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In the context of globalization, cross-border data circulation has brought many challenges to international investment law. Based on fuzzy theory, this paper constructs the affiliation function of cross-border data flow for the fuzzy set of international investment law based on fuzzy theory statistical experiment strategy, then establishes the fuzzy numerical analysis method, and uses the entropy weight method to strengthen the connection between the weights and the initial data for the problem that the index weights are not objective enough. The entropy-weight-based fuzzy numerical analysis method will then study the privacy risk, management risk, and strategic risk brought by cross-border data growth to international economic cooperation. From 2010 to 2019, the privacy risk of cross-border flowing data increased by 32.16% on average, the management risk increased by 37.84% on average, and the strategic risk increased by 167.31% on average. Although none of these 3 risk assessments have yet exceeded 50%, they still challenge major economies to balance the regulation of cross-border data security and promote capital cooperation and circulation. Faced with the challenges brought by cross-border data flow, countries should start by improving international investment agreements and enhancing international consensus, take advantage of the advantages of large data resource countries, and promote the establishment of new rules for cross-border data flow.

This paper utilizes the fuzzy numerical analysis method to display the customary activities using rich artistic elements and stylistic changes so that the value and quality of the works can be significantly improved. Folk art influences are divided by nature, adjacent structure weights are estimated, the scale of matrix elements is evaluated, and the art design vector is adjusted. Comprehensively evaluate and assign art design factors, establish the fusion judgment set and fuzzy evaluation matrix, and complete the research on the fusion of folk art elements and art design by adopting the principle of maximum affiliation. According to fuzzy numerical analysis, the fusion score is 0.9, the overall art design aesthetics is improved, and the fusion effect is better.

This paper describes the complexity and uncertainty of traditional culture and kindergarten drama and evaluates the impact on the integration by providing a reasonable measure of the degree of fuzziness of the fuzzy numerical analysis algorithm. Using the affiliation function for traditional culture and kindergarten theater for measurement, the fuzzy set affiliation function curve determines the corresponding element of the center of gravity of the theater, and that traditional culture element is used as the exact output value. It was found that the proportion of kindergarten drama education activities in appreciating drama works accounted for 56.75%, and the corresponding standard deviation in feeling traditional culture was the highest at 3.916. The importance of drama education activities with traditional culture as a carrier in the core literacy of young children cannot be ignored.

Compared with traditional monolithic carbide ceramics, Cu-based composite ceramics have the advantages of higher hardness, good wear resistance and oxidation resistance and are a new type of structural ceramics with wide application prospects. This paper first proposes a novel bi-directional freezing technique to construct a three-dimensional long-range ordered layer network hierarchical structure based on the pressure infiltration process. Secondly, a composite finite element model based on fuzzy numerical analysis is proposed for the vibroacoustic analysis of the periodic composite coupled system (PCSAS). Finally, thermal analysis experiments and mechanical property tests verify the effectiveness of Cu-based composites applied to ceramic matrices. The experimental results show that the toughness of Cu-based composite ceramics increases with the increase of TiC content, and the toughness increases from 2.15±0.27Mpa.m to 4.21±0.25Mpa.m compared with that of conventional monolithic carbide ceramics. The Cu-based composite ceramics designed in this paper give full play to the advantages of the high strength of ceramic particles and high toughness of metal matrix and develop an effective method to prepare structural metal-ceramic composites. This paper has developed an efficient route for preparing structural metal-ceramic composites, which can provide a reference for materials researchers to develop high-toughness composite ceramics.

Multi-state components, common cause failures (CCFs) and data uncertainty are the general problems for reliability analysis of complex engineering systems. In this paper, a method incorporating fuzzy probability and Bayesian network (BN) into multi-state systems (MSSs) with CCFs is proposed. In particular, basic theories of multi-state BN and fuzzy probability are developed. Moreover, a model integrating CCFs with BN has also been illustrated. In order to incorporate fuzzy probability into MSSs reliability evaluation considering common parent node generated by CCFs, fuzzy probability has to be translated into accurate probability through defuzzification and normalization methods which are both elaborated. In addition, quantitative analysis based on BN is carried out. In this paper, feed system of boring spindle in computer numerical control machine is analyzed as an example to validate the feasibility of the proposed method. It can improve the ability of BN on reliability evaluation of complex system with uncertainty issues.

In this paper, we present a fuzzy PID control system as a combination of a fuzzy PID controller and a fuzzy control process, which is represented by a fuzzy control differential equation in linear form. We use the concepts of the generalized Hukuhara differentiability and the fuzzy integral of fuzzy-valued functions to study some qualitative properties for this system in the space of fuzzy numbers. We also study the existence and uniqueness result for solutions of fuzzy PID control differential equations under some suitable conditions. A number of examples are also provided to illustrate the results of the theory.

Chaotic systems are hard to synchronize, and no general solution exists. The presence of hidden attractors makes finding a solution particularly elusive. Successful synchronization critically depends on the control strategy, which must be carefully chosen considering system features such as the presence of hidden attractors. We studied the feasibility of fuzzy control for synchronizing chaotic systems with hidden attractors and employed a special numerical integration method that takes advantage of the oscillatory characteristic of chaotic systems. We hypothesized that fuzzy synchronization and the chosen numerical integration method can successfully deal with this case of synchronization. We tested two synchronization schemes: complete synchronization, which leverages linearization, and projective synchronization, capitalizing on parallel distributed compensation (PDC). We applied the proposal to a set of known chaotic systems of integer order with hidden attractors. Our results indicated that fuzzy control strategies combined with the special numerical integration method are effective tools to synchronize chaotic systems with hidden attractors. In addition, for projective synchronization, we propose a new strategy to optimize error convergence. Furthermore, we tested and compared different Takagi–Sugeno (T–S) fuzzy models obtained by tensor product (TP) model transformation. We found an effect of the fuzzy model of the chaotic system on the synchronization performance.

Intuitionistic fuzzy competition graph as a generalization of competition graph is introduced. In this paper, two generalizations of intuitionistic fuzzy competition graphs as intuitionistic fuzzy k -competition graphs and p -competition intuitionistic fuzzy graphs are introduced. Also, intuitionistic fuzzy neighbourhood graphs, m -steps intuitionistic fuzzy competition graphs are defined and investigated many interesting results. A very appropriate application of intuitionistic fuzzy graph in ecosystem is discussed to highlight the importance and use of intuitionistic fuzzy graph in real life.

Sylvester Matrix Equations (SME) play a central role in applied mathematics, particularly in systems and control theory. A fuzzy theory is normally applied to represent the uncertainty of real problems where the classical SME is extended to Fully Fuzzy Sylvester Matrix Equation (FFSME). The existing analytical methods for solving FFSME are based on Vec-operator and Kronecker product. Nevertheless, these methods are only applicable for nonnegative fuzzy numbers, which limits the applications of the existing methods. Thus, this paper proposes a new numerical method for solving arbitrary Trapezoidal FFSME (TrFFSME), which includes near-zero trapezoidal fuzzy numbers to overcome this limitation. The TrFFSME is converted to a system of non-linear equations based on newly developed arithmetic fuzzy multiplication operations. Then the non-linear system is solved using a newly developed two-stage algorithm. In the first stage algorithm, initial values are determined. Subsequently, the second stage algorithm obtains all possible finite fuzzy solutions. A numerical example is solved to illustrate the proposed method. Besides, this proposed method can solve other forms of fuzzy matrix equations and produces finite fuzzy and non-fuzzy solutions compared to the existing methods.

Nowadays, many inventory practitioners give special attention to green inventory problems incorporating carbon emission issues throughout the world. In this study, a green inventory model is considered where the demand rate depends on selling price, stock and green concern level. The holding cost is considered a quadratic function of time, and preservation technology has been utilized to control carbon emissions. First of all, a profit maximization crisp model is developed. Then, due to market flexibility, the demand rate assumes uncertainty in nature, where the concept of membership value and nonmembership value exists. So, a fuzzy model is developed where the demand rate is assumed to be a pentagonal intuitionistic dense fuzzy number. A novel defuzzification technique and a solution algorithm have been presented to solve the proposed model. In the numerical illustration, a comparative study is given among crisp and other fuzzy environments. For numerical computation, LINGO 18.0 software has also been utilized. Findings reveal that the green concern is a vital factor for model optimization under uncertain system. Finally, graphical illustration and sensitivity analysis have been made to justify the proposed model.