Directional correlation coefficient measures for Pythagorean fuzzy sets: their applications to medical diagnosis and cluster analysis

Some complex probabilistic hesitant fuzzy aggregation operators and their applications to multi-attribute decision making

As a generalization of complex fuzzy set (CFS), complex hesitation fuzzy set (CHFS) is a powerful tool to express two-dimensional fuzzy information, but it ignores the randomness that exists widely in real life. Considering the randomness and ambiguity often simultaneously occur in real-world problems, we come up with an innovative fuzzy set called complex probabilistic hesitant fuzzy set (CPHFS) in this article, which is a joint extension of CFS and probabilistic hesitant fuzzy set (PHFS). Moreover, we establish four basic operations for complex probabilistic hesitant fuzzy element(CPHFE) and a series of useful operational laws are also developed. Secondly, several aggregation operators including complex probabilistic hesitant fuzzy weighted averaging operator(CPHFWA), complex probabilistic hesitant fuzzy weighted geometric operator(CPHFWG), complex probabilistic hesitant fuzzy Heronian Mean operator(CPHFHM) and complex probabilistic hesitant fuzzy Geometric Heronian Mean operator(CPHFGHM) as well as their weighted forms that can reflect the interrelationship among all decision attributes are proposed, which is of great use in multi-attribute decision making(MADM) or in multi-attribute group decision making(MAGDM) issues when we want to synthesize multiple evaluation values into one. Besides, we also present a number of valuable properties of these provided aggregation operators. Thirdly, a MADM process is built in the CPHF environment step by step based on the aggregation operators we have just established. Furthermore, we provide an example about purchasing a most suitable car to demonstrate the effectiveness and practicability of the proposed decision process. Finally, we point out the superiorities of MADM in working under the CPHF environment through comparing it with the existing method and also offer some possible prospects for further research. The method displayed in this work can effectively solve the MADM problems where the decision-making information is described by CPHFEs and the attributes are interactive.

Complex network-based multistep forecasting model for hyperchaotic time series

We present a method for predicting hyperchaotic time series using a complex network-based forecasting model. We first construct a network from a given time series, which serves as a coarse-grained representation of the underlying attractor. This network facilitates multistep forecasting by capturing the local nonlinearity of the dynamics and offers superior accuracy over more extended periods than traditional methods. The network is formed by converting the patterns of local oscillations into sequences of numerical symbols, which are then used to create nodes and edges in a network, capturing the system's dynamical behavior at a reduced resolution. The network allows predictions up to several steps ahead without the exponential error increase usually associated with linear first-order methods. The improved predictions result from the unique ability of the network to collect identical pattern transitions in the orbit dynamics into a system of neighborhoods in the network. The effectiveness of this approach is demonstrated through its application to several high-dimensional hyperchaotic systems, where it outperforms both the linear first-order and other network-based methods in terms of prediction accuracy and horizon. Besides enhancing the predictability of chaotic systems, this methodology also outlines a procedure to develop a discrete model flow within an attractor.

Utilizing aggregation operators based on q-rung orthopair neutrosophic soft sets and their applications in multi-attributes decision making problems

Neutrosophic sets provide greater versatility in dealing with a variety of uncertainties, including independent, partially independent, and entirely dependent scenarios, which q-ROF soft sets cannot handle. Indeterminacy, on the other hand, is ignored completely or partially by q-ROF soft sets. To address this issue, this study offers a unique novel concept as known as q-RONSS, which combines neutrosophic set with q-ROF soft set. This technique addresses vagueness using a set of truth, indeterminacy, and false membership degrees associated with the parametrization tool, with the condition that the sum of the qth power of the truth, indeterminacy, and false membership degrees be less than or equal to one. In addition, this study outlines operational laws for the suggested structure. The main purpose this article is to define some averaging and geometric operators based on the q-rung orthopair neutrosophic soft set. Furthermore, this article provides a step-by-step method and a mathematical model for the suggested techniques. To solve a MADM issue, this research article proposes a numerical example of people selection for a specific position in a real estate business based on a variety of criteria. Finally, to demonstrate the proposed model's superiority and authenticity, this article performs several analyses, including sensitivity analysis, to address the reliability and influence of various parameter "q" values on the alternatives and the ultimate ranking outcomes using the averaging and geometric operators. A comparison of the proposed operators to current operators demonstrates the validity of the proposed structure. Furthermore, a comparison of the proposed structure to current theories demonstrates its superiority by overcoming their limits and offering a more flexible and adaptable framework. Finally, this study reviews the findings and consequences of our research.

Three-way decisions in generalized intuitionistic fuzzy environments: survey and challenges

Enhancing decision-making under risks is crucial in various fields, and three-way decision (3WD) methods have been extensively utilized and proven to be effective in numerous scenarios. However, traditional methods may not be sufficient when addressing intricate decision-making scenarios characterized by uncertain and ambiguous information. In response to this challenge, the generalized intuitionistic fuzzy set (IFS) theory extends the conventional fuzzy set theory by introducing two pivotal concepts, i.e., membership degrees and non-membership degrees. These concepts offer a more comprehensive means of portraying the relationship between elements and fuzzy concepts, thereby boosting the ability to model complex problems. The generalized IFS theory brings about heightened flexibility and precision in problem-solving, allowing for a more thorough and accurate description of intricate phenomena. Consequently, the generalized IFS theory emerges as a more refined tool for articulating fuzzy phenomena. The paper offers a thorough review of the research advancements made in 3WD methods within the context of generalized intuitionistic fuzzy (IF) environments. First, the paper summarizes fundamental aspects of 3WD methods and the IFS theory. Second, the paper discusses the latest development trends, including the application of these methods in new fields and the development of new hybrid methods. Furthermore, the paper analyzes the strengths and weaknesses of research methods employed in recent years. While these methods have yielded impressive outcomes in decision-making, there are still some limitations and challenges that need to be addressed. Finally, the paper proposes key challenges and future research directions. Overall, the paper offers a comprehensive and insightful review of the latest research progress on 3WD methods in generalized IF environments, which can provide guidance for scholars and engineers in the intelligent decision-making field with situations characterized by various uncertainties.

An interval AQI combination prediction model based on multiple data decomposition and information aggregation operator

In this paper, an interval Air Quality Index (AQI) combination prediction model based on EEMD, VMD, and the weighted power average (WPA) operator is proposed. EEMD and VMD decompose complex AQI data effectively, while WPA operator reasonably aggregates the prediction results of different models. We validate the effectiveness of the proposed model using Shenzhen's daily interval AQI. Furthermore, three kinds of prediction models are compared with the proposed model to highlight its advantages from various perspectives. The results show that the introduction of data decomposition methods significantly improves the model's prediction accuracy, WPA operator further enhances the model's prediction capability, and the incorporation of EEMD and VMD enables the proposed model to have stronger feature extraction capabilities for complex time series. As a result, the model proposed in this paper demonstrates strong generalization ability and prediction accuracy, making it applicable not only for air quality prediction but also for other domains such as economics and environment.

Decision Support System for Prioritization of Offshore Wind Farm Site by Utilizing Picture Fuzzy Combined Compromise Solution Group Decision Method

The selection of offshore wind farm site (OWFS) has important strategic significance for vigorously developing offshore new energy and is deemed as a complicated uncertain multicriteria decision-making (MCDM) process. To further promote offshore wind power energy planning and provide decision support, this paper proposes a hybrid picture fuzzy (PF) combined compromise solution (CoCoSo) technique for prioritization of OWFSs. To begin with, a fresh PF similarity measure is proffered to estimate the importance of experts. Next, the novel operational rules for PF numbers based upon the generalized Dombi norms are defined, and four novel generalized Dombi operators are propounded. Afterward, the PF preference selection index (PSI) method and PF stepwise weights assessment ratio analysis (SWARA) model are propounded to identify the objective and subjective weight of criteria, separately. In addition, the enhanced CoCoSo method is proffered via the similarity measure and new operators for ranking OWFSs with PF information. Lastly, the applicability and feasibility of the propounded PF-PSI-SWARA-CoCoSo method are adopted to ascertain the optimal OWFS. The comparison and sensibility investigations are also carried out to validate the robustness and superiority of our methodology. Results manifest that the developed methodology can offer powerful decision support for departments and managers to evaluate and choose the satisfying OWFSs.

Subgroup analysis of scientific performance in the field of arthroplasty

Introduction

Arthroplasty is the final treatment option for maintaining mobility and quality of life in many primary degenerative and (post-) traumatic joint diseases. Identification of research output and potential deficits for specific subspecialties may be an important measure to achieve long-term improvement of patient care in this field.

Methods

Using specific search terms and Boolean operators, all studies published since 1945 to the subgroups of arthroplasty listed in the Web of Science Core Collection were included. All identified publications were analysed according to bibliometric standards, and comparative conclusions were drawn regarding the scientific merit of each subgroup.

Results

Most publications investigated the subgroups of septic surgery and materials followed by approach, navigation, aseptic loosening, robotic and enhanced recovery after surgery (ERAS). In the last 5 years, research in the fields of robotic and ERAS achieved the highest relative increase in publications In contrast, research on aseptic loosening has continued to lose interest over the last 5 years. Publications on robotics and materials received the most funding on average while those on aseptic loosening received the least. Most publications originated from USA, Germany, and England, except for research on ERAS in which Denmark stood out. Relatively, publications on aseptic loosening received the most citations, whereas the absolute scientific interest was highest for the topic infection.

Discussion

In this bibliometric subgroup analysis, the primary scientific outputs focused on septic complications and materials research in the field of arthroplasty. With decreasing publication output and the least financial support, intensification of research on aseptic loosening is urgently recommended.

Stochastic multiple attribute decision making with Pythagorean hesitant fuzzy set based on regret theory

The objective of this paper is to present an extended approach to address the stochastic multi-attribute decision-making problem. The novelty of this study is to consider the regret behavior of decision makers under a Pythagorean hesitant fuzzy environment. First, the group satisfaction degree of decision-making matrices is used to consider the different preferences of decision-makers. Second, the nonlinear programming model under different statues is provided to compute the weights of attributes. Then, based on the regret theory, a regret value matrix and a rejoice value matrix are constructed. Furthermore, the feasibility and superiority of the developed approach is proven by an illustrative example of selecting an air fighter. Eventually, a comparative analysis with other methods shows the advantages of the proposed methods.

Interval Type-II Fuzzy Fault-Tolerant Control for Constrained Uncertain 2-DOF Robotic Multi-Agent Systems with Active Fault Detection

This study proposed a novel adaptive interval Type-II fuzzy fault-tolerant control for constrained uncertain 2-DOF robotic multi-agent systems with an active fault-detection algorithm. This control method can realize the predefined-accuracy stability of multi-agent systems under input saturation constraint, complex actuator failure and high-order uncertainties. Firstly, a novel active fault-detection algorithm based on pulse-wave function was proposed to detect the failure time of multi-agent systems. To the best of our knowledge, this was the first time that an active fault-detection strategy had been used in multi-agent systems. Then, a switching strategy based on active fault detection was presented to design the active fault-tolerant control algorithm of the multi-agent system. In the end, based on the interval type-II fuzzy approximated system, a novel adaptive fuzzy fault-tolerant controller was proposed for multi-agent systems to deal with system uncertainties and redundant control inputs. Compared with other relevant fault-detection and fault-tolerant control methods, the proposed method can achieve predefinition of stable accuracy with smoother control input. The theoretical result was verified by simulation.

Combining SWOT analysis and neutrosophic cognitive maps for multi-criteria decision making: a case study of organic agriculture in India

The conventional agricultural system heavily depends on chemicals and inorganic fertilizers, which cause environmental issues. Organic agriculture impacts 6 of the 17 Sustainable Developmental Goals (SDGs) of the United Nations. Strategies to develop organic agriculture have used SWOT and MCDM techniques for analysis. However, the examination of the influence of one strategy over the other strategies has yet to be investigated. This paper proposes a model that combines the existing SWOT analysis with neutrosophic cognitive maps (NCM) models to analyze interconnections among the various strategies obtained from SWOT. This research deploys the proposed SWOT-NCM model to analyze the case study of developing organic farming in Tamil Nadu, India. It offers insights into the strategy's influence over other strategies so that the best is given maximum importance while implementing organic farming. The framework captures the interconnections and ranks the strategies by order of influence, providing fresh insights by taking the farmers' perspective while working with the strategies from the SWOT analysis to model an NCM. A comparative analysis of this SWOT-NCM model with other MCDM models that use SWOT to analyze the agriculture problem, and a sensitivity analysis of the proposed model, is performed. According to our study, the best possible strategy to encourage organic farming is minimum support price (MSP) and centralized procurement. This proposed model can analyze other MCDM problems that use SWOT analysis.

The Impact of the Implementation of International Law on Marine Environmental Protection on International Public Health Driven by Multi-Source Network Comment Mining

With the increase of people's living space, global warming caused by the decrease of greening urban spaces and the serious decline of greenspace quality has led to extreme weather events and coastal erosion, which has become the biggest threat to the ocean and has also led to the occurrence of international public safety incidents. Therefore, it is of great practical significance to explore the tense relationship between the current marine environmental protection and global public safety for the development of an international healthy community. Firstly, this paper discusses the influence of implementing the international law of marine environmental protection on global public health after the reduction of green urban space and the decline of green space quality. Secondly, K-means and discrete particle swarm optimization algorithms are introduced and the particle swarm optimization-K-means clustering (PSO-K-means) algorithm is designed to screen and deal with the mapping relationship between latent variables and word sets about the impact of implementing the international marine ecological protection law on the international public health community in network data information. Moreover, the influencing factors are clustered and the scenarios are evaluated. The results show that the clustering analysis of the marine environment can promote the clustering of marine characteristic words. Meanwhile, the PSO-K-means algorithm can effectively cluster vulnerability data information. When the threshold is 0.45, the estimated recall rate of the corresponding model is 88.75%. Therefore, the following measures have been formulated, that is, increasing greening urban spaces and enhancing the quality of green space to enhance the protection of marine environment, which has practical reference value for realizing the protection of marine environment and the sustainable development of marine water resources and land resources.

Research trends in the field of the gut-brain interaction: Functional dyspepsia in the spotlight – An integrated bibliometric and science mapping approach

Objectives

This study aims to perform a bibliometric analysis of functional dyspepsia (FD), which includes visualizing bibliographic information, in order to identify prevailing study themes, topics of interest, contributing journals, countries, institutions, and authors as well as co-citation patterns.

Methods

The Web of Science™ Core Collection Database was used to retrieve all peer-reviewed scientific publications related to FD research. The validated search terms were entered into the “title” and “author keywords” fields, and the results were sorted by publication year from 2006 to 2022. There were no restrictions on language. On 12 February 2023, a manual export of the complete metadata for each original publication and review article was performed. CiteSpace was used to reveal co-authorship, publication, and co-citation patterns to find prominent authors, organizations, countries, and journals in FD research as well as to identify author keywords with strong citation bursts, which could indicate an emerging research area. VOSviewer was used to build the co-occurrence indicator (co-word) to identify the main author keywords on which previous studies focused and to induce clustered scientific landscape for two consecutive periods to identify intriguing areas for future research.

Results

A search of the database retrieved 2,957 documents. There was a wave-like pattern in the number of publications until 2017, after which there was a spike in publication volume. The USA, China, and Japan provided the majority of contributions. In terms of institution, Mayo Clin, Univ Newcastle, and Katholieke Univ Leuven were found to be the prolific institutions. Additionally, the results indicate that eastern Asian researchers contributed significantly to the global knowledge of literature that led other countries; however, Canada, the USA, Australia, England, and Germany were found to have the highest degree of betweenness centrality. Nicholas J. Talley, Jan Tack, Gerald Holtmann, Michael Camilleri, Ken Haruma, and Paul Moayyedi occupied the top positions based on productivity and centrality indicators. Six thematic clusters emerged (Helicobacter pylori infection; pathophysiological mechanisms of FD; extraintestinal co-morbidities and overlap syndromes associated with FD; herbal medicine in FD; diabetic gastroparesis; and dietary factors in FD). “Acupuncture,” “duodenal eosinophilia,” “gut microbiota,” and others were among the author keywords with rising prevalence.

Conclusion

In FD research, eastern Asian countries have established themselves as major contributors with the highest publishing productivity; however, research has primarily been driven by North America, Europe, and Australia, where cooperation is generally more active and highly influential scientific results are produced. Our analysis suggests that increased investments, training of human resources, improved infrastructures, and expanded collaborations are essential to improving the quality of FD research in Asia. The emerging author keyword analysis suggests that eosinophil-mast cell axis, gut microbiota, mental disorders, and acupuncture are the key areas that attract researchers’ attention as future research boulevards. There is a highly skewed distribution of research output across Asia, with most focus on complementary and alternative medicine (CAM) coming from Chinese, Japanese, and South Korean centers. However, CAM remains an underexplored area of research in the context of FD, and it deserves greater research efforts in order to obtain quality scientific evidence. Furthermore, we propose that the research framework of CAM should not be limited to dysmotility; rather, it could be interpreted within a more holistic context that includes the brain-gut-microbiota axis, as well as novel concepts such as duodenitis, increased mucosal permeability, and infiltration and activation of eosinophils and mast cells, among others. Overall, we provided bibliometrics-based overviews of relevant literature to researchers from different backgrounds and healthcare professionals to provide an in-depth overview of major trends in FD research.

Carbon neutrality: a comprehensive bibliometric analysis

In recent years, excessive emissions of carbon dioxide have further intensified global warming, which poses a great threat to human society. The best way to reverse this situation is to take action to equalize the "carbon emissions" with the "carbon absorption," i.e., carbon neutrality (CN). To better understand the evolution and display a broad panorama of CN research, this paper provides a comprehensive bibliometric analysis of publications in the field of CN from 2006 to 2021. We use the Web of Science Core Collection as the data source, and a total of 633 publications have been retrieved. In the paper, we measure the productivity and influence of publications through recognized bibliometric metrics, and visually analyze publications using VOS Viewer and CiteSpace. The analysis results show that China is the most productive country/region. The study illustrates that in order to reach the goal of CN, it is necessary to reduce carbon emissions such as full using renewable energy. Simultaneously, it is also essential to enhance the "negative emissions" of carbon such as taking advantage of carbon sink and carbon capture, utilization, and storage. This paper provides some references for scholars who are interested or research in this field.

A hybrid decision support system with golden cut and bipolar q-ROFSs for evaluating the risk-based strategic priorities of fintech lending for clean energy projects

In the last decade, the risk evaluation and the investment decision are among the most prominent issues of efficient project management. Especially, the innovative financial sources could have some specific risk appetite due to the increasing return of investment. Hence, it is important to uncover the risk factors of fintech investments and investigate the possible impacts with an integrated approach to the strategic priorities of fintech lending. Accordingly, this study aims to analyze a unique risk set and the strategic priorities of fintech lending for clean energy projects. The most important contributions to the literature can be listed as to construct an impact-direction map of risk-based strategic priorities for fintech lending in clean energy projects and to measure the possible influences by using a hybrid decision making system with golden cut and bipolar q-rung orthopair fuzzy sets. The extension of multi stepwise weight assessment ratio analysis (M-SWARA) is applied for weighting the risk factors of fintech lending. The extension of elimination and choice translating reality (ELECTRE) is employed for constructing and ranking the risk-based strategic priorities for clean energy projects. In this process, data is obtained with the evaluation of three different decision makers. The main superiority of the proposed model by comparing with the previous models in the literature is that significant improvements are made to the classical SWARA method so that a new technique is created with the name of M-SWARA. Hence, the causality analysis between the criteria can also be performed in this proposed model. The findings demonstrate that security is the most critical risk factor for fintech lending system. Moreover, volume is found as the most critical risk-based strategy for fintech lending. In this context, fintech companies need to take some precautions to effectively manage the security risk. For this purpose, the main risks to information technologies need to be clearly identified. Next, control steps should be put for these risks to be managed properly. Furthermore, it has been determined that the most appropriate strategy to increase the success of the fintech lending system is to increase the number of financiers integrated into the system. Within this framework, the platform should be secure and profitable to persuade financiers.

Interval-valued Pythagorean fuzzy multi-criteria decision-making method based on the set pair analysis theory and Choquet integral

This paper proposes a novel fuzzy multi-criteria decision-making method based on an improved score function of connection numbers and Choquet integral under interval-valued Pythagorean fuzzy environment. To do so, we first introduce a method to convert interval-valued Pythagorean fuzzy numbers into connection numbers based on the set pair analysis theory. Then an improved score function of connection numbers is proposed to make the ranking order of connection numbers more in line with reality in multi-criteria decision-making process. In addition, some properties of the proposed score function of connection numbers and some examples have been given to illustrate the advantages of conversion method proposed in the paper. Then, considering interactions among different criteria, we propose a fuzzy multi-criteria decision-making approach based on set pair analysis and Choquet integral under interval-valued Pythagorean fuzzy environment. Finally, a case of online learning satisfaction survey and a brief comparative analysis with other existing approaches are studied to show that the proposed method is simple,convenient and easy to implement. Comparing with previous studies, the method in this paper, from a new perspective, effectively deals with multi-criteria decision-making problems that the alternatives cannot be reasonably ranked in the decision-making process under interval-valued Pythagorean fuzzy environment.

Investment decision making in the fuzzy context: An integrated model approach

With the implementation and steady progress of the Belt and Road (B&R) initiative, China’s investment in countries along the B&R has maintained a high growth trend. Generally speaking, investment problems are often accompanied by high risk and uncertainty, and how to make the suitable investment decision is a difficult issue. This paper investigates an investment decision approach under the probabilistic hesitant fuzzy environment. Firstly, a new probabilistic hesitant fuzzy distance and correlation coefficient are defined to overcome the defects of the existing probabilistic hesitant fuzzy information measures. Secondly, an attribute weight integrated model is constructed by combining the maximum deviation method, the CRITIC method and the maximum entropy principle, which is able to take into account the correlation between attributes and make full use of the decision information. In addition, a disappointment theory-based probabilistic hesitant fuzzy multi-attribute decision making (PHFMADM) method is proposed to solve the investment decision problem, which can integrate the psychological behavior of decision makers into the decision making process and make the decision results more authentic and reliable. Finally, the rationality and validity of the method are verified by comparing with the existing methods.

Classification of user queries according to a hierarchical medical procedure encoding system using an ensemble classifier

The Swiss classification of surgical interventions (CHOP) has to be used in daily practice by physicians to classify clinical procedures. Its purpose is to encode the delivered healthcare services for the sake of quality assurance and billing. For encoding a procedure, a code of a maximal of 6-digits has to be selected from the classification system, which is currently realized by a rule-based system composed of encoding experts and a manual search in the CHOP catalog. In this paper, we will investigate the possibility of automatic CHOP code generation based on a short query to enable automatic support of manual classification. The wide and deep hierarchy of CHOP and the differences between text used in queries and catalog descriptions are two apparent obstacles for training and deploying a learning-based algorithm. Because of these challenges, there is a need for an appropriate classification approach. We evaluate different strategies (multi-class non-terminal and per-node classifications) with different configurations so that a flexible modular solution with high accuracy and efficiency can be provided. The results clearly show that the per-node binary classification outperforms the non-terminal multi-class classification with an F1-micro measure between 92.6 and 94%. The hierarchical prediction based on per-node binary classifiers achieved a high exact match by the single code assignment on the 5-fold cross-validation. In conclusion, the hierarchical context from the CHOP encoding can be employed by both classifier training and representation learning. The hierarchical features have all shown improvement in the classification performances under different configurations, respectively: the stacked autoencoder and training examples aggregation using true path rules as well as the unified vocabulary space have largely increased the utility of hierarchical features. Additionally, the threshold adaption through Bayesian aggregation has largely increased the vertical reachability of the per node classification. All the trainable nodes can be triggered after the threshold adaption, while the F1 measures at code levels 3–6 have been increased from 6 to 89% after the threshold adaption.

Interaction hamy mean operators for complex pythagorean fuzzy information and their applications to security threats in computers

Complex Pythagorean fuzzy set (CPFS) is a massive influential principle for managing ambiguity and inconsistent information in genuine life dilemmas. To determine the relationship among any number of attributes, the Hamy mean (HM) operators based on interaction operational laws are very dominant and massive flexible to manage awkward and problematic information. This study aims to combine the complex Pythagorean fuzzy (CPF) information with interaction HM operators to initiate the CPF interaction HM (CPFIHM) operator, CPF interaction weighted HM (CPFIWHM) operator, CPF interaction dual HM (CPFIDHM) operator, CPF interaction weighted dual HM (CPFIWDHM) operator and their powerful properties. Additionally, a decision-making strategy for determining the security threats in the computer is elaborated under the interaction of HM operators based on the CPF setting. Numerous examples are illustrated with the help of presented operators to determine the consistency and flexibility of the investigated operators. Finally, with the help of sensitivity analysis, advantages, and geometrical representation, the supremacy, and efficiency of the presented works are also elaborated.

Primary node election based on probabilistic linguistic term set with confidence interval in the PBFT consensus mechanism for blockchain

This study proposes a primary node election method based on probabilistic linguistic term set (PLTS) for the practical Byzantine fault tolerance (PBFT) consensus mechanism to effectively enhance the efficiency of reaching consensus. Specifically, a novel concept of the probabilistic linguistic term set with a confidence interval (PLTS-CI) is presented to express the uncertain complex voting information of nodes during primary node election. Then, a novel score function based on the exponential semantic value and confidence approximation value for the PLTS-CI, called Score-ESCA, is used to solve the problems of comparing different nodes with various voting attitudes. This method helps select the node with the highest score by utilizing complex decision attitudes, making it an accurate primary node election solution. Furthermore, the feasibility of our proposed method is proved by both theoretical analysis and experimental evaluations.

An algorithm for identifying reference signals under the environment of complex fuzzy sets

 In this paper, we have discussed some new operations and results of set theory for complex fuzzy sets (CFSs). Moreover, we developed the basic results of CFSs under the basic operations such as complex fuzzy simple difference, bounded sum, bounded difference, dot product, bounded product, union, intersection, and Cartesian product. We explored the CFSs and discussed the related properties with examples such as complex fuzzy bounded sum over the intersection, complex fuzzy dot product over the union, etc. Identifying the reference signals under the environment of CFSs have always been a challenging. Many algorithms based on set theoretic operations and distance measures have been proposed for identifying a reference signal using any common system. But linear time invariant (LTI) system is considered easy to analyze the linear and time-varying signals. We used CFSs in signals and systems. We developed an algorithm based on convolution product and LTI system under the complex fuzzy environment. We identified a high degree of resemblance (reference signal) of the received signals to the reference signal in a linear time-invariant (LTI) system that receives an input signal and produces an output signal.

A new group decision making approach based on incomplete probabilistic dual hesitant fuzzy preference relations

As an enhanced version of probabilistic hesitant fuzzy sets and dual hesitant fuzzy sets, probabilistic dual hesitant fuzzy sets (PDHFSs) combine probabilistic information with the membership degree and non-membership degree, which can describe decision making information more reasonably and comprehensively. Based on PDHFSs, this paper investigates the approach to group decision making (GDM) based on incomplete probabilistic dual hesitant fuzzy preference relations (PDHFPRs). First, the definitions of order consistency and multiplicative consistency of PDHFPRs are given. Then, for the problem that decision makers (DMs) cannot provide the reasonable associated probabilities of probabilistic dual hesitant fuzzy elements (PDHFEs), the calculation method of the associated probability is given by using an optimal programming model. Furthermore, the consistency level for PDHFPRs is tested according to the weighted consistency index defined by the risk attitude of DMs. In addition, a convergent iterative algorithm is proposed to enhance the unacceptable consistent PDHFPRs’ consistency level. Finally, a GDM approach with incomplete PDHFPRs is established to obtain the ranking of the alternatives. The availability and rationality of the proposed decision making approach are demonstrated by analyzing the impact factors of haze weather.

Multi-criteria Optimization Technique with Complex Pythagorean Fuzzy N-soft Information

The main objective of this article is to lay the foundations of a novel multi-criteria optimization technique, namely, the complex Pythagorean fuzzy N-soft VIKOR (CPFNS-VIKOR) method that is highly proficient to express a great deal of linguistic imprecision and vagueness inherent in human assessments. This strategy provides a versatile decision-making tool for the ranking-based fuzzy modeling of two-dimensional parameterized data. The CPFNS-VIKOR method integrates the ground-breaking specialities of the VIKOR method with the outstanding parametric structure of the complex Pythagorean fuzzy N-soft model. It is exclusively designed for the specification of a compromise optimal solution having maximum group utility and minimum individual regret of the opponent by analyzing their weighted proximity from ideal solutions. The developed strategy factually permits specific linguistic terms to demystify the individual perspectives of the decision-making experts regarding the efficacy of the alternatives and the priorities of the applicable criteria. We comprehensively assemble these independent appraisals of all the experts using the complex Pythagorean fuzzy N-soft weighted averaging operator. Moreover, we calibrate the ranking measure by utilizing group utility measure and regret measure in order to specify the hierarchical outranking of the feasible alternatives. We demonstrate the systematic methodology and framework of the proposed method with the assistance of an explicative flow chart. We skilfully investigate an empirical analysis related to selection of constructive industrial robots for the modernization of a manufacturing industry which really justifies the remarkable accountability of the proposed strategy. Furthermore, we validate this technique by a comparative study with the existing complex Pythagorean fuzzy TOPSIS (CPF-TOPSIS) method, complex Pythagorean fuzzy VIKOR (CPF-VIKOR) method and Pythagorean fuzzy TOPSIS (PF-TOPSIS) method. The comparative study is exemplified with an illustrative bar chart that visually endorses the rationality of the proposed methodology by interpreting highly compatible and accurate final outcomes. Finally, we holistically analyze the functionality of the developed strategy to enlighten its merits and prominence over other available competent approaches.

A Theil coefficient-based combination prediction method with interval heterogeneous information for wind energy prediction

This paper constructs the continuous-Young optimal weighted arithmetic averaging (C-YOWA) operator and the continuous-Young optimal weighted geometric (C-YOWG) operator based on definite integral and Young inequality. A series of special cases and main properties of the proposed aggregation operators are also investigated. In order to integrate heterogeneous interval data and obtain more accurate prediction results, the heterogeneous interval combination prediction (HICP) model based on C-YOWA operator, C-YOWG operator and Theil coefficient is proposed. The HICP model consider not only the existence of both additive and multiplicative interval information, but also the preference information of experts. Finally, the model is applied to the empirical analysis of wind energy prediction. The comparison of results shows that the established model can effectively improve the accuracy of prediction.

Pythagorean fuzzy full implication multiple I method and corresponding applications

The overwhelming majority of existing decision-making methods combined with the Pythagorean fuzzy set (PFS) are based on aggregation operators, and their logical foundation is imperfect. Therefore, we attempt to establish two decision-making methods based on the Pythagorean fuzzy multiple I method. This paper is devoted to the discussion of the full implication multiple I method based on the PFS. We first propose the concepts of Pythagorean t-norm, Pythagorean t-conorm, residual Pythagorean fuzzy implication operator (RPFIO), Pythagorean fuzzy biresiduum, and the degree of similarity between PFSs based on the Pythagorean fuzzy biresiduum. In addition, the full implication multiple I method for Pythagorean fuzzy modus ponens (PFMP) is established, and the reversibility and continuity properties of the full implication multiple I method of PFMP are analyzed. Finally, a practical problem is discussed to demonstrate the effectiveness of the Pythagorean fuzzy full implication multiple I method in a decision-making problem. The advantages of the new method over existing methods are also explained. Overall, the proposed methods are based on logical reasoning, so they can more accurately and completely express decision information.

Quality evaluation of online courses during COVID-19 pandemic based on integrated FCE-AHP method

After sudden outbreak of COVID-19 pandemic, the university campuses were closed and millions of university teachers and students had to shift teaching and learning activities from the classrooms to online courses in China. The COVID-19 pandemic undoubtedly brought significant negative effects to university education activities. How does COVID-19 influenced teaching quality and the degree of influences have been studied by many researches. However, the online course quality which is influences by COVID-19 pandemic was commonly evaluated qualitatively rather than quantitatively. In order to obtain quantitative evaluation results of online course quality during the pandemic period, the integrated FCE-AHP evaluation was applied. Based on real case of online courses, the influence factors of online course quality were divided into four first-level indicators and further subdivided into 14 second level indicators. The weight vectors of evaluation indicators were determined based on experts’ comments from the Teaching Affairs Committee and the fuzzy evaluation memberships were calculated based on questionnaire results of 2021 students. The evaluation results revealed that the integral performance of online courses is acceptable and the performances of students and hardware are relative weaker. Finally, some improvement measures were conducted to deal with difficulties encountered in online courses during COVID-19 pandemic period.

Consistency Fuzzy Sets and a Cosine Similarity Measure in Fuzzy Multiset Setting and Application to Medical Diagnosis

The main purpose of this study is to construct a base for a new fuzzy set concept that is called consistency fuzzy set (CFS) which expresses the multidimensional uncertain data quite successfully. Our motive is to reduce the complexity and difficulty caused by the information contained in the truth sequence in a fuzzy multiset (FMS) and to present the data of the truth sequence in a more understandable and compact manner. Therefore, this paper introduces the concept of CFS that is characterized with a truth function defined on a universal set ${\left[\mathrm{0,1}\right]}^2$ . The first component of the truth pair of a CFS is the average value of the truth sequence of a FMS and the second component is the consistency degree, that is, the fuzzy complement of the standard deviation of the truth sequence of the same FMS. The main contribution of a CFS is the reflection of both the level of the average of the data that can be expressed with the different sequence lengths and the degree of the reasonable information in data via consistency degree. To develop this new concept, this paper also presents a correlation coefficient and a cosine similarity measure between CFSs. Furthermore, the proposed correlation coefficient and cosine similarity measure are applied to a multiperiod medical diagnosis problem. Finally, a comparison analysis is given between the obtained results and the existing results in literature to show the efficiency and rationality of the proposed correlation coefficient and cosine similarity measure.