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Following the devastating COVID pandemic, a new global strategy is required to switch from traditional education to blended or online learning method. Nevertheless, there is no adamant theoretical base available for such an important transition or similar situations in the future. On the other hand, educational systems encounter uncertainty as an integral part of multilayered teaching routes. To analyze the interactions among interconnected entities, soft computing methodologies can serve as an efficient tool to manage such systems with uncertain information through incorporating artificial intelligence (AI) techniques for assessing students performances. Nevertheless, the classical binary fuzzy relation and other existing theoretical models are not capable of explaining/configuring uncertain-based datum for multiplex correlations. To fill these gaps, the present study establishes a neoteric AI-base “Global Online Learning (GOL) theory” using the newly developed n-ary relation and n-ary fuzzy relation as the generalization of classical and binary fuzzy relations. Through the enhanced mathematical concepts and intelligent soft computing techniques, the convoluted multilayer relationships of entities can be punctiliously assessed for different values of n. Furthermore, a network-based perspective is proposed as a promising systematic model when systems are imperfect and prone to uncertainty. In the provided graphical context, the n-ary relation represents the hypergraph pattern, while the n-ary fuzzy relation refers to the generalized fuzzy hypergraph model. Fundamental characteristics of n-ary fuzzy relation, including reflexive, symmetric, transitive, composition, t-cut, support and Cartesian product, are systematically provided to extract mathematical interrelated expressions, as well as parametric connection between t-cut and Cartesian product. Based on the n-ary fuzzy relation, the n-ary fuzzy hyperoperation “$$\circ _{\rho }$$ ∘ ρ ” is assigned to construct fuzzy hyperalgebra as the extension of classical algebra with illustrative examples. The relationships between fuzzy hyperalgebra and hyperalgebra are investigated through the notation of $$(\circ _{\rho })_{t}$$ ( ∘ ρ ) t for $$t\in (0,1].$$ t ∈ ( 0 , 1 ] . With the introduced t-cut methodology, the corresponding hypergraph is derived to simplify the analysis of educational information. The AI-base GOL theory provides a solid gadget for learning data management, e.g., the grading evaluation of online assessments, where the evaluation of components is accomplished on real data in terms of fuzzy n-ary relation, t-cut and support through a graphical attitude. The results indicate that the AI-base GOL theory is a robust platform to meticulously manage and control uncertain-based intercorrelated information. This platform can be converted into a coding gadget for artificial intelligent educational online mega-systems.
Following the devastating COVID pandemic, a new global strategy is required to switch from traditional education to blended or online learning method. Nevertheless, there is no adamant theoretical base available for such an important transition or similar situations in the future. On the other hand, educational systems encounter uncertainty as an integral part of multilayered teaching routes. To analyze the interactions among interconnected entities, soft computing methodologies can serve as an efficient tool to manage such systems with uncertain information through incorporating artificial intelligence (AI) techniques for assessing students performances. Nevertheless, the classical binary fuzzy relation and other existing theoretical models are not capable of explaining/configuring uncertain-based datum for multiplex correlations. To fill these gaps, the present study establishes a neoteric AI-base “Global Online Learning (GOL) theory” using the newly developed n-ary relation and n-ary fuzzy relation as the generalization of classical and binary fuzzy relations. Through the enhanced mathematical concepts and intelligent soft computing techniques, the convoluted multilayer relationships of entities can be punctiliously assessed for different values of n. Furthermore, a network-based perspective is proposed as a promising systematic model when systems are imperfect and prone to uncertainty. In the provided graphical context, the n-ary relation represents the hypergraph pattern, while the n-ary fuzzy relation refers to the generalized fuzzy hypergraph model. Fundamental characteristics of n-ary fuzzy relation, including reflexive, symmetric, transitive, composition, t-cut, support and Cartesian product, are systematically provided to extract mathematical interrelated expressions, as well as parametric connection between t-cut and Cartesian product. Based on the n-ary fuzzy relation, the n-ary fuzzy hyperoperation “$$\circ _{\rho }$$ ∘ ρ ” is assigned to construct fuzzy hyperalgebra as the extension of classical algebra with illustrative examples. The relationships between fuzzy hyperalgebra and hyperalgebra are investigated through the notation of $$(\circ _{\rho })_{t}$$ ( ∘ ρ ) t for $$t\in (0,1].$$ t ∈ ( 0 , 1 ] . With the introduced t-cut methodology, the corresponding hypergraph is derived to simplify the analysis of educational information. The AI-base GOL theory provides a solid gadget for learning data management, e.g., the grading evaluation of online assessments, where the evaluation of components is accomplished on real data in terms of fuzzy n-ary relation, t-cut and support through a graphical attitude. The results indicate that the AI-base GOL theory is a robust platform to meticulously manage and control uncertain-based intercorrelated information. This platform can be converted into a coding gadget for artificial intelligent educational online mega-systems.
The manufacturing industry has always been in the dominant position in the development of China’s national economy. The present industrial structure and development mode of the manufacturing industry are in a critical transformation period. This study aims to explore the problems in the management of manufacturing enterprises in the era of big data. Supplier management is the top priority of manufacturing enterprise management. Regarding the performance appraisal of manufacturing enterprises, the management data of large manufacturing enterprises are collected by questionnaire. 226 questionnaires are issued, and 203 valid questionnaires are collected. The performance appraisal management of manufacturing enterprises is analyzed based on the analytic hierarchy process (AHP) of fuzzy multicriteria decision-making, and the evaluation system of enterprise performance management is established. The results show that the average value of the four indexes of enterprise marketing management, enterprise research and development (R&D) support, enterprise R&D achievement transformation efficiency, and enterprise production innovation is higher than 3.731, indicating that large manufacturing enterprises quite support marketing, R&D, and production innovation. This exploration can provide a theoretical basis for improving the management innovation ability of manufacturing enterprises and also has great reference value for expanding the market competitiveness of manufacturing enterprises.
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