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Purpose: The current article presents the results of a case study dealing with the historical roots of Eastern European researchers in computer science. Design/methodology/approach: The study is based on an analysis of cited references stemming from a collection of around 80,000 computer science papers by Eastern European researchers published from 1989 to 2014. By using a method called "reference publication year spectroscopy" (RPYS) for historical analyses based on bibliometric data, we analyze around 800,000 references cited in those papers. The study identifies the peak years, including most frequently cited publications (from 1952, 1965 and 1975), and focuses on these outstanding works for the field. The research shows how these influential papers were cited in Eastern Europe and in general, and on which scientific fields they have the most impact. Findings: A noteworthy publication that seems to have a tremendous effect on Eastern European computer science is Zadeh's "Fuzzy sets" article which appeared in Information and Control in 1965. The study demonstrates that computer scientists from Eastern Europe are more conservative in their citation behaviour and tend to refer to older and more established research than their counterparts from the West. Originality/value: Which are the historical roots of researchers working in a particular field or on a specific topic? Are there certain publications – landmark papers – which are important for their research? We guess that these are questions bothering researchers in many fields. [ABSTRACT FROM AUTHOR]

An AG-group is an algebraic structure that satisfies the left invertive law and includes its left identity and inverse elements. This framework is naturally suited for representing and manipulating various real-life applications in civil engineering, information engineering, artificial intelligence, and more. In this paper, we present the structural application of AG-groups in data encryption and in the rotational transformation of water molecules. Additionally, numerous authors have explored fuzzy set theory over AG-group systems, yielding many valuable results. Spherical fuzzy set theory, an extension of fuzzy set theory, allows for the representation of uncertainty in decision-making, where there may be multiple possible choices or uncertainty about the degree of membership of an element in a set. However, no prior work has combined spherical fuzzy set theory with AG-groups, which motivates our study. In this paper, we apply spherical fuzzy set theory to AG-groups and introduce the concept of spherical fuzzy AG-subgroupoids. We provide the characterization of spherical fuzzy AG-subgroupoids over AG-groupoids and examine their related properties. As an application of spherical fuzzy sets over AG-groups, we develop the concept of normal spherical fuzzy groups over AG-groups and investigate their various properties. [ABSTRACT FROM AUTHOR]

The rapid development of renewable energy presents challenges to the security and stability of power systems. Aiming at addressing the power system scheduling problem with load demand and wind power uncertainty, this paper proposes the establishment of different error fuzzy sets based on the Wasserstein probability distance to describe the uncertainties of load and wind power separately. Based on these Wasserstein fuzzy sets, a distributed robust chance-constrained scheduling model was established. In addition, the scheduling model was transformed into a linear programming problem through affine transformation and CVaR approximation. The simplex method and an improved differential evolution algorithm were used to solve the model. Finally, the model and algorithm proposed in this paper were applied to model and solve the economic scheduling problem for the IEEE 6-node system with a wind farm. The results show that the proposed method has better optimization performance than the traditional method. [ABSTRACT FROM AUTHOR]

The competition between real estate enterprises in the future is likely to be between supply chains, and strategic general contracting is an important part. Implementing strategic construction general contracting procurement is beneficial for improving procurement efficiency and transparency, saving procurement costs, improving procurement quality, achieving economies of scale, and opening up or enhancing the core competitiveness of real estate enterprises. It has practical and guiding significance for the long-term and good development of real estate enterprises. The capability evaluation of real estate general contractors is a multiple-attribute decision-making (MADM) problem. Recently, the Exponential TODIM(ExpTODIM) and (grey relational analysis) GRA technique has been used to cope with MADM issue. The hesitant triangular fuzzy sets (HTFSs) are used as a tool for characterizing uncertain information during the capability evaluation of real estate general contractors. In this paper, the hesitant triangular fuzzy Exponential TODIM-GRA (HTF-ExpTODIM-GRA) technique is built to solve the MADM under HTFSs. In the end, a numerical case study for capability evaluation of real estate general contractors and some comparative analysis is given to validate the proposed technique. The main contribution of this paper is managed: (1) The MEREC technique is constructed to obtain weight values under HTFSs; (2) an integrated HTF-ExpTODIM-GRA technique is constructed to manage the MADM issue; (3) An illustrative example for capability evaluation of real estate general contractors has accomplished to verify the HTF-ExpTODIM-GRA technique. [ABSTRACT FROM AUTHOR]

When information is incomplete or uncertain, Fermatean hesitant fuzzy sets (FHFSs) can provide more information to help decision-makers deal with more complex problems. Typically, determining attribute weights assumes that each attribute has a fixed influence. Introducing probability information can enable one to consider the stochastic nature of evaluation data and better quantify the importance of the attributes. To aggregate data by considering the location and importance degrees of each attribute, this paper develops a Fermatean hesitant fuzzy multi-attribute decision-making (MADM) method with probabilistic information and an ordered weighted averaging (OWA) method. The OWA method combines the concepts of weights and sorting to sort and weigh average property values based on those weights. Therefore, this novel approach assigns weights based on the decision-maker's preferences and introduces probabilities to assess attribute importance under specific circumstances, thereby broadening the scope of information expression. Then, this paper presents four probabilistic aggregation operators under the Fermatean hesitant fuzzy environment, including the Fermatean hesitant fuzzy probabilistic ordered weighted averaging/geometric (FHFPOWA/FHFPOWG) operators and the generalized Fermatean hesitant fuzzy probabilistic ordered weighted averaging/geometric (GFHFPOWA/GFHFPOWG) operators. These new operators are designed to quantify the importance of attributes and characterize the attitudes of decision-makers using a probabilistic and weighted vector. Then, a MADM method based on these proposed operators is developed. Finally, an illustrative example of selecting the best new retail enterprise demonstrates the effectiveness and practicality of the method. [ABSTRACT FROM AUTHOR]

In a complex financial market, people pay more attention to the portfolio selection model in some fuzzy environment. Some properties and definitions of semivariance and entropy are given and proved in this paper. Then, the fuzzy tri-objective mean-semivariance-entropy portfolio model is proposed based on credibility theory when the return rates are fuzzy numbers. We present a novel layer-by-layer tolerance evaluation method to solve the proposed model in this paper. Finally, a numerical example is given to illustrate the effectiveness of the model and method proposed in this paper. There are two improvements in our proposed method: one is that the evaluation function idea is considered in the process of laying objective functions; the other is that the preference degree and subjective wills are presented by tolerant amounts of objective function values. [ABSTRACT FROM AUTHOR]

Fuzzy posets can be regarded as a generalization of classical posets. Many concepts and results in posets can be generalized to fuzzy posets. In order to further improve the fuzzy poset theory, in this paper, we shall introduce the concept of prime (distributive) fuzzy posets which can be seen as the correspondence of prime (distributive) posets in fuzzy setting. First, we consider the extensions of fuzzy ideals in a fuzzy poset. Then by the extensions of fuzzy ideals, we give a characterization for prime (distributive) fuzzy posets, that is, a fuzzy poset X is prime (distributive) if and only if all extensions of normal fuzzy ideals of X are Frink (strong) fuzzy ideals. This paper generalizes the work of Halas in posets into fuzzy posets. [ABSTRACT FROM AUTHOR]

Purpose: A fleet of mobile robots has been effectively used in various application domains such as industrial plant inspection. This paper proposes a solution to the combined problem of task allocation and motion planning problem for a fleet of mobile robots which are requested to operate in an intelligent industry. More specifically, the robots are requested to serve a set of inspection points within given service time windows. In comparison with the conventional time windows, our problem considers fuzzy time windows to express the decision maker's satisfaction for visiting an inspection point. Design/methodology/approach: The paper develops a unified approach to the combined problem of task allocation and motion planning for a fleet of mobile robots with three objectives: (a) minimizing the total travel cost considering all robots and tasks, (b) balancing fairly the workloads among robots and (c) maximizing the satisfaction grade of the decision maker for receiving the services. The optimization problem is solved by using a novel combination of a Genetic Algorithm with pareto solutions and fuzzy set theory. Findings: The computational results illustrate the efficiency and effectiveness of the proposed approach. The experimental analysis leverages the potential for using fuzzy time windows to reflect real situations and respond to demanding situations. Originality/value: This paper provides trade-off solutions to a realistic combinatorial multi-objective optimization problem considering concurrently the motion and path planning problem for a fleet of mobile robots with fuzzy time windows. [ABSTRACT FROM AUTHOR]

Convolutional Neural Networks (CNNs) are a kind of artificial neural network designed to extract features and find out patterns for tasks such as segmentation, recognizing objects, and drawing up classification. Within a CNNs architecture, pooling operations are used until the number of parameters and the computational complexity are reduced. Numerous papers have focused on investigating the impact of pooling on the performance of Convolutional Neural Networks (CNNs), leading to the development of various pooling models. Recently, a fuzzy pooling operation based on type-1 fuzzy sets was introduced to cope with the local imprecision of the feature maps. However, in fuzzy set theory, it is not always accurate to assume that the degree of non-membership of an element in a fuzzy set is simply the complement of the degree of membership. This is due to the potential existence of a hesitation degree, which implies a certain level of uncertainty. To overcome this limitation, intuitionistic fuzzy sets (IFS) were introduced to incorporate the concept of a degree of hesitation. In this paper, we introduce a novel pooling operation based on intuitionistic fuzzy sets to incorporate the degree of hesitation heretofore neglected by a fuzzy pooling operation based on classical fuzzy sets, and we investigate its performance in the context of image classification. Intuitionistic pooling is performed in four steps: bifuzzification (by the transformation of data through the use of membership and non-membership maps), first aggregation (through the transformation of the IFS into a standard fuzzy set, second aggregation (through the transformation and use of a sum operator), and the defuzzification of feature map neighborhoods by using a max operator. IFS pooling is used for the construction of an intuitionistic pooling layer that can be applied as a drop-in replacement for the current, fuzzy (type-1) and crisp, pooling layers of CNN architectures. Various experiments involving multiple datasets demonstrate that an IFS-based pooling can enhance the classification performance of a CNN. A benchmarking study reveals that this significantly outperforms even the most recent pooling models, especially in stochastic environments. [ABSTRACT FROM AUTHOR]

A new methodology for solving the fuzzy multiobjective optimization problems is proposed in this paper by considering the fusion of cooperative game theory and genetic algorithm. The original fuzzy multiobjective optimization problem needs to be transformed into a scalar optimization problem, which is a conventional optimization problem. Usually, the assignments of suitable coefficients to the corresponding scalar optimization problem are subjectively determined by the decision makers. However, these assignments may cause some biases by their subjectivity. Therefore, this paper proposes a mechanical procedure to avoid this subjective biases. We are going to formulate a cooperative game using the α -level functions of the multiple fuzzy objective functions. Under this setting, the suitable coefficients can be determined mechanically by involving the core values of the cooperative game, which is formulated using the multiple fuzzy objective functions. We shall prove that the optimal solutions of the transformed scalar optimization problem are indeed the nondominated solutions of fuzzy multiobjective optimization problem. Since the core-nondominated solutions will depend on the coefficients that are determined by the core values of cooperative game, there will be a lot of core-nondominated solutions that will also depend on the corresponding coefficients. In order to obtain the best core-nondominated solution, we shall invoke the genetic algorithms by evolving the coefficients. [ABSTRACT FROM AUTHOR]

This paper investigates the performance of a two-stage multi-criteria decision-making procedure for order scheduling problems. These problems are represented by a novel nonlinear mixed integer program. Hybridizations of three Multi-Objective Evolutionary Algorithms (MOEAs) based on dominance relations are studied and compared to solve small, medium, and large instances of the joint order batching and picking problem in storage systems with multiple blocks of two and three dimensions. The performance of these methods is compared using a set of well-known metrics and running an extensive battery of simulations based on a methodology widely used in the literature. The main contributions of this paper are (1) the hybridization of MOEAs to deal efficiently with the combination of orders in one or several picking tours, scheduling them for each picker, and (2) a multi-criteria approach to scheduling multiple picking teams for each wave of orders. Based on the experimental results obtained, it can be stated that, in environments with a large number of different items and orders with high variability in volume, the proposed approach can significantly reduce operating costs while allowing the decision-maker to anticipate the positioning of orders in the dispatch area. [ABSTRACT FROM AUTHOR]

Intuitionistic fuzzy sets aims at taking the hesitancy of an expert into account in assigning a membership degree or a non-membership degree. The direct assignment of decimal numbers for membership and non-membership degrees of an element in intuitionistic fuzzy sets is not practical. Besides, the assigned degrees are generally composed of one digit or at most two digits after dot. This problem has not been addressed as much as it deserves in the literature. The hypothesis of the paper is that the determination of proportional relationships between membership and non-membership degrees is more appropriate than the direct assignment to obtain the degrees. Proportional intuitionistic fuzzy (PIF) sets require only the proportion relations between an intuitionistic fuzzy set's parameters. The accuracy of the results obtained with multi-criteria decision-making models definitely depends on how accurately the membership degrees are determined. In this paper, we extend Combinative distance-based assessment (CODAS) method by using single-valued proportional intuitionistic fuzzy sets. We compare the proposed PIF CODAS method with ordinary fuzzy CODAS method. A cloud service provider selection problem is handled to show the validity of the proposed PIF CODAS method. Additionally, a comparative analysis and a sensitivity analysis together with a discussion are presented. [ABSTRACT FROM AUTHOR]

To establish a student-centered teaching quality assurance system in English teaching in universities, it is necessary to establish an educational philosophy of survival based on quality, achieve student-centered learning, optimize the allocation of English teaching resources, and reform evaluation standards; To address the problems in English teaching, we need to raise awareness of the construction of a "student-centered" teaching quality assurance system, carry out "student-centered" teacher training activities, and improve teachers' professional skills; At the same time, we will establish a student-centered English curriculum system, promote the reform and innovation of teaching models, establish a diversified English teaching evaluation system, and ensure the high efficiency and quality of English teaching in universities. The college English teaching quality evaluation is the MAGDM. Recently, the TODIM and MABAC technique has been employed to manage MAGDM. The interval-valued intuitionistic fuzzy sets (IVIFSs) are employed as a useful tool for portraying uncertain information during the college English teaching quality evaluation. In this paper, the interval-valued intuitionistic fuzzy TODIM-MABAC (IVIF-TODIM-MABAC) technique is built to manage the MAGDM under IVIFSs. At last, the numerical example for college English teaching quality evaluation is employed to show the IVIF-TODIM-MABAC decision technique. The main contribution of this paper is outlined: (1) the TODIM technique based on MABAC has been extended to IVIFSs based on Entropy technique; (2) the Entropy technique is employed to manage weight based on score values under IVIFSs. (3) the IVIF-TODIM-MABAC technique is founded to manage the MAGDM under IVIFSs; (4) a numerical example for college English teaching quality evaluation and some comparative analysis is supplied to verify the proposed technique. [ABSTRACT FROM AUTHOR]

Many papers have been devoted to applying fuzzy sets to algebraic structures. In this paper, based on ideals, we investigate residuated lattices from fuzzy set theory, lattice theory, and coding theory points of view, and some applications of fuzzy sets in residuated lattices are presented. Since ideals are important concepts in the theory of algebraic structures used for formal fuzzy logic, first, we investigate the lattice of fuzzy ideals in residuated lattices and study some connections between fuzzy sets associated to ideals and Hadamard codes. Finally, we present applications of fuzzy sets in coding theory. [ABSTRACT FROM AUTHOR]

Sales performance is one of the critical roles in boosting firm performance, making motivating salespeople a concern for many managers. However, few existing studies on sales performance improvement from the holistic perspective exist. Based on triadic reciprocal determinism, this paper explores the combinations of the factors that may influence sales performance. Based on matching questionnaires from 154 salespeople and their supervisors, this paper employs fuzzy set qualitative comparative analysis (fsQCA) to delve into the inherent complexity of factors influencing sales performance. The results revealed that a combination of personal (family motivation, challenge stress and hindrance stress), behavioral (adaptive selling behavior) and environmental factors (organizational innovation climate and business environment) determine sales performance. Specifically, three paths lead to high sales performance, and one path leads to non-high sales performance. Significantly, the path with an organizational innovation climate can explain high sales performance more effectively than other paths. This paper makes a valuable contribution to the literature on B2B sales literature by exploring triadic reciprocal determinism. To the best of our knowledge, this is the first fsQCA attempt to address sales performance based on Chinese samples. This paper offers an essential basis for sales managers to plan sales strategies. The sales managers could refer to the three paths leading to high sales performance to achieve sales targets. Further, the one path leading to non-high sales performance should be avoided in strategy decision-making. The paper examines different approaches to achieving high and non-high sales performance using the fsQCA method, which offers a unique and relevant perspective on B2B sales literature. [ABSTRACT FROM AUTHOR]

We propose a new concept which is a generalization of fuzzy soft subset and fuzzy soft equal. Using such notions, we will be able to consider the distributive law of fuzzy soft sets. Using the distributive law of fuzzy soft sets, we point out that the distributive law of trapezoidal fuzzy soft sets as proposed by Xiao et al. (2012) is not true. The correction will further improve further extensions of the results of Xiao et al. (2012). We will also establish the generalized distributive law of trapezoidal fuzzy soft sets along with illustrative examples. [ABSTRACT FROM AUTHOR]

Nowadays, to achieve sustainable development and avoid devastating impacts on the environment, India is making rapid and broad changes to green energy technology. In order to provide long-term energy security with lower emissions, renewable energy sources are essential. It is well known that renewable energy technologies, or RETs, have the capacity to significantly meet the demand for electricity while lowering pollution levels. The nation has set up an ecologically friendly energy route in recent years. In this paper, we apply multi-criteria decision making (MCDM) models to determine the best renewable energy technology for India. We use the MULTIMOORA model to identify the best technology under the pythagorean neutrosophic fuzzy set (PNFS) and the FUCOM to obtain the criteria weights. In this study, we investigate sources of renewable energy using the newly developed idea of the PNFS and recommend the best renewable energy source for India. [ABSTRACT FROM AUTHOR]

This paper is dedicated to defining and studying for the first time a two-fold algebra over the neutrosophic real number ring by merging the fuzzy set mapping with the algebraic operations of the neutrosophic real number ring. Also, we study the elementary algebraic properties of the defined two-fold algebra through its algebraic operations and substructures such as homomorphisms and ideals. [ABSTRACT FROM AUTHOR]

This paper is dedicated to defining and studying for the first time the concept of fuzzy metric spaces based on two-fold fuzzy algebras, where the elementary properties of this new concept will be studied and presented by many theorems and related examples that explain the validity of our work. Also, many different types of open and closed balls will be discussed, as well as the relationships between these metric substructures. Keywords: fuzzy metric space, two-fold algebra, open ball, closed ball, torus Introduction and basic concepts The applications of neutrosophic sets and fuzzy sets are very wide and open research areas. In the literature, we can find many neutrosophic and fuzzy algebraic structures with deep connection with applied mathematics and number theory [5-11]. The concept of two-fold algebra was presented by Smarandache in [4], where many suggestions for the algebraic structure related to this algebra were defined and presented. This new idea has been used in [1] to study the two-fold algebra based on the standard fuzzy number theoretical system [3]. In [2], Hatip et.al. proposed the two-fold vector space and two-fold algebraic module based on fuzzy mappings, where they have studied the elementary properties of these new generalizations with many interesting examples. This work is motivated by the modern idea of two-fold algebra, and metric spaces, where we can combine those to different structures in one algebraic structure called two-fold. [ABSTRACT FROM AUTHOR]

The transportation problem is one of the most significant mathematical programming applications that appears in various real-world decision-making problems. In an actual scenario, the supply, demand, and cost parameters of a transportation problem cannot be exactly quantified due to market instability. To deal with such types of impreciseness, the researchers have widely used fuzzy numbers and their extensions. Pythagorean fuzzy set theory is a prominent tool for handling uncertain and vague information in complex decision-making situations. This paper aims to develop a solution approach to solve the transportation problem with uncertainty in input parameters by incorporating Pythagorean fuzzy numbers. To do so, first, a new score function is proposed to rank Pythagorean fuzzy numbers more efficiently. A comparative study highlights some flaws in existing score functions, which depicts the advantages of the proposed score function over existing ones. Afterward, we solve the Pythagorean fuzzy transportation problem using the proposed score function. The solution technique is demonstrated with the help of some numerical examples. In addition, a comparative study is also included to show the efficacy of the proposed approach over existing ones. [ABSTRACT FROM AUTHOR]

This paper describes a generalized Diophantine fuzzy sets, which can be seen as a generalization of both Diophantine fuzzy sets and Pythagorean fuzzy sets. We define the basic properties of generalized Diophantine fuzzy set, as well as their relationships and distances. We compare Diophantine fuzzy sets with other Diophantine Pythagorean fuzzy sets to demonstrate their importance in the literature. We introduce new operators including necessity, possibility, accuracy function and score function. Furthermore, we discuss the new distance between normalized Euclidean distance and normalized Hamming distance. For a generalized Diophantine fuzzy relation, image and inverse image functions are defined. Numerous real-world applications can be found for the prevalent ideas of intuitionistic fuzzy sets, Pythagorean fuzzy sets, Diophantine fuzzy sets and q-rung orthopair fuzzy sets. Regretfully, these theories about the membership and non-membership grades have their own limits. We provide a new idea the generalized Diophantine fuzzy set that eliminates these limitations by including reference parameters. Compared to other kinds of fuzzy sets, there are more applications for generalized Diophantine fuzzy sets. We offer practical examples that show how different enhanced distances might be used in everyday situations. Additionally, to demonstrate the effectiveness of the suggested approach, flowchart based multi-criteria decision-making is provided and used to a numerical example. The outcomes are assessed for various parameter values. Furthermore, a comparative analysis developed to demonstrate the superiority of the suggested technique over current methodologies. [ABSTRACT FROM AUTHOR]

In this paper, first the fuzzy set and i-(m,n)-near ring then fuzzy subgroups, fuzzy (m,n)-subnear ring and finally fuzzy ideals are defined. We state and prove theorems in these cases. Also in the next chapter, normal fuzzy subnear ring expressed and theorems about normal fuzzy subnear rings is expressed and proved. [ABSTRACT FROM AUTHOR]

Belief and plausibility functions based on evidence theory (ET) have been widely used in managing uncertainty. Various generalizations of ET to fuzzy sets (FSs) have been reported in the literature, but no generalization of ET to q-rung orthopair fuzzy sets (q-ROFSs) has been made yet. Therefore, this paper proposes a novel, simple, and intuitive approach to distance and similarity measures for q-ROFSs based on belief and plausibility functions within the framework of ET. This research addresses a significant research gap by introducing a comprehensive framework for handling uncertainty in q-ROFSs using ET. Furthermore, it acknowledges the limitations inherent in the current state of research, notably the absence of generalizations of ET to q-ROFSs and the challenges in extending belief and plausibility measures to certain aggregation operators and other generalizations including Hesitant fuzzy sets, Bipolar fuzzy sets, Fuzzy soft sets etc. Our contribution lies in the proposal of a novel approach to distance and similarity measures for q-ROFSs under ET, utilizing Orthopairian belief and plausibility intervals (OBPIs). We establish new similarity measures within the generalized ET framework and demonstrate the reasonability of our method through useful numerical examples. Additionally, we construct Orthopairian belief and plausibility GRA (OBP-GRA) for managing daily life complex issues, particularly in multicriteria decision-making scenarios. Numerical simulations and results confirm the usability and practical applicability of our proposed method in the framework of ET. [ABSTRACT FROM AUTHOR]

China is at a critical moment of transforming high-speed development to high-quality development, and it is significant to improve the efficiency of green technological innovation. In this paper, under the perspective of two-stage innovation value chain, we construct the evaluation index system of green technology innovation efficiency, adopt the super efficiency SBM model to measure the green technology innovation efficiency of China's high-tech industries, and based on the results obtained, we assume the fuzzy set qualitative comparative analysis method (fs-QCA) based on the group theory to explore the complex causal mechanism and grouping paths of the interaction between enterprises, government and market that affects the green technology innovation efficiency Mechanism and group path. The study results show that (1) enterprise, government, and market are not necessary conditions to influence the efficiency of green technological innovation, and even if a particular party plays a central role, it needs the assistance of other parties. (2) The improvement of green technological innovation efficiency requires the interaction of enterprises, government, and market, and even if any party does not have the core conditions, it can still produce high green technological innovation efficiency. (3) The path of the "innovative compensation" effect is identified, which indicates that enterprises will generate a high level of green innovation efficiency under sufficient investment brought about by the enterprise scale effect and matched with a good level of economic development. (4) The market economy-led pathway suggests that when the market economy is highly developed, firms do not need environmental regulation and government support to generate efficient levels of green technological innovation. [ABSTRACT FROM AUTHOR]

Twin support vector machine (TSVM) is an effective machine learning tool for classification problems. However, TSVM classifier works on empirical risk principle only and also while training, each sample contributes equally, even if it is a noise or an outlier. It does not incorporate the uncertainties associated with data into modeling and hence its generalization ability declines. To address these issues, intuitionistic fuzzy regularized least square twin support vector machine having intuitionistic fuzzy network has been proposed in this paper. The non-parallel classifiers are obtained by solving two systems of linear equations only rather than the solution of two quadratic programming problems as in TSVM, which leads to speed up the training process. Moreover, the method follows both structural risk and empirical risk minimization principles. In order to de-escalate the effect of pollutant patterns, their contribution of the patterns into learning the decision function has been made according to their importance in the classification. The significance of the training patterns is measured in terms of intuitionistic fuzzy numbers based on their geometrical locations and surroundings. The method is further extended to find non-parallel decision planes in the feature space using nonlinear kernel function, which also gives rise to the solution of two systems of linear equations. To show the efficacy of the proposed method, computer simulations on fourteen standard and six big UCI datasets using linear and Gaussian kernels are performed and their results have been compared with well-established methods in the literature. The experimental results are represented in terms of accuracy, computational time, F-measure, sensitivity and specificity rates. The outcomes demonstrate that the proposed method outperforms the existing methods and is also feasible for big datasets. The comparison and statistical inferences using two non-parametric: Friedman and Nemenyi tests, conclude that the proposed approach is fast and yields better generalization. [ABSTRACT FROM AUTHOR]

Data envelopment analysis (DEA) is one of the widely used methods to measure the efficiency scores of decision making units (DMUs). Conventional DEA is unable to consider both uncertainty in data and decision makers' (DMs) judgments in the evaluations. This study, to address the shortcomings of the conventional DEA, proposes a new best worst method (BWM)- robust credibility DEA (BWM-RCDEA) model to estimate the efficiency scores of DMUs considering DMs' preferences and uncertain data, simultaneously. First, to handle uncertainty in input and output variables, fuzzy credibility model has been applied. Additionally, uncertainty in constructing fuzzy sets is modeled using robust optimization with fuzzy perturbation degree. In this paper, two new types of RCDEA models are proposed: RCDEA model with exact perturbation in fuzzy inputs and outputs and RCDEA model with fuzzy perturbation in fuzzy inputs and outputs. In addition, to deal with flexibility of weights and incorporating DMs' judgement into the RCDEA model, a bi-objective BWM-RCDEA model is introduced. Finally, the proposed bi-objective model is solved using min–max approach. To illustrate the usefulness and capability of the proposed model, efficiency scores of 39 distribution companies in Iran is investigated and results are analyzed and discussed. Finally, based on the results, recommendations have been made for policy makers. [ABSTRACT FROM AUTHOR]

Excessive environmental regulation can achieve environmental improvement, but it is not conducive to sustainable environmental improvement. This paper takes the “one-size-fits-all” (OFA) in the process of China’s central environmental protection inspection (CEPI) as an example to explore the occurrence mechanism from the perspective of multiple co-governance. Using the fuzzy set qualitative comparative analysis (fsQCA), we find that four distinct mechanisms can result in OFA. Based on the four distinct mechanisms, we find that even if the pollution behavior of enterprises is not serious, local governments may still adopt OFA under a combination of other conditions; non-key cities of environmental protection are more prone to OFA; giving full play to the role of public inspection is a key step to avoiding local government violations. However, the effectiveness of public environmental attention is insufficient under the dual driving force of pollution and the economy under the lack of vertical environmental regulatory pressure. [ABSTRACT FROM AUTHOR]

Due to the substantial economic and environmental repercussions of improper E-waste management and treatment, the issue has gained indispensable attention. In recent years, the research has been done about the selection of proper E-waste management methods like site selection, disposal method selection, etc. with fuzzy environments. But in real situations, the major reasons for improper e-waste management are lack of awareness and improper disposal with sustainability. In finding a sustainable awareness-creating program and disposal method for E-waste, the uncertainty and its sustainability of the information make challenges to decision makers, so the problem becomes a two-dimensional problem with uncertainty. This paper uses complex fuzzy terms to illustrate this two-dimensional uncertain information, in which amplitude term represents the uncertainty about alternative and phase term represents the uncertainty about the sustainability of an alternative. First, we present a new framework MULTIMOORA under complex fuzzy structure. Then, in order to solve two-dimensional uncertain information about E-waste, the proposed complex fuzzy-MULTIMOORA method is applied, in which E-waste awareness-creating program and treatment technology selection are done. The sensitivity and comparative analysis are further delivered to validate the effectiveness of the proposed technique. [ABSTRACT FROM AUTHOR]

This paper presents a method for improving the accuracy of determining a person's proximity to a building entrance in urban and indoor settings, where the Global Positioning System (GPS) and Wireless Fidelity (WiFi) signals are often interfered with. Fuzzy logic can be applied to variations in signal strengths in order to interpret the inverse relationship between GPS signals weakening and WiFi signals strengthening as a person approaches or enters a building. As a result, a fuzzy set for GPS signal strengths between 14 and 33 dBm and WiFi signal strengths between –68 and –31 dBm is created, separating them into weak, medium, and strong signals. By using fuzzy rules, the system can accurately determine if a user is 'far,' 'near,' or 'at' an entrance, mimicking real-life transitions from outdoor to indoor environments. The accuracy of this approach exceeded 90% based on real-world data, and it significantly improved user experience in navigation applications, particularly in cases where GPS does not work well. [ABSTRACT FROM AUTHOR]

This paper aims to present a new concept of sets known as fuzzy neutrosophic Q^*-closed sets in fuzzy neutrosophic topology. In this study, we explore and investigate more novel properties of these classes by some new definitions, theorems, and propositions. Therefore, a group of examples is presented and discussed to clarify the relationships between the new study of Q^*-closed sets with other sets. [ABSTRACT FROM AUTHOR]

With the use of cutting-edge technologies like artificial intelligence (AI), robotics, and the Internet of Things (IoT), Industry 5.0 represents a breakthrough move towards a sustainable and human-centered industrial future. Industry 5.0 endeavors to transform industries such as consumer electronics by emphasizing sustainability and collaboration, in contrast to its predecessors, who only concentrated on automation and efficiency. Along with improved manufacturing efficiency and product innovation, this change in the consumer electronics sector also redefines the human-machine interaction. This paper proposes a novel hybrid integrating model that combines the Entropy Weight Method (EWM), Best-Worst Method (BWM), and an acronym in Portuguese for Interactive Multicriteria Decision Making (TODIM) using single-valued neutrosophic trapezoidal numbers to evaluate Industry 5.0 enablers. The EWM provides objective weight for criteria, while the BWM captures the subjective preferences of decision-makers. The TODIM method ranks alternatives based on these weighted criteria using single-valued neutrosophic trapezoidal numbers, which effectively handle uncertainties and imprecise information inherent in decision-making processes. The proposed hybrid model effectively evaluates the Industry 5.0 consumer electronics sector using an empirical study emphasizing personalization, sustainability, resilience, and smart manufacturing criteria. The model enhances decision-making by balancing objective metrics with subjective preferences, thus guiding stakeholders toward informed and sustainable technological investments. The hybrid EWM-BWMTODIM method with single-valued neutrosophic trapezoidal numbers demonstrated robustness in accommodating subjective and objective criteria weights. Sensitivity analysis revealed variations in aggregation methods and values significantly influenced final rankings, emphasizing the method's adaptability and responsiveness to decision-maker preferences and environmental changes. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concepts of cubic soft (CS) algebra, CS o-subalgebra, and CS ideals within the framework of B-algebra. We provide comprehensive characterizations of these new structures, elucidating their unique properties and interrelationships. Specifically, we present detailed conditions under which a CS subalgebra can be classified as a closed CS ideal. Our analysis explores the intricate relationships among closed cubic soft ideals, cubic soft subalgebras, and cubic soft o-subalgebras. By doing so, we aim to provide a deeper understanding of how these structures interact and coexist within the broader context of B-algebra The findings offer significant insights into the application and theoretical underpinnings of cubic soft sets in algebraic systems, contributing to the ongoing evolution of fuzzy set theory and its applications in various mathematical domains. Our work not only broadens the scope of B-algebra but also enhances its utility in solving complex problems where traditional algebraic approaches may fall short. Through this exploration, we seek to advance the field and open new avenues for research and practical applications in mathematical sciences. [ABSTRACT FROM AUTHOR]

An essential and quite different class of functions is the triangular norm and its related operators (uninorms, nullnorms, and associative copulas). They are used widely in many disciplines, including fuzzy set theory, probability and statistics, decision sciences, and others. This paper proposes the notion of hybrid Ξ -norm and defines the concepts of Ξ -hybrid ideals, Ξ -hybrid h -ideals in a hemiring . Some equivalent conditions are obtained for a hybrid structure to be a Ξ -hybrid left h -ideal, and it is proved that every imaginable Ξ -hybrid left h -ideal of hemiring is a hybrid left h -ideal, but not conversely by an example. [ABSTRACT FROM AUTHOR]

This paper presents new classes of strong fuzzy negations, fuzzy implications and Copulas. It begins by presenting two theorems with function classes involving the construction of strong fuzzy negations. These classes are based on a well-known equilibrium point theorem. After that, a construction of fuzzy implication is presented, which is not based on any negation. Finally, moving on to the area concerning copulas, we present proof about the third property of copulas. To conclude, we will present two original constructions of copulas. All the above constructions are motivated by a specific formula. For some specific conditions of the variables x, y and other conditions for the function f(x), the formula presented produces strict and strong fuzzy negations, fuzzy implications and copulas. [ABSTRACT FROM AUTHOR]

An intuitionistic fuzzy set is a more generalised tool than a fuzzy set for handling unpredictability as, in an intuitionistic fuzzy set, there is scope for considering a grade of non-membership, independent of the grade of membership, only satisfying the condition that their sum is less or equal to 1. The motivation of this paper is to introduce the notion of intuitionistic type-2 fuzzy normed linear space (IT2FNLS). Here, to each vector x, we assign two fuzzy real number valued grades, one for its norm and the other for the negation of its norm. A theorem of the decomposition of the intuitionistic type-2 fuzzy norm into a family of pairs of Felbin-type fuzzy norms is established. Also, we deal with Cauchyness and convergence of sequences in the IT2FNLS. Later on, in the finite-dimensional IT2FNLS, the completeness property and compactness property are explored. Finally, we define two types of intuitionistic type-2 fuzzy continuity and examine the relations between them. [ABSTRACT FROM AUTHOR]

Since the 1970s and 1980s, significant contributions have been made by Weiss, Butnariu, Heilpern, Chitra, Subrahmanyam, and others, extending fixed-point theorems to fuzzy mappings and topological spaces. This paper provides two generalizations of two important fixed-point theorems, one provided by Butnariu and the other provided by Chitra. The first generalization ensures that, under certain conditions, an acyclic fuzzy mapping has a fixed point. The second result ensures the existence of a point in the intersection of two or more fuzzy mappings considering contractible finite dimensional ANR spaces, which is a generalization of the statement provided by Chitra. [ABSTRACT FROM AUTHOR]

With the energy revolution and the proposal of "double carbon" background, hydrogen energy with rich reserves, clean and low carbon and broad application prospects has gradually become a global hot spot. The combination of seawater hydrogen production and offshore wind power is undoubtedly the focus of research in this field. However, this new research field is not yet mature and is still in its infancy, so in order to reduce unnecessary losses, it is crucial to identify the key risks and prevent them. Secondly, the adaptability of a single model is no longer reliable for the risk assessment of this emerging field, especially the conversion from offshore wind to electric energy to hydrogen energy. Based on the above, this paper first considers the ambiguity and uncertainty of information, as well as the risk attitude of decision makers in the evaluation process, and develops a novel evaluation model. The reliability and optimization of the model are verified by sensitivity analysis and comparative analysis, and a case is introduced for practical analysis. The final results show that the key risks of hydrogen production from offshore wind power are seawater electrolysis technology, hydrogen energy storage technology and high-quality wind energy resources. The overall risk is 0.4198, which is medium risk. Decision-making managers can make targeted risk prevention to reduce losses and promote the stable operation of offshore wind power hydrogen production. [Display omitted] • Offshore wind power combined with seawater hydrogen production. • An improved model based on spherical fuzzy theory and cumulative prospect theory. • Taking China 's first large-scale offshore wind power hydrogen production project as a case study. • Key risks: seawater electrolysis technology, hydrogen storage technology and wind energy resources. • The quantitative result of the overall risk assessment was 0.4198. [ABSTRACT FROM AUTHOR]

In this paper, by integrating the advantages of multi-granulation fuzzy rough set (MGFRS) and variable precision fuzzy rough set (VPFRS), we introduce a new model of multi-granulation granular variable precision fuzzy rough set (MGVPFRS) and study its basic properties. The new model includes three basic models: optimistic, pessimistic, and compromise variable precision model, so it has better tolerance and diversity. Later, by combining MGVPFRS with traditional TOPSIS method, we propose a novel multi-criteria decision-making method (MCDM). In which, MGVPFRS is applicable to acquire criterion weights. This acquisition method is more convincing, because the criteria weights are computed, not given by experts. Finally, we apply our novel method to the challenging bone graft selection problem. Through a series of experiments and comparative analysis, the validity and reliability of our model are tested. In particular, the three strategies of optimism, pessimism, and compromise enable doctors and patients to make decisions according to their personal preferences. [ABSTRACT FROM AUTHOR]

This paper presents a thorough review of our state-of-the-art technique for enhancing dynamic grid partitioning and scheduling in multi-energy source systems. We use a hybrid approach to T-spherical fuzzy sets, combining the alternative ranking order method accounting for the two-step normalization (AROMAN) method for alternating ranking order to enable two-step normalisation with the method based on removal effects of criteria (MEREC) for eliminating criteria effects. This enables us to obtain the highest level of accuracy from our findings. To ascertain the relative importance of these criteria, we use MEREC to perform a rigorous examination of the influence that each evaluation criterion has on the outcomes of the decision-making process. In addition, we use AROMAN to provide a strong foundation for assessing potential solutions by accounting for spherical fuzzy sets to account for any ambiguity. We illustrate how our approach successfully considers several factors, such as social acceptability, technical feasibility, environmental sustainability, and economic feasibility, through the analysis of an extensive case study. Our approach provides decision-makers (DMs) with a rigorous and rational framework for assessing and choosing the best grid division and scheduling options. This is done in an effort to support the administration and design of resilient and sustainable multi-energy systems. This research contributes to the growing body of knowledge in this area by offering insights that help to direct policy, planning, and investment decisions in the shift towards more sustainable energy infrastructures. Moreover, it adds to the growing body of information on multi-criteria decision-making (MCDM) in energy system optimization. [ABSTRACT FROM AUTHOR]

Crude oil, the backbone of modern industry, holds unparalleled significance as a global energy cornerstone. Unlocking its potential hinges on effective pretreatment techniques, ensuring purity, and maximizing efficiency. This study extends the established Spherical Fuzzy Set paradigm to explore the domain of Disc Spherical Fuzzy Sets (D-SFSs) in critical decision-making for crude oil preparation. Investigating D-SFSs within the Aczel Alsina norm, the research employs comparison rules, conversion rules, and distance metrics. Primary operations of the Aczel Alsina norm in D-SFSs are examined, laying the groundwork for introducing unique aggregation operations within this framework. The paper's primary aim is to propose a hybrid method, termed MEREC-SWARA-MARCOS-D-SFSs Multiple Attribute Group Decision Making, which integrates the aforementioned aggregation procedures. A case study on crude oil pretreatment validates the effectiveness of the proposed method. Furthermore, a comprehensive comparison with CoCoSo underscores the reliability of the method. This study represents a significant stride in enhancing decision-making by providing a robust framework to tackle complex situations, particularly in the critical domain of crude oil pretreatment. [ABSTRACT FROM AUTHOR]

This study investigates the philosophical foundations of the neutrosophic set(ℕS), as first proposed by Smarandache. It clarifies the connection between single-valued ℕs and their function as a specialized subset in the larger context of Nss, particularly in the fields of science and engineering. This paper investigates neutrosophic INK-ideals(NINK-Is) within INK-algebras(INK-A) by using the notion of translation, which is positioned as an extension of intuitionistic fuzzy sets. The notion of translation neutrosophic INK-algebras(NTINK-A) is introduced and their fundamental characteristics are explored. In addition, properties associated with the translation of INK-subalgebra(INK-Ss) and INK-ideals(INK-I) are investigated, along with the dynamics of their multiplications, unions, and intersections in the context of neutrosophic INK-ideals(NINK-I). Further definitions and theorems are added in the article, providing comprehensive insights complexities of NINK-A. [ABSTRACT FROM AUTHOR]

A neutrosophic fuzzy set that generalizes the classical set is represented by a closed interval [0,1]. Let us generalize the fuzzy set to the Neutrosophic set, which is defined as three membership functions between interval]-0,1+ [. This paper examines the bird collision problem within a more grounded Neutrosophic framework. The collision between the bird and the aircraft is represented in the Neutrosophic domain as a stationary point because it occurs at a distance too great for any other auditory signal to discern. Numerous methods exist for solving the airplane problem, including a Julia set in complex numbers. Bird collisions resulting from aircraft crashes add complication. An aviation signal is utilized to avoid an accident in a bird strike or bird collision. [ABSTRACT FROM AUTHOR]

An investigation is conducted in this paper into a performance analysis of fully intuitionistic fuzzy multi-objective multi-item solid fractional transport model (FIF-MMSFTM). It is to be anticipated that the parameters of the conveyance model will be imprecise by virtue of numerous uncontrollable factors. The model under consideration incorporates intuitionistic fuzzy (IF) quantities of shipments, costs and profit coefficients, supplies, demands, and transport. The FIF-MMSFTM that has been devised is transformed into a linear form through a series of operations. The accuracy function and ordering relations of IF sets are then used to reduce the linearized model to a concise multi-objective multi-item solid transportation model (MMSTM). Furthermore, an examination is conducted on several theorems that illustrate the correlation between the FIF-MMSFTM and its corresponding crisp model, which is founded upon linear, hyperbolic, and parabolic membership functions. A numerical example was furnished to showcase the efficacy and feasibility of the suggested methodology. The numerical data acquired indicates that the linear, hyperbolic, and parabolic models require fewer computational resources to achieve the optimal solution. The parabolic model has the greatest number of iterations, in contrast to the hyperbolic model which has the fewest. Additionally, the elapsed run time for the three models is a negligible amount of time: 0.2, 0.15, and 1.37 s, respectively. In conclusion, suggestions for future research are provided. [ABSTRACT FROM AUTHOR]

The novelty of this work is that it is the first to introduce complex-valued suprametric spaces and apply it to Fractal Generation and mixed Volterra–Fredholm Integral Equations. In the realm of fuzzy logic, complex-valued suprametric spaces provide a robust framework for quantifying the similarity between fuzzy sets; for instance, utilizing a complex-valued suprametric approach, we compared the similarity between fuzzy sets represented by complex-valued feature vectors, yielding quantitative measures of their relationships. Thereafter, we establish related fixed point results and their applications in algorithmic and numerical contexts. The study then delves into the generation of fractals, exemplified by the Barnsley Fern fractal, utilizing sequences of affine transformations within complex-valued suprametric spaces. Moreover, this article presents two algorithms for soft computing and fractal generation. The first algorithm uses complex-valued suprametric similarity for fuzzy clustering, iteratively assigning fuzzy sets to clusters based on similarity and updating cluster centers until convergence. The distinctive pattern of the Barnsley Fern fractal is produced by the second algorithm's repetitive affine transformations, which are chosen at random. These techniques demonstrate how well complex numbers cluster and how simple procedures can create complicated fractals. Moving beyond fractal generation, the paper addresses the solution of mixed Volterra–Fredholm integral equations in the complex plane using our results, demonstrating numerical illustrations of complex-valued integral equations. [ABSTRACT FROM AUTHOR]

This paper's findings are related to geometric function theory (GFT). We employ one of the most recent methods in this area, the fuzzy admissible functions methodology, which is based on fuzzy differential subordination, to produce them. To do this, the relevant fuzzy admissible function classes must first be defined. This work deals with fuzzy differential subordinations, ideas borrowed from fuzzy set theory and applied to complex analysis. This work examines the characteristics of analytic functions and presents a class of operators in the open unit disk J η , ς κ (a , e , x) for ς > − 1 , η > 0 , such that a , e ∈ R , (e − a) ≥ 0 , a > − x . The fuzzy differential subordination results are obtained using (GFT) concepts outside the field of complex analysis because of the operator's compositional structure, and some relevant classes of admissible functions are studied by utilizing fuzzy differential subordination. [ABSTRACT FROM AUTHOR]

The purpose of this paper is the study of the eigenvalues of the second order fuzzy boundary value problem (FBVP). By using the (α-β)-level set of intuitionistic fuzzy numbers and Zadeh's extension principle, the FBVP is solved with the proposed method. Furthermore, a numerical example is illustrated and the advantages of the proposed approach are compared with other well-known methods such as the solutions based on the generalized Hukuhara derivative. [ABSTRACT FROM AUTHOR]

BACKGROUND: In recent times, there has been widespread deployment of Internet of Things (IoT) applications, particularly in the healthcare sector, where computations involving user-specific data are carried out on cloud servers. However, the network nodes in IoT healthcare are vulnerable to an increased level of security threats. OBJECTIVE: This paper introduces a secure Electronic Health Record (EHR) framework with a focus on IoT. METHODS: Initially, the IoT sensor nodes are designated as registered patients and undergo initialization. Subsequently, a trust evaluation is conducted, and the clustering of trusted nodes is achieved through the application of Tasmanian Devil Optimization (STD-TDO) utilizing the Student's T-Distribution. Utilizing the Transposition Cipher-Squared random number generator-based-Elliptic Curve Cryptography (TCS-ECC), the clustered nodes encrypt four types of sensed patient data. The resulting encrypted data undergoes hashing and is subsequently added to the blockchain. This configuration functions as a network, actively monitored to detect any external attacks. To accomplish this, a feature reputation score is calculated for the network's features. This score is then input into the Swish Beta activated-Recurrent Neural Network (SB-RNN) model to classify potential attacks. The latest transactions on the blockchain are scrutinized using the Neutrosophic Vague Set Fuzzy (NVS-Fu) algorithm to identify any double-spending attacks on non-compromised nodes. Finally, genuine nodes are granted permission to decrypt medical records. RESULTS: In the experimental analysis, the performance of the proposed methods was compared to existing models. The results demonstrated that the suggested approach significantly increased the security level to 98%, reduced attack detection time to 1300 ms, and maximized accuracy to 98%. Furthermore, a comprehensive comparative analysis affirmed the reliability of the proposed model across all metrics. CONCLUSION: The proposed healthcare framework's efficiency is proved by the experimental evaluation. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to identify different combinations of causal conditions (celebrity attributes) that explain our outcome: destination image. More specifically, three main research questions guide our work: (1) Which attributes should an outstanding sportsperson have to enhance the image of his/her country as a destination image? (2) Are these the same for different product categories? (3) Do tourists and residents differ? Design/methodology/approach: To this end, the fuzzy-set Qualitative Comparative Analysis (fsQCA) was used with a sample of 187 participants (105 tourists and 82 residents). Findings: Results show that some attributes of a sports celebrity are more critical than others in enhancing destination image. Those attributes of sports celebrities appearing in the intermediate and parsimonious analysis should be prioritized. This is the case of trustworthiness. Second, experience is a peripheral requirement (only appeared in the intermediate analysis). Third, attractiveness is unnecessary and an even and undesired attribute in many solutions. Fourth, when comparing tourists and residents, both groups value the role of football players, while residents also appreciate the role of marathon runners. Tennis players are the less relevant sports celebrities to build Spain's destination image. Originality/value: First, a new statistical analysis in the marketing discipline, QCA, has been used. The use of qualitative approaches to investigate destination images has been scarce. Second, the study of the role of sports celebrity endorsement on brand–place attachment has yet to be investigated. Third, studies about the role of residents in the image of a tourism destination/city are scarce. Tourists and residents must be investigated because they can benefit from sports celebrities' activities. [ABSTRACT FROM AUTHOR]