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Zadeh introduced fuzzy sets to study imprecision in real life after which many variants of fuzzy sets have been developed in literature. In this paper, new variants of fuzzy sets named Hybrid fuzzy sets and Hybrid intuitionistic fuzzy sets have been defined based on some real life scenarios where conventional fuzzy sets are not applicable for dealing Multi-Criteria Decision Making (MCDM) problems. Further, total ordering algorithms on those proposed sets based on scoring functions are defined and applied in MCDM problems where decision matrix is incomplete with respect to some criteria. The major drawback of MCDM problems is non-availability / missing of data values for some alternatives with respect to some criteria while collecting data from the experts. To overcome this, researchers infuse the missing data for one expert from the corresponding data collected from the other expert or deleting that criteria to form a single complete MCDM table. But there are situations in which decisions should be taken with single MCDM matrix with missing data points. In this paper, we have proposed a new method in which we find the unknown data from known values / other entries of the table using relative performances of the alternatives with respect to other criteria through which we attain a ranking of the alternatives of MCDM using total ordering defined on the hybrid intuitionistic fuzzy sets. Further, we proposed another method in which we obtain the score of missing values based on the scores defined on the hybrid intuitionistic fuzzy sets through which final decision / ranking is made. Finally, the applicabilities of new types of fuzzy sets and total ordering methods are established in the field of Fuzzy decision making by comparing with existing imputation methods in the literature. [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]

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]

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]

Large-scale group decision-making (LSGDM) involves aggregating the opinions of participating decision-makers into collective opinions and selecting optimal solutions, addressing challenges such as a large number of participants, significant scale, and a low consensus. In real-world scenarios of LSGDM, various challenges are often encountered due to factors such as fuzzy uncertainties in decision information, the large size of decision groups, and the diverse backgrounds of participants. This paper introduces a dual fine-tuning-based LSGDM method using an online review. Initially, the sentiment analysis is conducted on online review data, and the identified sentiment words are graded and quantified into a fuzzy data set to understand the emotional tendencies of the text. Then, the Louvain algorithm is used to cluster the decision-makers. Meanwhile, a method combining Euclidean distances with Wasserstein distances is introduced to accurately measure data similarities and improve clustering performances. During the consensus-reaching process (CRP), a two-stage approach is employed to adjust the scores: to begin with, by refining the scores of the decision representatives via minor-scale group adjustments to generate a score matrix. Then, by identifying the scores corresponding to the minimum consensus level in the matrix for adjustment. Subsequently, the final adjusted score matrix is integrated with the prospect–regret theory to derive the comprehensive brand scores and rankings. Ultimately, the practicality and efficiency of the proposed model are demonstrated using a case study focused on the purchase of solar lamps. In summary, not only does the model effectively extract the online review data and enhance decision efficiency via clustering, but the dual fine-tuning mechanism in the model to improve consensus attainment also reduces the number of adjustment rounds and avoids multiple cycles without achieving the consensus. [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]

Based on the configuration theory, this paper discusses the multiple concurrent causes and causal complex mechanisms affecting the performance differences among different new farmers. Using the fuzzy set qualitative comparative analysis method, taking 40 cases of CCTV’s “ZHI FU JING” column as samples, the paper analyzes the necessary conditions for new farmers to produce high performance by the anthefactory-variable configuration composed of human capital, social capital, psychological capital, entrepreneurial learning and entrepreneurial opportunity identification. The results show that: (1) high human capital is the necessary core condition for new farmers to produce high entrepreneurial performance, lack of high entrepreneurial learning and lack of high entrepreneurial opportunity identification is the core necessary condition for low entrepreneurial performance; (2) the driving mechanism of new farmers’ high entrepreneurial performance is divided into three paths, and the driving mechanism of new farmers’ low entrepreneurial performance is divided into two paths; and (3) the ways of inhibiting new farmers’ performance and promoting their performance are asymmetrical. [ABSTRACT FROM AUTHOR]

Lexicographic orders produce a total order over a set of fuzzy numbers by comparing several real-valued functions of each fuzzy number under consideration following a strictly hierarchical method. Lexicographic orders present advantages such as simplicity, consistency with human intuition, and power of discrimination. In this paper, we move one step forward in the search for simplicity by proposing a simplified version of lexicographic orders that focuses on the defining parameters of fuzzy numbers instead of using more complex functions as is common in the existing methodologies. More precisely, we show that two lexicographic methods described in the literature for trapezoidal and triangular fuzzy numbers are equivalent to the lexicographic order of a reorganization of the vector of defining parameters, reducing the complexity of the methods. We illustrate our approach through numerical examples and a case study about capital adequacy in the banking sector. [ABSTRACT FROM AUTHOR]

Relieving the emotions of the public through government response is an important part of government emergency management. How governments respond in different situations can avoid stimulating negative emotions during emergencies? This paper analyzes the problem from the perspective of configuration; that is, this paper explores the combined effects of multiple factors on emotions. We construct the theoretical framework "Situation-Responder-Content" from situation, responder and response content, and use the government microblogs (n= 1517) from 23 major production accidents in China for the discussion with the use of fuzzy set qualitative comparison analysis (fsQCA). According to the results, the effective response types of different agencies in emergencies are summarized. Local authorities can respond in ways that include "Measures type" and "Measures-Emotion type". Functional agencies can respond through "Measures type", "Measures-Emotion type" and "Government feature-Driven" type. This study emphasizes that government response in emergencies is a systematic process. Responsive agencies need to release effective information on the basis of fully considering the situation and other factors. Configuration analysis should also be an important direction in government response research, which is helpful to the practice of government response in emergencies. [ABSTRACT FROM AUTHOR]

Grey target decision-making, as an effective method for multi-attribute decision problems, has been applied to evaluations in various domains. However, existing grey target decision-making method fails to mitigate the inherent subjectivity of decision-makers' preferences and cannot address the dependency issues in raw data. To address these limitations, this paper proposes an extended model of grey target decision-making based on prospect theory in a dual hesitant fuzzy environment. Firstly, by referencing the positive, negative, and median expected points of each dual hesitant fuzzy decision matrix and employing the prospect theory value function for numerical transformation, a dual hesitant fuzzy prospect matrix is formed. Secondly, utilizing the projection distance and the rewardpenalty principle, the comprehensive target center distance of the decision matrix is calculated to identify the superiority or inferiority of different alternatives. Furthermore, a nonlinear model with minimal comprehensive target center distance is established based on the principle of maximum entropy to optimize attribute weights. Finally, the effectiveness and rationality of the proposed decision-making method are validated through a case study of ecological assessment in the aviation industry cluster. [ABSTRACT FROM AUTHOR]

In our paper, we continue the study of the theory of fuzzy soft sets and their properties. Based on the singular values of the corresponding matrix, we define the energy of a fuzzy soft set, as well as the λ-energy of a fuzzy soft set, allowing us to introduce an effective method for decision-making. Then, we consider the limits of the defined energies, which are essentially non-negative numerical values. The paper demonstrates through examples how the introduced method can be successfully applied to many problems containing uncertainties. Additionally, the paper includes comparisons of the introduced method with other methods addressing similar problems. [ABSTRACT FROM AUTHOR]

With the rapid development of China's economy and society, the innovation of grassroots social governance has become increasingly important. This paper constructs 35 grassroots social governance innovation samples. Using the TOE theoretical framework and a fuzzy set qualitative comparative analysis (fsQCA), this paper analyzes the joint effects and interactive relationships of multiple factors on grassroots social governance innovation performance from three dimensions: technology, organization, and environment. The research reveals that internal environmental openness is a necessary condition for achieving high innovation performance in grassroots social governance, and proposes four grouping models that affect the performance of grassroots social governance innovation. This paper explores the inner logic of grassroots social governance innovation from a histological perspective, and on this basis proposes an adaptive path to enhance the performance of grassroots social governance innovation. [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]

From the perspective of configuration, this paper takes the region of manufacturing efficiency as the explanatory variable, selects eight antecedent conditions, and applies fuzzy set qualitative comparative analysis (fsQCA) to study the paths and methods of improving manufacturing emission efficiency. The results of the study show that there are two configuration paths of carbon emission efficiency in manufacturing industry, namely, research frontier and technological innovation level and labour force structure, R&D investment, science and technology innovation level, manufacturing output value, and environmental regulation synergistic path. [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]

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]

This article presents a pioneering mathematical model, fuzzy bipolar hypersoft (FBHS) sets, which combines the bipolarity of parameters with the fuzziness of data. Motivated by the need for a comprehensive framework capable of addressing uncertainty and variability in complex phenomena, our approach introduces a novel method for representing both the presence and absence of parameters through FBHS sets. By employing two mappings to estimate positive and negative fuzziness levels, we bridge the gap between bipolarity, fuzziness, and parameterization, allowing for more realistic simulations of multifaceted scenarios. Compared to existing models like bipolar fuzzy hypersoft (BFHS) sets, FBHS sets offer a more intuitive and user-friendly approach to modeling phenomena involving bipolarity, fuzziness, and parameterization. This advantage is underscored by a detailed comparison and a practical example illustrating FBHS sets' superiority in modeling such phenomena. Additionally, this paper provides an in-depth exploration of fundamental FBHS set operations, highlighting their robustness and applicability in various contexts. Finally, we demonstrate the practical utility of FBHS sets in problem-solving and introduce an algorithm for optimal object selection based on available information sets, further emphasizing the advantages of our proposed framework. [ABSTRACT FROM AUTHOR]

In crisp graph theory, there are numerous topological indices accessible, including the Misbalance Prodeg Index, which is one of the most well-known degree-based topological indexes. In crisp graphs, both vertices and edges have membership values of 1 or 0, whereas in fuzzy graphs, both vertices and edges have different memberships. This is an entire contrast to the crisp graph. In this paper, we introduce the Fuzzy Misbalance Prodeg Index of a fuzzy graph, which is a generalized form of the Misbalance Prodeg Index of a graph. We find bounds of this index and find bounds of certain classes of graphs such as path graph, cycle graph, complete graph, complete bipartite graph, and star graph. We give an algorithm to find the Fuzzy Misbalance Prodeg Index of a graph for the model of multi-criteria decision-making is established. We present applications from daily life in multi-criteria decision-making. We apply our obtained model of the Fuzzy Misbalance Prodeg Index for the multicriteria decision-making to the choice of the best supplier and we also show the graphical analysis of our index with the other indices that show how our index is better than other existing indices. [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]

In this paper, we introduce a distance measure on single-valued neutrosophic sets by sine function which is a generalization of intuitionistic fuzzy sine distance measure. The axiom of metric on single-valued neutrosophic sets is verified and shows that the difference of distance measure from unity is a similarity measure. A new methodology for multi-attribute decision-making problems (MADM) is developed for the most common decision by the smallest measure value of the proposed single-valued neutrosophic distance measure. We further apply this distance measure to a multi-attribute decision-making problem (MADM) for student career determination in a neutrosophic environment to find the best career for suitable students. Finally, the comparison is made between the proposed distance measure and the other distance measures for the final decision chosen from the most common decisions of them. [ABSTRACT FROM AUTHOR]

Rough fuzzy clustering algorithms have received extensive attention due to the excellent ability to handle overlapping and uncertainty of data. However, existing rough fuzzy clustering algorithms generally consider single view clustering, which neglects the clustering requirements of multiple views and results in the failure to identify diverse data structures in practical applications. In addition, rough fuzzy clustering algorithms are always sensitive to the initialized cluster centers and easily fall into local optimum. To solve the above problems, the multi-view and transfer learning are introduced into rough fuzzy clustering and a robust multi-view knowledge transfer-based rough fuzzy c-means clustering algorithm (MKT-RFCCA) is proposed in this paper. First, multiple distance metrics are adopted as multiple views to effectively recognize different data structures, and thus positively contribute to clustering. Second, a novel multi-view transfer-based rough fuzzy clustering objective function is constructed by using fuzzy memberships as transfer knowledge. This objective function can fully explore and utilize the potential information between multiple views and characterize the uncertainty information. Then, combining the statistical information of color histograms, an initialized centroids selection strategy is presented for image segmentation to overcome the instability and sensitivity caused by the random distribution of the initialized cluster centers. Finally, to reduce manual intervention, a distance-based adaptive threshold determination mechanism is designed to determine the threshold parameter for dividing the lower approximation and boundary region of rough fuzzy clusters during the iteration process. Experiments on synthetic datasets, real-world datasets, and noise-contaminated Berkeley and Weizmann images show that MKT-RFCCA obtains favorable clustering results. Especially, it provides satisfactory segmentation results on images with different types of noise and preserves more specific detail information of images. [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]

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]

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]

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]

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]

Current design decision-making methods ignore the fuzzy relationship between Kansei images, and the use of constant weights reduces the accuracy of cognitive evaluation results. To solve these problems, this paper proposes a grey decision-making method for product form driven by the fuzzy relationship between Kansei images. First, according to the initial weight of the Kansei images, variable weight theory is used to determine the Kansei image variable weights of the samples, and the variable weight comprehensive evaluation results for each sample are obtained. Then, based on the correlation and angle of the Kansei images, a cobweb diagram is drawn to represent the fuzzy relationship between the Kansei images of each sample. Combined with the cobweb grey target decision-making model (CGTDM) for multiple Kansei images, decision coefficients are calculated. The decision coefficients are compared and ranked to determine the relatively optimal design reference sample. Finally, the constructed model is compared with the CGTDM for multiple Kansei images and TOPSIS. The results show that the difference coefficient of the proposed method is the largest, and it can reflect the decision-making thinking of the designers and improve the discrimination among the decision-making results to a certain extent. [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]

Atanassov's intuitionistic fuzzy sets (IFSs) are a very convenient tool for describing alternatives/options while making decisions because they make it possible to naturally represent the pros, cons, and hesitation. The IFSs have attracted a significant interest and have been applied in various fields. Of course, their use poses some challenges. One of the main challenges is the ranking of alternatives/options described by the intuitionistic fuzzy sets, to be called for brevity the intuitionistic fuzzy alternatives. This is a crucial issue, notably for the applications, for instance, in decision making. We first present in detail and analyze the benefits of a method we introduced previously (cf. Szmidt and Kacprzyk [1]). For this method, we augment the original assumptions with an additional assumption, which is justified and inherently reasonable. As a result, we obtain formulas which are better justified than those previously used as they explicitly consider the arguments in favor (pro), against (con), and hesitance. Since the intuitionistic fuzzy alternatives can not be linearly ranked, then the additional assumptions during the ranking process are necessary. We address these issues and analyze examples to clarify our new approach. We examine some other methods discussed in the literature and analyze their results, and show that the new assumptions reconcile some misconceptions raised by those other papers. [ABSTRACT FROM AUTHOR]

The integration of Distributed Energy Resources utilizing Renewable Energy Sources, Energy Storage Systems, and Information and Communication Technologies is transforming traditional energy systems into adaptable, flexible, and sustainable systems, with the Smart Grid concept playing a pivotal role. This paper surveys intelligent techniques and methods applied in various markets and applications, particularly focusing on their potential adaptation for negotiation processes in Smart Grid contexts. The negotiation mechanisms, crucial for prosumers who engage in real-time transactions, are analyzed with a focus on fuzzy logic tools, specifically q-Rung Orthopair Fuzzy Sets. These tools are evaluated for their capability to handle negotiation tasks and Multi-Criteria Decision-Making problems. The paper proposes a negotiation schema for healthcare buildings, especially hospitals, given their significant environmental impact, providing insight for future research. [ABSTRACT FROM AUTHOR]

Featured Application: The research in this paper can provide a feasible technical means for the assembly sequence optimization of aviation reducers with complex structures, effectively promote the progress of the complex assembly sequence optimization technology of aviation reducers, and realize the comprehensive evaluation of the overall assembly quality and performance index of aviation reducer products. It can be applied to the assembly control of tanks, armored vehicles, ships, and other complex equipment to improve their assembly quality. An assembly sequence evaluation is one of the most important research directions of assembly sequence planning (ASP) for complex mechanical transmission products. Currently, aviation reducers lack a multi-perspective and multi-level evaluation of their assembly sequence. The existing evaluation indicators vary. The evaluation methods have low effectiveness and poor practicability. Therefore, a comprehensive multidimensional evaluation method for complex assembly sequences is proposed in this paper. A multidimensional comprehensive evaluation of the overall assembly quality and performance indices of aviation reducer products is realized. Firstly, the main factors affecting assembly sequence planning are considered: the attributes of the basic unit parts and the cost control of the assembly process. An evaluation index system of assembly sequence planning based on the two dimensions of assembly cost and ontology is constructed. Then, according to the multidimensional evaluation index, fuzzy evaluation theory is used to establish a fuzzy set and a matrix for each dimensional evaluation index. The index weight is divided. A comprehensive evaluation model and the function of each dimension are established. After a comprehensive evaluation, the multidimensional assembly sequence evaluation method for aviation reducers is formed. Finally, the method is applied to the assembly process of the primary reducer of a helicopter's main reducer, and a comprehensive evaluation of its assembly sequence scheme is completed to verify the feasibility of the proposed method. This article constructs a complex assembly sequence evaluation method that includes 12 evaluation indicators, improves the assembly sequence planning evaluation index system of aviation reducers, and can effectively promote the progress of optimization technology for complex assembly sequences of aviation reducers. [ABSTRACT FROM AUTHOR]

Multispectral image registration is the process of aligning the spatial regions of two images with different distributions. One of the main challenges it faces is to resolve the severe inconsistencies between the reference and target images. This paper presents a novel multispectral image registration network, Multi-scale Intuitionistic Fuzzy Set Feature-guided Registration Network (IFSrNet), to address multispectral image registration. IFSrNet generates pseudo-infrared images from visible images using Cycle Generative Adversarial Network (CycleGAN), which is equipped with a multi-head attention module. An end-to-end registration network encodes the input multispectral images with intuitionistic fuzzification, which employs an improved feature descriptor—Intuitionistic Fuzzy Set–Scale-Invariant Feature Transform (IFS-SIFT)—to guide its operation. The results of the image registration will be presented in a direct output. For this task we have also designed specialised loss functions. The results of the experiment demonstrate that IFSrNet outperforms existing registration methods in the Visible–IR dataset. IFSrNet has the potential to be employed as a novel image-to-image translation paradigm. [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]

This paper presents simplest fuzzy logic controller (SFLC) PLC's based implementation applied to the cascade control strategy. Level and flow control loops are important and widely used in the oil and manufacturing industries to ensure a quality product. The control is used to maintain the level of the liquid in the tank at the desired value by manipulating the liquid in the reservoir. Two fuzzy sets on each input variable, five fuzzy sets on the output variable, five linear control rules, algebraic product bounded AND/OR operator, Larsen product inference and Centre of Sums (CoS) defuzzification are the components of this simplest nonlinear fuzzy controller to be implemented. The proposed work deals with the real implementation of a simplest fuzzy logic cascade control strategy designed on SIMATIC S7-300 Plc based on ladder diagram (LD) programming. In this paper, we have presented the results of the experimental tests of the conventional PI control strategy as well as the simplest fuzzy PI implementation applied to a PUL-2/EV cascade control device. Experimental results using this simplest fuzzy PI controller with the setpoint error shown that the setpoint tracking rise time can be reduced by 30% and the disturbance rejection time is decreased at 7sec compared to the conventional PID-PLC based controller, and concluded by stressing the importance of this new controller implementation. [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]

This document is a special issue of the journal Nonlinear Studies, featuring interdisciplinary perspectives in applied mathematics. It includes articles on consumer behavior, diffusion of innovation, numerical methods, game theory, and optimization, covering domains such as engineering, management, and physics. The papers have undergone peer review and offer original and high-quality research. The document compiles research contributions on reliability analysis, mathematical modeling, differential equations, and optimization problems, with references for further exploration. The authors express gratitude to the contributors and reviewers for their valuable contributions. [Extracted from the article]

The Spherical Neutrosophic Set is a generalization of Spherical Fuzzy Set. In this paper, we define Algebraic sum and Algebraic product of spherical neutrosophic sets (SNSs) and investigate their desirable properties. Further, we construct scalar multiplication (nA) and exponentiation (An) operations of a spherical neutrosophic sets. Finally, define a new operation(@) on spherical neutrosophic sets and discuss distributive law in the case where the operations of <8>, A and V are combined each other. Significant Statement: The important methodological problems of other analyzed theories were revealed and discussed. Many of the novel theories, such as Neutrosophic, Pythagorean, Spherical and Picture sets theories, were developed to solve interior problems of the Atanassov's intuitionistic fuzzy sets. Since the results obtained within the framework of these criticized novel theories appeared to be significantly worse than expected, in this paper, an alternative approach based on the extension of the Spherical fuzzy Sets in the framework of the Spherical Neutrosophic Sets theory is proposed. Our study is actually the study of an important type of advanced fuzzy algebraic structure. [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]

Spatial and temporal uncertainties are found in data for many critical applications. This paper describes the use of interval-based representations of some spatial and temporal information. Uncertainties in the information can arise from multiple sources in which degrees of support and non-support occur in evaluations. This motivates the use of intuitionistic fuzzy sets to permit the use of the positive and negative memberships to capture these uncertainties. The interval representations will include both simple and complex or nested intervals. The relationships between intervals such as overlapping, containing, etc. are then developed for both the simple and complex intervals. Such relationships are required to support the aggregation approaches of the interval information. Both averaging and merging approaches to interval aggregation are then developed. Furthermore, potential techniques for the associated aggregation of the interval intuitionistic fuzzy memberships are provided. A motivating example of maritime depth data required for safe navigation is used to illustrate the approach. Finally, some potential future developments are discussed. [ABSTRACT FROM AUTHOR]

The Circular Economy (CE) is receiving more attention, especially in Industry 4.0 (I4.0). In the face of several ambiguous and uncertain information, fuzzy techniques based on Fuzzy Set Theory (FST) are essential for developing CE strategies. This paper uses bibliometric methods to analyze the characteristics of the authors, nations/regions, institutions of the literature of FST and CE, and the collaborations relations between them, and then summarize the literature on fuzzy techniques in the CE and identify the specific role that FST can play in each stage of CE, its primary effects on the CE's pre-preparation stage, design and production stage, and recycling and reuse stage. Meanwhile, the paper explores the advantages of I4.0 technologies for CE and analyzes the research on the role of fuzzy techniques based on FST for CE and I4.0 technologies. Last but not least, this paper is concluded by summarizing the knowledge gained from the bibliometric and content analyses of the literature and suggesting further research directions of investigation. This research will draw attention to FST's contribution and encourage its advancement in CE and I4.0 technologies. [ABSTRACT FROM AUTHOR]

This paper introduces a novel approach to obtaining analytical solutions for fuzzy fractional differential equations in the context of weighted Caputo-type generalized Hukuhara derivatives. The paper proposes the use of non-singular kernels to improve the accuracy of fractional calculus in fuzzy space and establishes the uniqueness of solutions for fuzzy fractional differential equations. The paper also introduces the concept of fuzzy Laplace transforms to facilitate the solution of these equations. Practical examples, such as the fuzzy fractional Newton’s law of heating and cooling, are provided to demonstrate the effectiveness of the proposed method. Overall, this paper contributes to the development of practical solutions for real-world problems in fuzzy space and enhances the accuracy of fractional calculus in this context. [ABSTRACT FROM AUTHOR]

This paper investigates the complex causal relationships between various types of environmental regulatory instruments (ERI) and agri-firms' technological innovation employing fuzzy set qualitative comparative analysis (fsQCA). The study finds a well-designed set of ERI can promote technological innovation in agribusiness; control-command ERI cannot promote technological innovation in agribusiness solely, market-incentivized ERI is indispensable in promoting firms' innovation performance, implicit ERI plays an important role in promoting firms' innovation and voluntary ERI does not play a significant role in promoting firms' technological innovation. The government should coordinate among various types of ERI and improve the design of ERI to achieve a win-win situation for both economic and environmental performance in the agriculture sector. [ABSTRACT FROM AUTHOR]