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Abstract Fuzzy rough set models are useful tools for dealing with fuzzy and real-valued data. They have been used in many real-world applications. In this paper, we investigate the fuzzy rough set model based on triangular norms and fuzzy implications. First, we extend some results in the published literature by removing the condition that is the continuity of triangular norms, and obtain more general conclusion about fuzzy upper approximation operators. Then, for the fuzzy neighborhood and the fuzzy lower approximation operator based on fuzzy implications, we investigate their characterization with each other. Finally, we establish the relationships between fuzzy rough sets and fuzzy topology. In this work, researches on the properties of fuzzy rough sets based on triangular norms which need not be continuous provide generalization results for fuzzy rough set theory from viewpoint of mathematics.

The complementary dual of entropy is termed “knowledge measure” in recent studies concerning fuzzy and intuitionistic fuzzy sets. A picture fuzzy set is an extended and generalized form of fuzzy and intuitionistic fuzzy sets. The broader perspective of the picture fuzzy set inculcated the possibility of the formulation of a picture fuzzy knowledge measure and its potential implications. In this paper, we set up an axiomatic framework for obtaining a complementary dual of the picture fuzzy entropy. Subsequently, we derive two new knowledge measures that strictly follow the axiomatic requirements. Some empirical investigations establish the advantages of our proposed knowledge measure over the existing measures. We also present a novel multiple attribute decision-making (MADM) algorithm, wherein the proposed knowledge measure computes attribute weights and exhibits encouraging performance. The comparative analysis shows the potential implications and advantages of the proposed measures.

Abstract Background By analyzing 23 evaluation indicators included in 14 national basic public health service programs in a region of Hohhot City, Inner Mongolia Autonomous Region, China, the performance of basic public health services in the region in 2021 were analyzed to clarify the implementation and conduct of relevant programs. We also use this study as a basis to radiate the work of municipal basic public health services centered on the region and the outstanding problems reflected and to provide theoretical contents and suggestions that can be referred to for the same regions in central and western China as well as worldwide. Methods Using the TOPSIS method as the basis for the data analysis method, the evaluation indexes are ranked in terms of their proximity to the idealized target, and combined with the entropy value method, Technique for order preference by similarity to an ideal solution (TOPSIS) and rank-sum ratio (RSR) were used to rank 14 basic health care providers by grade. A comprehensive evaluation of the performance of basic public health services in a region of Hohhot City, Inner Mongolia Autonomous Region in 2021 was conducted through a joint model of entropy -weighted TOPSIS and RSR, making full use of the characteristics and advantages of the fuzzy joint, and conducting a comprehensive analysis from the perspective of the ratio weight and the method of graded calculation, making the study more distinguishable and measureable. Results In this study, for the regional basic public health services, a total of 23 evaluation indicators of basic public health service projects were included, among which the top three indicators with the weight of the entropy value method indicators were found to include the rate of Chinese medicine health management for the elderly, the rate of health management for the elderly, and the BCG vaccination rate after the analysis of the weight of the indicators; After the entropy-weighted TOPSIS evaluation showed that the Ci values of the regions were found to be between 0.378 and 0.715 through the calculation of the positive and negative ideal values of each indicator; RSR staging method evaluation showed that three community health centers (X2, X10, X12) had excellent evaluations of basic public health services; The number of evaluations as poor and moderate are 2 (X3, X9) and 9 (X1, X4, X5, X6, X7, X8, X11, X13, X14), respectively; Finally, the results of the entropy-weighted TOPSIS method and the fuzzy joint model of RSR staging method are basically consistent with the overall trend of the above two methods, and the reliability and credibility of the research results are high. Conclusion The entropy-weighted TOPSIS and RSR joint model can evaluate the effectiveness of basic public health services in a more comprehensive and holistic way. The results of the RSR staging results and the related weight ratio analysis show that the basic public health service programs in Hohhot, Inner Mongolia Autonomous Region are relatively balanced, but there are some differences; The same genus of elderly Chinese medicine health management rate, health management rate of the elderly, BCG vaccination rate several indicators accounted for a higher weight, its correlation with the key population-related items is high, suggesting that the future key population health service items should be focused on, and future research should be suggested from two key research.

The best way to achieve sustainable construction is to choose materials with a smaller environmental impact. In this regard, specialists and architects are advised to take these factors into account from the very beginning of the design process. This study offers a framework for selecting the optimal sustainable building material. The core goal of this article is to depict a novel structure of a neutrosophic soft expert set hybrid called an interval-valued neutrosophic soft expert set for utilization in construction supply chain management to select a suitable supplier for a construction project. This study applies two different techniques. One is an algorithmic technique, and the other is set-theoretic. The first one is applied for the structural characterization of an interval-valued neutrosophic expert set with its necessary operators like union and OR operations. The second one is applied for the construction of a decision-making system with the help of pre-described operators. The main purpose of the algorithm is to be used in supply chain management to select a suitable supplier for construction. This paper proposes a new model based on interval-valued, soft expert and neutrosophic settings. In addition to considering these settings jointly, this model is more flexible and reliable than existing ones because it overcomes the obstacles of existing studies on neutrosophic soft set-like models by considering interval-valued conditions, soft expert settings and neutrosophic settings. In addition, an example is presented to demonstrate how the decision support system would be implemented in practice. In the end, analysis, along with benefits, comparisons among existing studies and flexibility, show the efficacy of the proposed structure.

Fuzzy systems of equations often appear while modeling physical systems with imprecisely defined parameters. Many mathematical methods are available to investigate them, but handling them is challenging due to the computational complexity and difficult implementation. As such, in this paper, the Inner-Outer Direct Search (IODS) optimization technique is extended in the fuzzy environment to solve a fuzzy system of nonlinear equations. The main purpose of the extension is to study the system variables in the presence of fuzzy information. To manage fuzziness, a fuzzy parametric form is employed in the uncertain system and controls the search process toward the optimal solution. The proposed approach of fuzzy IODS converts the fuzzy system of nonlinear equations to an unconstrained fuzzy optimization problem. Then, the unconstrained fuzzy optimization problem is studied through the IODS technique. To solve the unconstrained fuzzy optimization problem, the fuzzy objective function is minimized with the help of exploratory and pattern search approaches. These searches are performed with inner and outer computations. Then, the obtained united solution provides the desired solution which minimizes the objective function. From the same the uncertain system, variables are derived. To verify the solution and proposed algorithm, convergence analysis is performed. Three case studies are considered with only fuzzy and fully fuzzy systems, and various cases are discussed. A comparison with other methods is made to test the efficacy of the method. The proposed algorithm is coded with the help of MATLAB software, and the results are analyzed graphically. Finally, the simple procedure and computationally efficient approach may help to implement the same in many engineering and science problems that can be modeled into systems of equations.

As the increasing environmental issues, various companies have take initiatives to produce green products or to select green suppliers which maximize the business performance and minimize the environmental pollution. The real numbers data have imbiguity and uncertainty due to described by classical tools. Therefore, we consider a new type of fuzzy set, fuzzy credibility rough sets. In fuzzy credibility rough set has credibility membership of positive membership and they reduced the imbiguity in data information. In this paper we have defined a new set called fuzzy credibility rough set (FCRS), after that we defined Frank operational laws for FCRS information. Using these operational laws, we defined a series of aggregation operators that is fuzzy credibility Frank rough weigthed averaging aggregation operators, fuzzy credibility Frank rough ordered weigthed averaging aggregation operators, fuzzy credibility Frank rough hybrid weigthed averaging aggregation operators and its basic properties like boundedness, monotonicity and idempotency.As there is no work which is based on Frank norms aggregation operators under FCRS information. So, we defined a series of aggregation operators that can help us to collect the data for various green suppliers management.We developed a new set called fuzzy credibility rough set (FCRS). We developed a new Frank norms operational laws under FCRS information. We developed a series of aggregation operators. We developed and extend various steps of GRA, VIKOR and TOPSIS method under FCRS information. We explained the application of our proposed work to a real life decision making problem (green supplier management).All the proposed work is to applied to real life decision making problems (green supplier management) to find the best optimal result. Firstly we can collect the data from the decision makers using the proposed aggregation operators and then we applied all the steps of developed method to find the solution in case of green supplier management.

The integration of industry and education is an effective way to optimize the structure of talent training and promote the transformation of scientific and technological achievements. The improvement of traditional education quality can be promoted by promoting digital reform as a national strategic goal. The teaching model of industry-education integration for sports talents is built on the axis of co-creation and the SECI knowledge creation model in this paper. Finally, with the perspective of ecosystem theory, the factors influencing the integration of the university sports industry and education are screened from the three levels of the main body of industry-teaching integration, environment, and mechanism. The fuzzy set and evaluation laboratory method (DEMATEL) are comprehensively applied to determine the importance degree and hierarchical structure of the factors influencing the integration of university sports production and education so as to propose the strategy of digital teaching to deepen the integration of university production and education. The results of the study show that student benefit acquisition and the motivation of industry-teaching integration are 1.9650 and 2.2157, respectively, and the correlation coefficient of the two is 0.537. That is to say, for every level of university sports industry-teaching integration, the level of university sports professional talent cultivation will increase by 0.537 points. This study provides a basic theoretical basis for the subsequent construction of a collaborative training model for sports talent in the context of university industry-teaching integration and the exploration of collaborative paths.

This article analyzes the impact of the Internet on college students’ reading habits and preferences, emphasizing that short reading, micro-reading, and miscellaneous reading have become trends. The article discusses the intelligent transformation of libraries, proposes strategies such as enhancing resource publicity, strengthening academic resource construction and providing personalized services, and analyzes the effect of brilliant reading promotion assessed by WeChat Communication Index (WCI). The results show that reading speed in the virtual reality environment is significantly faster than in the traditional environment, but deep comprehension takes longer. The time spent by mobile college students on entertaining videos, WeChat public numbers, etc. reached a ratio of 0.6740 and 0.5637. PC students spent more time on professional academic journals, academic MOOC videos, etc. The results of the WCI index for March-September 2022 showed that the WCI before the beginning of the school year was 176.23, and the highest in the middle of the semester reached 387.63, which proved the effectiveness of the intelligent transformation of the Library. The article demonstrates college students’ new trend of reading behavior in the Internet era and the effectiveness of Library coping strategies.

As society requires a deeper understanding and demand for the actual abilities of students in higher education institutions, traditional assessment tests no longer meet the current needs. This paper first divides assessment techniques into two main categories from an application perspective: assessment of student learning performance and in-depth cognitive diagnosis. Students are automatically provided with appropriate learning content based on their ability level and learning style, providing them with accurate and timely feedback. Secondly, a new fuzzy inference model is proposed to determine students’ student outcomes by addressing the obvious shortcomings of the fuzzy sets usually used for student outcome assessment. Finally, the validity and usefulness of its assessment model are verified by the student learning performance on a real data set. The results show that the fuzzy inference assessment model designed in this paper can obtain an assessment accuracy of 85.8% for the learner’s learning outcomes, which has a good assessment effect. And the fuzzy inference assessment model also retains the greatest advantage of linear fitting regression, which reflects the correlation between the parameters of students’ learning behaviors and the final learning outcomes. The assessment method based on the fuzzy inference model predicts learners’ learning risks and provides learning interventions in advance for smart learning, and also provides new ideas for deepening education reform.

This paper introduces the concept of dominance degree in ecology and constructs a model of the dominant degree of inbound tourism flow gathering and dispersal in Chinese provinces and cities along the Belt, and Road advocated based on the optimization of the entropy value method. In order to further analyze the model, the obtained tourism flow gathering and dispersal dominance degrees are first integrated into a fuzzy set of tourism flow gathering and dispersal dominance degrees. The natural sequence of fuzzy numbers is obtained by screening the fuzzy set, and the fuzzy indexes are obtained after the distribution fuzzy calculation, and finally, the evaluation model of tourism flow gathering and dispersal advantage degree is constructed based on the index matrix and the combination assignment method. After analysis, it is obtained that the inbound tourism distribution of Chinese provinces and cities along the route from 2005 to 2020, the fourth tier of provinces and cities increased, the proportion by 41.02%, the number of the third tier decreased, the proportion decreased to 29.33%, and the uneven distribution of the advantage of inbound tourism distribution was strengthened.

A fuzzy parameterized neutrosophic hypersoft expert set (FpNHse-set) is one of the family members of fuzzy parameterized structures and a valuable extension of the neutrosophic soft expert set as well as the neutrosophic hypersoft set. This structure involves a multi-argument approximate function that has the ability to change the sub-characteristic pairs in the form of power set of universe. The main function of this structure is the classification of each character into sub-characteristic valued sets. Due to this prominent property, this mathematical structure is useful for uncertainties and also helps make the decision-making process more adaptable and dependable. By using the algebraic and basic ideas of the FpNHse-sets, a useful strategy, especially for medical diagnosis, known as Sanchez’s method has been used in this study. To see a reformed process for the medical diagnosis of heart disease, a useful combination of FpNHse-set and a modified Sanchez’s method has been made in this context. By using the real data from the Cleveland data set for heart disease, the implementation of the reform process has been made to see its veracity. Finally, a clear comparison of the used study with its existing studies has been made for the purpose of benefits.

A new area of research called intuitionistic fuzzy soft expert set is expected to overcome the drawbacks of an intuitionistic fuzzy soft set in terms of eligibility for soft expert-argument approximate function. This type of function views the power set of the universe as its co-domain and the cartesian product of attributes, experts, and their opinions as its domain. The domain of this function is larger as compared to the domain of a soft approximation function. It can manage a situation in which several expert opinions are taken into account by a single model. For the soft expert-argument approximate function with intuitionistic fuzzy setting, concepts such as set inclusion, [Formula: see text]-convexity(concave) sets, strongly [Formula: see text]-convexity (concave) sets, strictly [Formula: see text]-convexity (concave) sets, convex hull, and convex cone are conceived in this paper. Some set-theoretic inequalities are established with generalized properties and results on the basis of these specified notions. Additionally, by using a theoretic cum analytical approach, various elements of computational geometry, such as convex hull and convex cone, are theorized and some pertinent results are generalized.

In this study, we investigate a possible relationship between fuzzy differential subordination and the theory of geometric functions. First, using the Al-Oboudi differential operator and the Babalola convolution operator, we establish the new operator BS α , λ m , t : A n → A n in the open unit disc U. The second step is to develop fuzzy differential subordination for the operator BS α , λ m , t . By considering linear transformations of the operator BS α , λ m , t , we define a new fuzzy class of analytic functions in U which we denote by T ϝ λ , t (m , α , δ) . Several innovative results are found using the concept of fuzzy differential subordination and the operator BS α , λ m , t for the function f in the class T ϝ λ , t (m , α , δ) . In addition, we explore a number of examples and corollaries to illustrate the implications of our key findings. Finally, we highlight several established results to demonstrate the connections between our work and existing studies. [ABSTRACT FROM AUTHOR]