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In the fuzzy theory of sets and groups, the use of α-levels is a standard to translate problems from the fuzzy to the crisp framework. Using strong α-levels, it is possible to establish a one to one correspondence which makes possible doubly, a gradual and a functorial treatment of the fuzzy theory. The main result of this paper is to identify the class of fuzzy sets, respectively, fuzzy groups, with subcategories of the functorial categories Set (0, 1], resp., Gr (0, 1]. In this line, the algebraic potential of this theory will be reached, in forthcoming papers. [ABSTRACT FROM AUTHOR]

New mathematical theories are being increasingly valued due to their versatility in the application of intelligent systems that allow decision-making and diagnosis in different real-world situations. This is especially relevant in the field of health sciences, where these theories have great potential to design effective solutions that improve people's quality of life. In recent years, several prediction studies have been performed as indicators of vocal dysfunction. However, the rapid increase in new prediction studies as a result of advancing medical technology has dictated the need to develop reliable methods for the extraction of clinically meaningful knowledge, where complex and nonlinear interactions between these markers naturally exist. There is a growing need to focus the analysis not only on knowledge extraction but also on data transformation and treatment to enhance the quality of healthcare delivery. Mathematical tools such as fuzzy set theory and soft set theory have been successfully applied for data analysis in many real-life problems where there is presence of vagueness and uncertainty in the data. These theories contribute to improving data interpretability and dealing with the inherent uncertainty of real-world data, facilitating the decision-making process based on the available information. In this paper, we use soft set theory and fuzzy set theory to develop a prediction system based on knowledge from phonoaudiology. We use information such as patient age, fundamental frequency, and perturbation index to estimate the risk of voice loss in patients. Our goal is to help the speech-language pathologist in determining whether or not the patient requires intervention in the presence of a voice at risk or an altered voice result, taking into account that excessive and inappropriate voice behavior can result in organic manifestations. [ABSTRACT FROM AUTHOR]

A multisensor alliance is established by the activation of tasks or occurrences. It is also characterized as a multisensor dynamic alliance since it originates with mission development and disintegrates with task accomplishment. To overcome the constraint that a single sensor can only gather a one-sided, little amount of erroneous target information, each sensor in the dynamic alliance has diverse information collection capabilities and implements a cooperative methodology to complete the target mission. This paper emphasizes on alliance formation in multisensor dynamic alliance control under diverse missions. To begin with, we investigate the problem at the sensor recognition level for each target feature, delving into the concepts of alliance formation, renewal, and dissolution and emphasizing the fuzzy relationship in the multisensor dynamic alliance for multitarget. Moreover, dynamic alliance models are constructed using the fuzzy set calculation algorithm, which is powered by target detection, recognition, and tracking tasks in that sequence. Last but not least, simulation experiments demonstrated that the proposed model and algorithm outperform the existing models and algorithms. We may achieve the optimal alliance scheme by introducing the fuzzy set calculation algorithm into the dynamic alliance establishment process, which completely nullifies information redundancy and enhances the monitoring capabilities of the sensor network. [ABSTRACT FROM AUTHOR]

Architecture is one of the key and important parts of a city. Various kinds of buildings have absolute control over the quantity and area and are the key factors for the appearance of a city. With the development of cities and the increase of population, high-rise residential buildings can effectively alleviate the shortage of urban residential land, but at the same time, it also brings some problems, such as monotonous elevation of high-rise residential buildings, improper selection of elevation forms. As people's aesthetic awareness is getting higher and higher, people's requirements for the image of residential buildings are getting higher and higher. However, the research on the elevation design of high-rise residential buildings is relatively lagging behind. Therefore, it is necessary to enrich and expand the elevation design of high-rise residential buildings. Image binarization is an important technology in image preprocessing. It plays an important role in pattern recognition, optical character recognition, and medical imaging. Binary image is a simple image format. It has only two gray levels, but it occupies an important position in the field of image processing. In specific image processing application systems, it is often necessary to obtain binary values. The binary image processing arithmetic is developed from set theory under mathematical morphology. Although its basic arithmetic is simple, it can produce complex results. Based on the characteristics of binary image and the complex effect it produces, this paper finds out its regularity, finds a design method of building elevation, and realizes the application of binary image in building elevation design. [ABSTRACT FROM AUTHOR]

The construction of credit evaluation index system of Chinese family farm and pasture is not only a theoretical problem but also of great practical significance. In this paper, based on the depth-weighted Bayesian theory and fuzzy mathematics, the improved depth-weighted fuzzy Bayesian hybrid algorithm model is proposed to solve the unbalanced problem of default status of family farm and pasture and to build the index system with the ability of three categories of default identification. In this paper, the characteristics of the first one is based on fuzzy set theory, the definition of fuzzy linguistic assessment of different default set, family ranches characteristic is converted to the corresponding index of pasting with triangular fuzzy mathematical model, and then through the inner method converting triangular fuzzy number into accurate output data to deal with the blur and uncertainty about the state of the fuzzy default transformation is realized. Second, based on the insensitive characteristic of ROC curve to skewness samples, the depth weighting of characteristic indexes in nondefault, low default and high-default states was completed by constructing multiclassification ROC curve, which solved the practical problem of sample imbalance in different default states of family farms and ranches, and selected the index system with significant discrimination ability for default states by integrating default identification ability. [ABSTRACT FROM AUTHOR]

Edge detection consists of a set of mathematical methods which identifies the points in a digital image where image brightness changes sharply. In the traditional edge detection methods such as the first-order derivative filters, it is easy to lose image information details and the second-order derivative filters are more sensitive to noise. To overcome these problems, the methods based on the fractional differential-order filters have been proposed in the literature. This paper presents the construction and implementation of the Prewitt fractional differential filter in the Asumu definition sense for SARS-COV2 image edge detection. The experiments show that these filters can avoid noise and detect rich edge details. The experimental comparison show that the proposed method outperforms some edge detection methods. In the next paper, we are planning to improve and combine the proposed filters with artificial intelligence algorithm in order to program a training system for SARS-COV2 image classification with the aim of having a supplemental medical diagnostic. [ABSTRACT FROM AUTHOR]

The study of engineering geology emphasizes the combination of theory and practice, and it highlights the comprehensive cultivation of curricular theory, curricular practice, and comprehensive skills. It is necessary to establish a set of effective methods to evaluate the achievement of training objectives to track, test, and improve the quality of curricular learning. In this paper, the principle of the fuzzy analytic hierarchy process based on entropy is used to construct an evaluation index system for the goal achievement degree of engineering geology courses, and the primary indicators mainly include knowledge, ability, and quality. Based on the actual situation, five curricular achievement levels are determined, that is, the comment set V = {very low, low, medium, high, very high}. Relying on the engineering geology course resource database of Xuchang University, the course goal achievement degree is evaluated, and the results show that the engineering geology course achievement degree is high. This method is suitable not only for the evaluation of the achievement of curricular objectives but also for the evaluation of the achievement of engineering education graduation requirements. This method can also help us find different courses and teaching weak links supporting the index points, indicate the direction and provide support for teachers to continuously improve their teaching and management methods, and effectively promote a continuous improvement in teachers' teaching level and teaching quality. [ABSTRACT FROM AUTHOR]

In this paper, we generalize the concept of interval‐valued bipolar fuzzy sets (IVBFSs) and define interval‐valued bipolar fuzzy subsemigroups (IVBF‐subsemigroup) and interval‐valued bipolar fuzzy left (right, two‐sided) ideals (IVBF‐left [right, two‐sided] ideals) over semigroups, which is a generalization of the concept of an bipolar valued fuzzy set (BVFS) in a semigroup. The purpose of this paper is to deal with the algebraic structure of semigroups by applying IVBFS theory. We give characterizations of different classes of (intra‐regular, left [right] regular, regular, semisimple) semigroups by the properties of their IVBF‐ideals. We also characterize these classes in terms of IVBF‐left ideals, IVBF‐right ideals, and IVBF‐two‐sided ideals. In this respect, we prove that a semigroup is regular if and only if for every IVBF‐right ideal A˜=μAP˜,μAN˜ and every IVBF‐left ideal B˜=μBP˜,μBN˜ over S, we have A˜∩B˜=A˜⊙B˜. Further, we characterize intra‐regular and regular semigroups and prove that a semigroup is intra‐regular and regular if and only if for every IVBF‐left ideal A˜=μAP˜,μAN˜ and every IVBF‐right ideal B˜=μBP˜,μBN˜ over S we have A˜∩B˜≼A˜⊙B˜. [ABSTRACT FROM AUTHOR]

In wireless networks, a change in network state is unpredictable because of the movement of network nodes, which is not conducive to the stability of the network and poses an especially serious challenge to network routing technology. To adapt to the flexibility of business, consider the impact of environmental changes on the bottom layer of a network, and improve the utilization of network resources, this paper proposes a multipath routing decision strategy restricted by multiple QoS attributes based on an intuitionistic fuzzy set of entropy weights. Cross-layer technology is applied to minimally meet the QoS needs based on multipath routing to discover and maintain multiple transmission paths. Moreover, intuitionistic fuzzy set theory is utilized to reflect the performance indexes of these multiple paths through fuzzy normalization to create a multiparameter multipath routing decision matrix. The weight of each parameter is objectively computed according to information entropy theory. The performance ranking of the multiple paths is determined with the TOPSIS method. As reflected by the results, the TOPSIS decision method based on an intuitionistic fuzzy set of entropy weights effectively solves the optimization problem for multiple paths in mobile ad hoc networks restricted by multiple parameters, and the resulting network is suitable for sensitive network applications involving multiple businesses in mobile environments. According to the simulation results, the proposed routing scheme reduces average network delay by 17% and routing overhead by 21% when compared to the current routing protocols. [ABSTRACT FROM AUTHOR]

This paper investigates the algebraic formulation and stability analysis for a class of Markov jump networked evolutionary games by using the semitensor product method and presents a number of new results. Firstly, a proper algorithm is constructed to convert the given networked evolutionary games into an algebraic expression. Secondly, based on the algebraic expression, the stability of the given game is analyzed and an equivalent criterion is given. Finally, an example works out to support the new results. [ABSTRACT FROM AUTHOR]

With the growing emergence of the Internet connectivity in this era of Gen Z, several IoT solutions have come into existence for exchanging large scale of data securely, backed up by their own unique cloud service providers (CSPs). It has, therefore, generated the need for customers to decide the IoT cloud platform to suit their vivid and volatile demands in terms of attributes like security and privacy of data, performance efficiency, cost optimization, and other individualistic properties as per unique user. In spite of the existence of many software solutions for this decision-making problem, they have been proved to be inadequate considering the distinct attributes unique to individual user. This paper proposes a framework to represent the selection of IoT cloud platform as a MCDM problem, thereby providing a solution of optimal efficacy with a particular focus in user-specific priorities to create a unique solution for volatile user demands and agile market trends and needs using optimized distance-based approach (DBA) aided by Fuzzy Set Theory. [ABSTRACT FROM AUTHOR]

Mass customization logistics service mode provides a new way to maintain the sustainable cooperative relationship between customers and integrators. One of the key factors to maintain the sustainable development of logistics service supply chain under MC mode is to locate a suitable customer order decoupling point (CODP) location. This paper investigates the problem of CODP in the logistics service supply chain based on the fuzzy set theory under the mass customization mode. With the help of a fuzzy QFD method and a new service quality function that we constructed, this paper quantifies the quality of a logistics service when the LSI selects a different CODP. Then, the fuzzy set of the high-quality logistics service and the fuzzy set of the satisfactory delivery time are built. Based on those two new fuzzy sets, this paper builds a new fuzzy programming model on CODP positioning. The solving methods of this model under different conditions are given. Finally, the influence of some important parameters on the optimal CODP position is studied by sensitivity analysis on a specific numerical case. [ABSTRACT FROM AUTHOR]

This paper proposes a fault-tolerant cooperative control (FTCC) scheme for multiple UAVs in a distributed communication network against input saturation, full-state constraints, actuator faults, and unknown dynamics. Firstly, by considering physical limitations, an auxiliary control signal is designed to simplify the analysis process. Secondly, to avoid the difficulty in the back-stepping design caused by full-state constraints, virtual control signals are constructed to transform constrained variables, while the dynamic surface control is adopted to avoid the phenomenon of "differential explosion." Thirdly, a disturbance observer (DO) is designed to estimate the unknown uncertainty caused by parameter uncertainty and actuator fault. Moreover, a recurrent wavelet fuzzy neural network (RWFNN) is used to compensate for the estimation errors of DO. Finally, it is proved that all states are uniformly ultimately bounded (UUB) by Lyapunov and invariant set theory. The effectiveness of the proposed scheme is further demonstrated by the simulation results. [ABSTRACT FROM AUTHOR]

Supplier selection is vital for enterprises to operate stably and achieve and sustain a competitive advantage. However, from the initial establishment to the gradual development and maturity of the enterprise, the supplier selection criteria change dynamically, and decision‐makers are hardly in agreement in each stage, which creates challenges for enterprises when choosing suitable suppliers. As such, this paper proposes a multicriteria group decision‐making method based on an interaction and feedback mechanism (IFM) and q‐rung orthopair fuzzy sets theory. We introduce an IFM to achieve consensus among different decision‐makers. We then develop the q‐rung orthopair fuzzy weighted partitioned Bonferroni mean (q‐ROFWPBM) operator to address the aggregation problem of dynamic multicriteria. A group decision‐making algorithm combining the IFM and q‐ROFWPBM operator is proposed to analyze the Hongxing Erke supplier selection. The results show that the proposed method can not only account for large differences of opinion among decision‐makers during group decision‐making but also consider the dynamic changes of supplier selection criteria in different stages of enterprise development and help enterprises choose suppliers suitable for their own development characteristics. [ABSTRACT FROM AUTHOR]

Tourist-dedicated train is the product of the combination of railway transportation and tourism, and its tour line selection includes the selection of nodes and lines. Based on the principle of decision-making, taking technical factors, tourism factors, regional economic factors, and passenger flow factors as criteria, this paper analyzes the decision-making indices affecting the tour line and establishes the decision-making index system. Subsequently, the prospect theory considering the bounded rationality and psychological factors of decision makers is combined with vague set fuzzy decision theory, and a comprehensive decision method based on vague set and prospect theory is proposed. Finally, the feasibility of the proposed decision method is verified by an example. The research shows that the established decision-making index system is representative, and the proposed decision-making method is scientific and effective for the decision making of tourist lines of tourist-dedicated train. The decision-making results can be used as a reference for the formulation of tour lines and line plans of tourist-dedicated train. [ABSTRACT FROM AUTHOR]

At this stage, in the research process of sports public service efficiency evaluation and analysis, due to the use of accurate data analysis methods, there are problems of low evaluation reliability and low analysis speed. Based on this, this paper studies the application of an information strategy based on the intuitionistic fuzzy data matching method in the evaluation and analysis of sports public service efficiency. The efficiency evaluation and analysis model of sports public service based on the intuitive fuzzy information algorithm is established. According to the characteristics of different types of sports public service, different types of data analysis methods are used to evaluate the efficiency, and the optimization of the efficiency analysis model of sports public service is realized according to the service demand and data type of different sports events. Finally, an experiment is designed to quantitatively evaluate the accuracy, stability, and reliability of the sports public service analysis model. The results show that the efficiency intelligent evaluation and analysis model based on the intuitive fuzzy information algorithm can effectively select the optimal sports public service evaluation countermeasures and rules according to the characteristics and data types of different sports events, realize the multi-dimensional accuracy classification of different types of sports events, and effectively improve the reliability of sports public service efficiency evaluation. [ABSTRACT FROM AUTHOR]

It is often said that mathematical modeling is an implementation of mathematics in real-world problems with the aim of better understanding them, so we can say that mathematical modeling is linked to the solution of problems. Some of the essential principles and procedures of mathematical modeling are discussed using formulas and equations. We investigate the stability and convergence characteristics and demonstrate the suitability of different mathematical methods in a set of numerical examples. The described methods in our paper are the best choices for the simulation of linear phenomena and are more efficient for use with high-order spatial discretization. We emphasized the importance of mathematical modeling technologies used in computational tools. Our study shows that these new methods are more stable with lower errors. [ABSTRACT FROM AUTHOR]

In this paper, we present a new computational method based on an exponential spline for solving a class of delay differential equations with a negative shift in the differentiated term. When the shift parameter is O ε , the proposed method works well and also controls the oscillations in the solution's layer region. To accomplish this, we included a parameter in the proposed numerical scheme that is based on a special type of mesh, and the parameter is evaluated using the theory of singular perturbation. Maximum absolute errors and convergences of numerical solutions are tabulated to demonstrate the efficiency of the proposed computational method and to support the convergence analysis of the presented scheme. [ABSTRACT FROM AUTHOR]

Recently, wide applications of fuzzy set theory have attracted the attention of both researchers and practitioners. Fuzzy portfolio develops as a new area in the research field of investment portfolio. This paper investigates the major research hotspots, development trend, and evolution of fuzzy portfolio, which provides a systematic review of the current fuzzy portfolio literature. CiteSpace, the most commonly used bibliometrics software, is used in this article. According to the 602 articles with 15132 references, several conclusions can be summarized as follows: (1) Fuzzy portfolio becomes increasingly interdisciplinary with the connections among "Computer Science" and so on. (2) Most contributive authors are Markowitz and Zadeh. (3) South China University of Technology makes excellent performance in this research area and China is the most influential country. (4) European Journal of Operations Research is the cradle of plenty of crucial fuzzy portfolio investigations. (5) We find some research hotspots helpful to make scientific predictions of future trends by analyzing the keywords. By utilizing the effective bibliometric methods, we provide a comprehensive analysis and deep insights into the fuzzy portfolio research, enabling the individuals, especially the new beginners who are interested in this area to learn fuzzy portfolio, which will be of great help for their future explorations. [ABSTRACT FROM AUTHOR]

In systems with uncertain information, ambiguity must be taken into account. In this paper, fuzzy set theory concepts are incorporated into support vector machines (SVM). This ensemble preserves the benefits of SVM regression models and fuzzy regression models, where SVM learning theory describes the properties of learning machines that enable them to generalize well, and fuzzy set theory offers an efficient method for capturing the approximate, imprecise properties of the real world. In accordance with the phase space reconstruction theory of dynamical systems, a fuzzy model for enterprise supply chain risk assessment is proposed using the robust nonlinear mapping capability of support vector machines and the characteristic of fuzzy logic that makes it easy to combine prior system knowledge into fuzzy rules. The results demonstrate that the prediction model can not only automatically acquire knowledge from learning data to generate fuzzy rules but can also extract support vectors that can represent the inherent laws of enterprise supply chain risks, drastically reduce the number of support vectors, and accurately predict. Future risk can be accurately predicted. This conclusion suggests that the support vector machine based on a fuzzy model is an effective method for analyzing enterprise supply chain risk. [ABSTRACT FROM AUTHOR]

Fuzzy soft set is the most powerful and effective extension of soft sets which deals with parameterized values of the alternative. It is an extended model of soft set and a new mathematical tool that has great advantages in dealing with uncertain information and is proposed by combining soft sets and fuzzy sets. Many fuzzy decision making algorithms based on fuzzy soft sets were given. However, these do not consider the external effective on the decision it depends on the parameters without considering any external effective. In order to solve these problems, in this paper, we introduce the concept of effective fuzzy soft set and its operation and study some of its properties. We also give an application of this concept in decision making (DM) problem. Finally, we give an application of this theory to medical diagnosis (MD) and exhibit the technique with a hypothetical case study. [ABSTRACT FROM AUTHOR]

In this paper, new theoretical results for reasoning with belief functions are obtained and discussed. After a judicious decomposition of the set of focal elements of a belief function, we establish the total belief theorem (TBT). which is the direct generalization of the total probability theorem when working in the framework of belief functions. The TBT is also generalized for dealing with different frames of discernments thanks to Cartesian product space. From TBT, we can derive and define formally the expressions of conditional belief functions, which are consistent with the bounds of imprecise conditional probability. This work provides a direct establishment and solid justification of Fagin–Halpern belief conditioning formulas. The well‐known Bayes' theorem of probability theory is then generalized in the framework of belief functions, and we illustrate it with an example at the end of this paper. [ABSTRACT FROM AUTHOR]

Some extensions of fuzzy sets such as interval‐valued fuzzy sets, intuitionistic fuzzy sets, interval‐valued intuitionistic fuzzy sets, type n‐fuzzy sets, and neutrosophic sets provided powerful and practical tools for dealing with uncertainty in decision‐making problems. Neutrosophic set is defined with three‐dimensional membership functions to describe the degrees of truth, indeterminacy, and falsity. Neutrosophic set theory is a useful instrument to handle incomplete, inconsistent, and indeterminate information. In this paper, we first propose a modified score function for ranking single‐valued neutrosophic numbers. Then, we suggest a TOPSIS method based on the proposed function for decision‐making under group recommendation. The method is applied to deal with the hotel location selection problem, where the decision values of the attributes for alternatives and the weights of the attributes are given by decision‐makers based on single‐valued neutrosophic sets. Finally, numerical experiments are done. They show that the given method is more efficient as well as more reasonable tool for decision‐making in contrast to the other existing methods. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the concept of multiple‐attribute group decision‐making (MAGDM) problems with interval‐valued Pythagorean fuzzy information is developed, in which the attribute values are interval‐valued Pythagorean fuzzy numbers and the information about the attribute weight is incomplete. Since the concept of interval‐valued Pythagorean fuzzy sets is the generalization of interval‐valued intuitionistic fuzzy set. Thus, due the this motivation in this paper, the concept of interval‐valued Pythagorean fuzzy Choquet integral average (IVPFCIA) operator is introduced by generalizing the concept of interval‐valued intuitionistic fuzzy Choquet integral average operator. To illustrate the developed operator, a numerical example is also investigated. Extended the concept of traditional GRA method, a new extension of GRA method based on interval‐valued Pythagorean fuzzy information is introduced. First, utilize IVPFCIA operator to aggregate all the interval‐valued Pythagorean fuzzy decision matrices. Then, an optimization model based on the basic ideal of traditional grey relational analysis (GRA) method is established, to get the weight vector of the attributes. Based on the traditional GRA method, calculation steps for solving interval‐valued Pythagorean fuzzy MAGDM problems with incompletely known weight information are given. The degree of grey relation between every alternative and positive‐ideal solution and negative‐ideal solution is calculated. To determine the ranking order of all alternatives, a relative relational degree is defined by calculating the degree of grey relation to both the positive‐ideal solution and negative ideal solution simultaneously. Finally, to illustrate the developed approach a numerical example is to demonstrate its practicality and effectiveness. [ABSTRACT FROM AUTHOR]

Due to the superiority in expressing the uncertain and vague information, the hesitant fuzzy set (HFS) is regarded as an important tool to deal with multiattribute decision-making (MADM) problems. Quantitative and qualitative fuzzy measures have been proposed to solve such problems from different points. However, most of the existing information measures for HFSs are related to such fuzzy measures as distance, similarity, entropy, and correlation coefficients. The grey relational analysis is omitted. Besides, the existing grey relational analysis for HFSs only considers the range or distance between HFSs data which is only a partial measure of the HFSs. Therefore, in this paper, we improve the grey relational analysis for HFSs and explore a novel slope grey relational degree by considering another factor of HFSs data: the slope. Further, we combine both the distance and slope factors of HFSs data to construct a synthetic grey relational degree that describes the closeness and variation tendency of HFSs simultaneously, greatly enriching the fuzzy measures of HFSs. Furthermore, with the help of the TOPSIS method, we develop the grey relational based MADM methodology to solve the HFSs MADM problems. Finally, combining with two practical MADM examples about energy policy selection and multisensor target recognition, we obtain the most desirable decision results. Compared with the previous methods, the validity, comprehensiveness, and discrimination of the proposed synthetic grey relational degree for HFSs are demonstrated in detail. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we propose three similarity measure methods for single‐valued neutrosophic refined (SVNR) sets and interval neutrosophic refined (INR) sets based on Jaccard, Dice, and Cosine similarity measures of SVN‐sets and interval neutrosophic sets. Furthermore, we suggest two multicriteria decision‐making (MCDM) methods under SVNR environment and INR environment, and give applications of proposed MCDM methods. Finally, we suggest a consistency analysis method for proposed similarity measures between INR‐sets and give an application to demonstrate process of the method. [ABSTRACT FROM AUTHOR]

Abstract: Entropy is commonly used as a way to measure the uncertainty of random variables. In uncertain set theory, a concept of entropy for uncertain sets has been defined by using logarithm. However, such an entropy fails to measure the uncertain degree of some uncertain sets. This paper aims at proposing a concept of elliptic entropy for uncertain sets and investigating its properties such as translation invariance and positive linearity. It also provides some formulas for calculating the elliptic entropy via inverse membership functions. Additionally, elliptic relative entropy for uncertain sets is presented as a measure of the difference between two membership functions, and some applications are considered in portfolio selection and clustering. [ABSTRACT FROM AUTHOR]

Abstract: Semiuninorm‐based ordered weighted averaging (SUOWA) operators are a specific case of Choquet integrals that allow us to generalize simultaneously weighted means and ordered weighting averaging (OWA) operators. Although SUOWA operators possess some very interesting properties, their main weakness is that, sometimes, the game used in their construction is not monotonic and it is necessary to calculate its monotonic cover. In this paper, we introduce a new family of weighting vectors, called unimodal weighting vectors, which embrace some of the most outstanding weighting vectors used in the framework of OWA operators, and we show that when using these weighting vectors and a specific semiuninorm we directly get normalized capacities. Moreover, we also show that these operators satisfy some properties which are very useful in practice. [ABSTRACT FROM AUTHOR]

Undoubtedly, most of the information conveyed is full of impreciseness or vagueness. In such situation, fuzzy set theory is a proper tool to handle these types of impreciseness or vagueness. Fuzzy numbers are also of different types based on the presence of uncertainty. Neutrosphic numbers are one type of fuzzy number that consists of three types of membership functions, namely, truth, indeterminacy and falsity. In fact, neutrosophic numbers are generalization of intuitionistic fuzzy numbers. These numbers might be used in decision making problems, where it is essential to rank those numbers. So, ordering of these numbers becomes a new trends with more challenges. In this paper, an innovative ranking approach of single‐valued neutrosophic number has been put forwarded. The method is based on value, ambiguity and θ function. Value and ambiguity are defined on three functions of the neutrosophic numbers. Further, the reliability of the proposed method is established by considering the reasonable properties of ranking method. One important aspect of ranking neutrosophic numbers is to consider the consistency in ordering the neutrosophic numbers and their corresponding images. It is worth to mention that the current approach consistently ranks the single‐valued neutrosophic numbers as well as their corresponding images. [ABSTRACT FROM AUTHOR]

With the development of shallow surface mineral resources in metal mines, it is gradually turning to the stage of deep mining. According to the current mining depth and the average annual depth, during the period of "14th Five-Year Plan," one-third of the underground metal mines will reach or exceed the mining depth of 1,000 m, with the deepest being 2,000 m. In the stage of deep mining, mines will face the conditions of high stress, high temperature, high well depth, and strong mining disturbance, which will greatly increase the difficulty of large-scale deep mining. Among them, the high ground stress environment is the principal problem of many technical problems in deep mining. The selection of mining method has become a prerequisite for solving the problem of efficient and safe mining of deep deposits. In this paper, the vague set theory was introduced into the selection of mining methods and a vague set model for deep unloading mining schemes was established. Taking the Jinchuan No. 2 mining area as the engineering background, four unloading schemes for deep mining were proposed, and the Vague set model was used for optimization. It is concluded that the mining approach with large-section unloading is the optimal unloading mining plan. The application shows that it has the advantages of high unloading efficiency, large production capacity, and low loss index. It has been fully promoted in the deep mining of the mining area. It is feasible and effective to use the vague set theory in the selection of deep unloading mining schemes, which provides a proper approach in the selection of deep unloading mining schemes. [ABSTRACT FROM AUTHOR]

This study aims to explore the application of blockchain technology in smart healthcare, establish a hierarchical theoretical framework of smart healthcare, reveal the impact of blockchain on smart healthcare, and finally, construct a development application system of smart healthcare under the blockchain based on stakeholder theory. However, such a hierarchical theoretical framework should consider not only the necessary attributes and the interrelationship among various aspects and attributes but also the role of multiple stakeholders. Therefore, the paper uses fuzzy set theory to filter unnecessary attributes, proposes a decision-making and experimental evaluation laboratory (DEMATEL) to manage the complex interrelationships between various aspects and attributes, and uses Interpretive Structure Modeling (ISM) to divide the hierarchy and construct a hierarchical theoretical framework. The results show that (1) the top-level design, the medical record management, and the doctor management are the root causes of system. (2) The specific application of blockchain in the field of smart healthcare is mainly carried out around the intelligent contract, which relies on the medical record management and is constrained by the system, and optimization of application is the key to system upgrading. (3) The internal and external regulation, the medical insurance, and the environmental governance play a guaranteed role for the development of the system and effectively safeguard the interests of stakeholders. (4) The application system of smart healthcare under the blockchain needs to be built based on three layers: the transaction layer, information layer, and stakeholder layer. The theoretical hierarchical framework is intended to guide smart healthcare towards blockchain applications, and stakeholders are suggested to participate in the development application systems. [ABSTRACT FROM AUTHOR]

In this paper, value stream mapping (VSM) is integrated with fuzzy set theory to incorporate variability and uncertainty in the lean production system. VSM is one of the primary analytical tools for identifying waste and optimizing a production line. However, the standard VSM fails to consider the variability in manufacturing environments, which is, in fact, one of the root causes of waste. Therefore, this article proposes fuzzy VSM to overcome this weakness. Two alternative forms of fuzzy numbers, triangular fuzzy numbers (TFNs) and normal fuzzy numbers (NFNs), are applied, respectively, to depict time intervals, inventories, and other operating variables in VSM. An industrial case for assessing the validity of the proposed approaches is presented. Both approaches make it possible to incorporate and analyze variability in VSM and can be easily applied to industrial cases, as they only require basic algebraic operations. The obtained results are compared and the choice between TFNs and NFNs is discussed accordingly. A triangular fuzzy VSM tends to overestimate the variability of the process in complex production environment with complicated operational processes. However, it permits a more accurate description of variation in the environment where the optimistic and pessimistic values have very different variations from the core. [ABSTRACT FROM AUTHOR]

Taking the Suiqi coalfield located in North China as the object, where the coal seam burial depth is more than 1100 m, the water abundance of the roof pore thermal storage aquifer is better than average, the ground temperature is abnormally high, and hydrogeological data are relatively lacking, this paper selects and determines eight index factors that influence the mining of the coalfield. Based on the analytic hierarchy process (AHP), the index factor weight is defined, and then, the threat degree of the roof thermal storage aquifer to the coal mining is quantitatively evaluated and divided by using the fuzzy variable set theory. The evaluation results show that the threat degree of the roof in the eastern region is generally greater than that in the western region and that the closer it is to the coal seam outcrop line, the higher the threat degree is; near the boreholes, in the areas Qs1,Qs5, Qs8, Sx1, Tk5, Zc4, and Zc7, which are close to the hidden outcrop line of the coal seam, the classification characteristic value of the threat degree is greater than 3.5, which is in the high-threat zone for disasters caused by roof thermal storage aquifers during coal seam mining. The area above the medium-threat zone accounts for 71.82% of the total study area, indicating that deep coal mining is affected by multiple factors and that roof water and heat disasters are more likely to occur. [ABSTRACT FROM AUTHOR]

Resource risk caused by specific resource sharing or competition among projects due to resource constraints is a major issue in project portfolio management, which challenges the application of risk analysis methods effectively. This paper presents a methodology by using a fuzzy Bayesian network to assess the project portfolio resource risk, determine critical resource risk factors, and propose risk-reduction strategies. In this method, the project portfolio resource risk factors are first identified by taking project interdependency into consideration, and then the Bayesian network model is developed to analyze the risk level of the identified risk factors in which expert judgments and fuzzy set theory are integrated to determine the probabilities of all risk factors to deal with incomplete risk data and information. To reduce the subjectivity of expert judgments, the expert weights are determined by combining experts' background and reliability degree of expert judgments. A numerical analysis is used to demonstrate the application of the proposed methodology. The results show that project portfolio resource risks can be analyzed effectively and efficiently. Furthermore, "poor communication and cooperation among projects," "capital difficulty," and "lack of sharing technology among projects" are considered the leading factors of the project portfolio resource risk. Risk-reduction strategic decisions based on the results of risk assessment can be made, which provide project managers with a useful method or tool to manage project risks. [ABSTRACT FROM AUTHOR]

In recent years, fuzzy set theory and possibility theory have been widely used to deal with an uncertain decision environment characterized by vagueness and ambiguity in the financial market. Considering that the expected return rate of investors may not be a fixed real number but can be an interval number, this paper establishes an interval-valued possibilistic mean-variance portfolio selection model. In this model, the return rate of assets is regarded as a fuzzy number, and the expected return rate of assets is measured by the interval-valued possibilistic mean of fuzzy numbers. Therefore, the possibilistic portfolio selection model is transformed into an interval-valued optimization model. The optimal solution of the model is obtained by using the order relations of interval numbers. Finally, a numerical example is given. Through the numerical example, it is shown that, when compared with the traditional possibilistic model, the proposed model has more constraints and can better reflect investor psychology. It is an extension of the traditional possibilistic model and offers greater flexibility in reflecting investor expectations. [ABSTRACT FROM AUTHOR]

Agroecology was born as a competing theory to sciences derived from the Green Revolution like conventional agronomy or modernized animal husbandry. In recent years, several theoretical models or approaches have been developed in order to explain this science. However, any of them can explain its change or difference with its rival theories in a rational manner that allows assessment of its success. As a result, the aim of this study was to propose a rational model of scientific change based on main and auxiliary hypotheses. We found that seven basic principles have been formulated throughout theoretical books and papers as well as several auxiliary hypotheses that can be derived from them. These principles are as follows: (1) characteristic systemic principle of agroecology, (2) principle of biomimicry, (3) principle of biodiversity, (4) principle of specificity of agroecosystems, (5) principle of governance, (6) principle of socioecological resilience, and (7) principle of vulnerability. Also, three principles for food systems approach were retrieved. This model shows agroecology more like an organic theory that moves in different scales than a set of rival theories competing for success. However, a proper articulation and discussion of these basic principles is yet to be done. [ABSTRACT FROM AUTHOR]

The unicost set covering problem and the attribute reduction problem are NP-complete problems. In this paper, the relationship between these two problems are discussed. Based on the transformability between attribute reductions and minimal solutions in unicost set covering models, two methods are provided. One is to induce an information table from a given unicost set covering model. With no doubt, it shows that the unicost set covering problem can be investigated by rough set theory. The other is to induce a unicost set covering model from a given information table. Similarly, it shows that the attribute reduction problem can be studied by set covering theory. As an application of the proposed theoretical results, a rough set heuristic algorithm is presented for the unicost set covering problem. [ABSTRACT FROM AUTHOR]

This research work conducts an investigation of the stability issues of neutral-type Cohen–Grossberg neural network models possessing discrete time delays in states and discrete neutral delays in time derivatives of neuron states. By setting a new generalized appropriate Lyapunov functional candidate, some novel sufficient conditions are proposed for global asymptotic stability for the considered neural networks of neutral type. This paper exploits some basic properties of matrices in the derivation of the results that establish a set of algebraic mathematical relationships between network parameters of this neural system. A key feature of the obtained stability criteria is to be independent from time and neutral delays. Therefore, the derived results can be easily tested. Moreover, a constructive numerical example is studied to check the verification of presented global stability conditions. [ABSTRACT FROM AUTHOR]

To reduce costs and improve organizational efficiency, the adoption of innovative services such as Cloud services is the current trend in today's highly competitive global business venture. The aim of the study is to guide the software development organization (SDO) for Cloud-based testing (CBT) adoption. To achieve the aim, this study first explores the determinants and predictors of Cloud adoption for software testing. Grounded on the collected data, this study designs a technology acceptance model using fuzzy multicriteria decision-making (FMCDM) approach. For the stated model development, this study identifies a list of predictors (main criteria) and factors (subcriteria) using systematic literature review (SLR). In the results of SLR, this study identifies seventy subcriteria also known as influential factors (IFs) from a sample of 136 papers. To provide a concise understanding of the facts, this study classifies the identified factors into ten predictors. To verify the SLR results and to rank the factors and predictors, an empirical survey was conducted with ninety-five experts from twenty different countries. The application value in the industrial field and academic achievement of the present study is the development of a general framework incorporating fuzzy set theory for improving MCDM models. The model can be applied to predict organizational Cloud adoption possibility taking various IFs and predictors as assessment criteria. The developed model can be divided into two main parts, ranking and rating. To measure the success or failure contribution of the individual IFs towards successful CBT adoption, the ranking part of the model will be used, while for a complete organizational assessment in order to identify the weak area for possible improvements, the assessment part of the model will be used. Collectively, it can be used as a decision support system to gauge SDO readiness towards successful CBT. [ABSTRACT FROM AUTHOR]

Surface defects of autobody panels have the greatest impact on the surface quality of the automobile body, but many enterprises lack a scientific and reasonable evaluation method of surface quality, relying solely on the subjective judgment of decision makers which will lead to an increase in the probability of misjudgment. In this paper, the subjective weight is determined by the genetic algorithm based on optimization, and the objective weight is determined by the improved deviation maximization method. Combining the hesitant fuzzy set theory, the hesitant fuzzy mixed weighted arithmetic average operator (HFHWA), and the score function, the surface defect information of the panel is quantified. On this basis, a complete set of hesitant fuzzy multiattribute evaluation model of surface defect information is proposed. Taking a batch of inner panels of the automobile door produced by A automobile enterprise as an example, five common defects including hidden pit, bump and scratch, rust, indentation pockmark, and ripple are selected as evaluation attributes to evaluate their surface quality, which verifies the validity and practicability of the model. [ABSTRACT FROM AUTHOR]

Given that there are problems of difficulty to identify accurately the poverty alleviation subjects' demands. This research puts forward and applies the fuzzy proximity method on the basis of the fuzzy set theory. The method can identify accurately the demands of poverty alleviation subjects. This study calculated the fuzzy proximity vector and the positive and negative ideal grades of the four demand types, according to six poverty characteristic indexes. The demand types are determined. Then, the paper takes a case about the demand identification of a poverty alleviation subject in a village, Shanxi province in China. The application result showed that (1) the demand identification model can help identify accurately the demands of poverty alleviation subjects; (2) the poverty alleviation strategies provide a reference for the government to carry out poverty alleviation work. [ABSTRACT FROM AUTHOR]

In order to clarify the achievement and efficiency of enterprise learning in the process of cooperative innovation, a comprehensive criteria framework for the evaluation of enterprise learning performance is constructed taking the learning process and learning results as the construction idea based on organizational learning theory. And this paper proposes a novel dynamic evaluation method considering the interaction between attributes of learning performance. In this study, the criterion framework for the evaluation of enterprise learning performance in the process of cooperative innovation includes learning process performance and learning outcomes performance. The original matrices are given by managers and experts using fuzzy set theory, and a dynamic time sequence weight vector is calculated based on information entropy and time degree. The weight of learning performance attributes under different time series is calculated based on entropy measure method. The interactive information of learning performance attributes is integrated through the weight of learning performance attributes and the three-parameter weighted Heronian mean operator considering the interaction between attributes. And then, the dynamic and comprehensive evaluation result of learning performance in the process of cooperative innovation could be computed by integrating the learning performance information under different time series with time sequence weight vector. Finally, a real case is studied to verify the scientificity and validity of the criteria framework for the evaluation of enterprise learning performance and the method proposed in this study. This study not only helps cooperative enterprises get feedback in time and adjust cooperative relationships and learning styles but also enriches the theory of interorganizational management and provides a theoretical basis for the process of enterprise cooperative innovation. [ABSTRACT FROM AUTHOR]

In this paper, the auxiliary principle technique is extended to study a system of generalized nonlinear mixed variational-like inequalities problem for set-valued mappings without compact values in Banach spaces with p-uniformly convex bidual spaces. First, the existence of the solutions of the related auxiliary problem is proved. Then, a new iterative algorithm based on the system of auxiliary variational inequalities is constructed. Finally, both the existence of the solutions of the original problem and the convergence of the iterative sequences generated by the algorithm are proved. And we also present a numerical example to demonstrate the result. Our results improve and extend some known results. [ABSTRACT FROM AUTHOR]

Sentiment word identification, or SWI, is one of the most basic and important techniques in sentiment analysis. Many existing methods depend on the seed word, and such dependence leads to low robustness. In this paper, we propose a novel method utilizing propagation and optimization model, PRopagation-based Constrained Optimization Model (PR-COM) for SWI. Unlike the previous research, we exploit an iterative algorithm to expand the seed word set from the candidate word set, which brings higher robustness. Experimental results on several data sets show that our PR-COM method is effective and outperforms the state-of-art methods. [ABSTRACT FROM AUTHOR]

In this paper, we first study some basic properties of Stepanov-like asymptotical almost periodic functions including the completeness of the space of Stepanov-like asymptotical almost periodic functions. Then, as an application, based on these and the contraction mapping principle, we obtain sufficient conditions for the existence and uniqueness of Stepanov-like asymptotical almost periodic solutions for a class of semilinear delay differential equations. [ABSTRACT FROM AUTHOR]

As an extension of Pawlak’s rough sets, rough fuzzy sets are proposed to deal with fuzzy target concept. As we know, the uncertainty of Pawlak’s rough sets is rooted in the objects contained in the boundary region, while the uncertainty of rough fuzzy sets comes from three regions (positive region, boundary region, and negative region). In addition, in the view of traditional uncertainty measures, the two rough approximation spaces with the same uncertainty are not necessarily equivalent, and they cannot be distinguished. In this paper, firstly, a fuzziness-based uncertainty measure is proposed. Meanwhile, the essence of the uncertainty for rough fuzzy sets and its three regions in a hierarchical granular structure is revealed. Then, from the perspective of fuzzy distance, we introduce a modified uncertainty measure based on the fuzziness-based uncertainty measure and present that our method not only is strictly monotonic with finer approximation spaces, but also can distinguish the two rough approximation spaces with the same uncertainty. Finally, a case study is introduced to demonstrate that the modified uncertainty measure is more suitable for evaluating the significance of attributes. These works are useful for further study on rough sets theory and promote the development of uncertain artificial intelligence. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a series of similarity measures based on point operators for Pythagorean fuzzy sets are proposed. Using the proposed similarity measures, two new aggregation operators, viz., Pythagorean fuzzy‐dependent averaging operator and Pythagorean fuzzy‐dependent geometric operator, are developed. The advantage of using these operators is that the influence of unfair arguments of aggregated results could be eliminated, since the associated weights are taken from the aggregated Pythagorean fuzzy arguments. Also, the proposed operators have the capability to adjust the degree of aggregated arguments with the controlling parameters. To establish the application potentiality of those operators, a methodology for solving multicriteria group decision‐making problems having Pythagorean fuzzy arguments is developed. A numerical example is provided to demonstrate the proficiency of the proposed method. The achieved results are compared with the results of other existing technique. [ABSTRACT FROM AUTHOR]

Robust optimization is a powerful and relatively novel methodology to cope with optimization problems in the presence of uncertainty. The positive aspect of robust optimization approach is its computational tractability that attracts more and more attention. In this paper, we focus on an ambiguous P-model where probability distributions are partially known. We discuss robust counterpart (RC) of uncertain linear constraints under two refined uncertain sets by robust approach and further find the safe tractable approximations of chance constraints in the ambiguous P-model. Because of the probability constraints embedded in the ambiguous P-model, it is computationally intractable. The advantage of our approach lies in choosing an implicit way to treat stochastic uncertainty models instead of solving them directly. The process above can enable the transformation of proposed P-model to a tractable deterministic one under the refined uncertainty sets. A numerical example about portfolio selection demonstrates that the ambiguous P-model can help the decision maker to determine the optimal investment proportions of various stocks. Sensitivity analyses explore the trade-off between optimization and robustness by adjusting parameter values. Comparison study is conducted to validate the benefit of our ambiguous P-model. [ABSTRACT FROM AUTHOR]

This paper is concerned with the property of asymptotic hyperstability of a continuous-time linear system under a class of continuous-time nonlinear and perhaps time-varying feedback controllers belonging to a certain class with two main characteristics; namely, (a) it satisfies discrete-type Popov’s inequality at sampling instants and (b) the control law within the intersample period is generated based on its value at sampling instants being modulated by two design weighting auxiliary functions. The closed-loop continuous-time system is proved to be asymptotically hyperstable, under some explicit conditions on such weighting functions, provided that the discrete feed-forward transfer function is strictly positive real. [ABSTRACT FROM AUTHOR]