system and evaluation system. In order to improve the practical effect of sports rehabilitation activities, this paper successively introduces the matrix normal mixed model and the fuzzy clustering algorithm based on the K-L information entropy regularization and the matrix normal mixed model. Moreover, this paper uses the expectation maximization algorithm to estimate the parameters of the model, discusses the framework, key technologies and core services of the development platform, and conducts certain research on the related technologies of the three-tier architecture. At the same time, according to the actual needs of sports rehabilitation training, this paper designs the functions required for exercise detection and prescription formulation. In addition, this paper analyzes and designs the database structure involved in each subsystem. Finally, this paper designs experiments to verify the performance of the model constructed in this paper. The research results show that the performance of the model constructed in this paper meets the expectations of model construction, so it can be applied to practice.

Fuzzy processing system for psychological pressure of English teachers at work based on analysis of online teaching video

Due to the fast pace of modern online English teaching and the complicated teaching relationship, English teachers face increasing pressure in teaching work, which easily leads to various psychological problems. In view of this, based on theoretical results and expert experience in the field of psychological pressure of English teachers, this paper uses fuzzy processing systems and fuzzy weighted logic inference theory to establish a knowledge base in the field of psychological health and an evaluation model for psychological pressure of English teachers. Moreover, this paper carries out knowledge representation and reasoning on the knowledge of psychological health theory, and applies the evaluation reasoning model to the expert system of psychological health evaluation of English teachers to finally design and realize the expert system of psychological health evaluation of English teachers based on fuzzy weighted logic. Finally, this paper designs experiments to verify the system performance. The research results show that the system’s data processing speed and the accuracy of the evaluation results of psychological stress of English teachers meet the actual needs.

The system for relieving students’ boring emotion in English learning based on fuzzy neural network

The ability to perceive students’ emotions in real time is related to whether the description of the student’s state is accurate, and it is also related to whether the goal of achieving the students’ individual learning needs can be achieved. This paper studies the students’ boring emotion in English learning, and builds the recognition system of students’ boring emotion in English learning based on fuzzy neural network. Moreover, this paper combines the actual needs to construct the system function modules, and carries out the algorithm analysis and framework construction, and uses the mathematical modeling method to add the emotional factor to the English learner state modeling. In addition, according to the actual needs of the system constructed in this paper, the boring emotion of English learners is recognized. In addition, this paper designs experiments to verify the performance of the model, and analyze the system reliability from the theoretical perspective and the practical perspective. The experimental research results show that the model constructed in this paper meets the expected goals.

Research on the data analysis system of student stress in English MOOC based on fuzzy C-means algorithm

In order to improve the recognition accuracy of students’ psychological stress data in the English MOOC classroom teaching process, this paper improves the traditional fuzzy C-means algorithm, and uses the deviation value to represent the difference between the average algebraic distance of the neighborhood point and the center pixel. By calculating the deviation value, the influence of the neighborhood point on the center point can be measured, and the noise resistance of the algorithm can be improved. Moreover, this paper constructs a quantitative identification model of student stress data based on the needs of English MOOC teaching stress analysis, and uses image database to verify the basic performance of the algorithm, and constructs a data analysis system of student stress in English MOOC classroom, which is used in practice. In addition, this paper uses student facial expression recognition as a basis for quantitative identification of student stress, and designs experiments to analyze the reliability of the system. From the statistical results, it can be seen that the data analysis system of the students’ psychological stress in the English MOOC classroom teaching process constructed in this paper is effective.

Music psychology using fuzzy models to promote mental health

Music psychology can play an important role in the diagnosis and rehabilitation of mental health patients. Under the guidance of music psychology, this paper combines fuzzy models to process data, which effectively solves the problem that the number of categories in the fuzzy c-means algorithm needs to be manually given. The AFCC algorithm effectively combines the idea of semi-supervised clustering with the CA algorithm. Through two sets of must-link and cannot-link, this paper introduces the constraint penalty item into the objective function, which greatly improves the clustering accuracy. On this basis, this paper constructs a fuzzy model of psychological rehabilitation and diagnosis based on music psychology, designs experiments to verify the performance of this model, and conducts research results statistics from two aspects of diagnosis and rehabilitation. The research results show that the model constructed in this paper has certain practical effects.

Research on decision support system of sports assistant teaching and training based on association rules and support vector machine

In the decision-making system of sports assistant teaching and training, the performance of such system is not robust to different situations with a low accuracy. To solve the problems in the decision-making system, we proposed a decision-making method combining association rules and support vector machine (SVM) in this paper. First of all, we give a computer-aided decision support system for sports assistant learning and teaching training, which is fully elaborated from three aspects: virtual reality (VR) technology, VR based sports assistant learning and teaching and situational cognition, and VR based sports assistant learning and teaching mode. After that, the paper gives the feature extraction of sports auxiliary teaching training through association rules and the decision-making of the extracted association rules by SVM. We have done two different experiments for both association rules mining and SVM on both experiment group and control group of databases. Experimental results have shown that the training characteristics of sports auxiliary teaching very well. In the decision support of association rules, compared with the existing BP neural network, linear discriminant analysis and naive Bayes and other methods, the SVM method has better effect of action recognition in decision support system of sports assistant teaching and training. The robustness is the best for the application of SVM. We provide a new perspective for the decision support of sports auxiliary teaching training by using association rules and SVM. Through the method of this paper, we can obtain better decision-making effect and more robust process of sports auxiliary teaching and training.

Large-scale group decision-making based on Pythagorean linguistic preference relations using experts clustering and consensus measure with non-cooperative behavior analysis of clusters

To represent qualitative aspect of uncertainty and imprecise information, linguistic preference relation (LPR) is a powerful tool for experts expressing their opinions in group decision-making (GDM) according to linguistic variables (LVs). Since for an LV, it generally means that membership degree is one, and non-membership and hesitation degrees of the experts cannot be expressed. Pythagorean linguistic numbers/values (PLNs/PLVs) are novel choice to address this issue. The aim of this paper which we propose a GDM problem involved a large number of the experts is called large-scale GDM (LSGDM) based on Pythagorean linguistic preference relation (PLPR) with a consensus model. Sometimes, the experts do not modify their opinions to achieve consensus. Therefore, the experts’ proper opinions’ management with their non-cooperative behaviors (NCBs) is necessary to establish a consensus model. At the same time, it is essential to ensure the proper adjustment of the credibility information. The proposed model using grey clustering method is divided with the experts’ similar evaluations into a subgroup. Then, we aggregate the experts’ evaluations in each cluster. A cluster consensus index (CCI) and a group consensus index (GCI) are presented to measure consensus level among the clusters. Then, we provide a mechanism for managing the NCBs of the clusters, which contain two parts: (1) NCB degree is defined using CCI and GCI for identifying the NCBs of the clusters; (2) implemented the weight punishment mechanism of the NCBs clusters to consensus improvement. Finally, an example is offered for usefulness of the proposed approach.

Classification of trapezoidal bipolar neutrosophic number, de-bipolarization technique and its execution in cloud service-based MCGDM problem

Neutrosophic set can deal with the uncertainties related to the information of any decision making problem in real life scenarios, where fuzzy set may fail to handle those uncertainties properly. In this study, we present the perception of trapezoidal bipolar neutrosophic numbers and its classification in different frame. We introduce the idea of disjunctive structures of trapezoidal bipolar neutrosophic numbers namely type-1 trapezoidal bipolar neutrosophic number, type-2 trapezoidal bipolar neutrosophic numbers, and type-3 trapezoidal bipolar neutrosophic number based on the perception of dependency among membership functions in neutrosophic set. In any neutrosophic decision-making problem, the decision maker uses the comparison of neutrosophic numbers to choose among alternatives solutions. Here, we introduce a ranking method, i.e., De-bipolarization scheme for trapezoidal bipolar neutrosophic number (TrBNN) using removal area technique. We also describe the utility of trapezoidal bipolar neutrosophic number and its appliance in a multi criteria group decision making problem (MCGDM) for distinct users in trapezoidal bipolar arena which is more ethical, precise and reliable in neutrosophic field.

A new approach to evaluate linear programming problem in pentagonal neutrosophic environment

In this paper, authors disclose a new concept of pentagonal neutrosophic (PN) approach to solve linear programming (LP) problem. To best of our insight, there is no approach for solving PNLP problem. For the first time, we take up the PNLP problem where the objectives, constraints are considered as pentagonal neutrosophic numbers (PNN). To deign our algorithm, we described the PN arithmetic operation laws and mathematical computation in PNN environment. This proposed method is based on ranking function and convert to its equivalent crisp LP (CrLP) problem. The obtained CrLP issue is presently being tackled by any LP method which is effectively accessible. To legitimize the proposed technique, some numerical tests are given to show the adequacy of the new model.