Artificial Intelligence (AI) tools, i.e., ChatGPT (Chat Generative Pre-Trained Transformer), are positively and negatively revolutionizing the culture of industries, science, and education. The main objectives of this study are to address uncertainty and vagueness in ChatGPT systems, apply bipolarity as two-sided states of data, model generalized graph-based network with derivations, develop bipolar multi-dimensional fuzzy relation, advance entropy metrics for quantifying ambiguity, cluster entities based on level cuts, present pattern recognition in terms of statistical correlation coefficient, analyze speech recognition framework, and schedule online surgeries on the basis of blockchain technology. The outlined innovation pinpoints on the self-evaluation of ChatGPT systems, merging the bipolarity and generalized fuzzy hypergraph approach, developing the interpretation of graph-based patterns, and benchmarking the AI analysis and metrics advancement. To assess the efficiency of AI bipolar generalized fuzzy hypergraph (BGFH) model, the key conceptual benchmarks are clustering technique for detecting patterns and similar groups of data, statistical methods for the analysis of pattern recognition, and entropy metrics for quantifying the fuzziness within a system. This layout furnishes important characteristics such as union, intersection, complement, homomorphism, isomorphism, verifying the overlapping (intersection) and complement of two strong BGFHs as a strong BGFH. In addition, certain specifications of reflexive, symmetric, transitive, overlapping and integration, are defined using bipolar multi-dimensional fuzzy relation. Eleven classes are derived based on different values within \(t\in [0,1]\) and \(s\in [-1,0],\) classifying analogous data that aids the similarity detection of generated outputs. Through this approach, a new pattern recognition is used as a data evaluation technique to intelligently facilitate the process in terms of correlation coefficient. It is revealed that the highest magnitude of 0.145 is adopted for patterns \(C_{1}\) and D, indicating the most positive correlation between patterns, while patterns \(C_{4}\) and D with the value of \(-0.35\) are negatively correlated. The results verify that the entropy measure of visual data (0.75) is higher than the entropy measure of textual data with the value of 0.68, indicating more vagueness and ambiguity in visual generated systems. The corresponding textual data \(E^{P}(U)\) and \(E^{N}(U)\) are, respectively, calculated as 0.62 and 0.45 for human-created contents and ChatGPT-generated contents, whilst for visual data, the entropy measures \(E^{P}(U)\) and \(E^{N}(U)\) are, respectively, 0.25 and 0.66, showing the higher values for the entropy measure of ChatGPT-generated visual data compared to the ChatGPT-generated textual data. In relation to the speech recognition analysis, the highest human performance degree is affiliated to word “a” (0.89), while the lowest degree belongs to word “i” (0.81). The highest AI performance degree is allocated to word “it” \((-0.7),\) and the lowest degree is affiliated to word “the” \((-0.88).\) The overall entropy measure is calculated by 0.23, and the entropy measure of AI-based data is 0.35, on the other hand, the entropy measure of human-based data is equal to 0.29, representing higher vagueness for AI-based data. According to the obtained results in surgical case scheduling, the bipolar value of \((0.9,-0.1)\) is allocated to the surgeon who has the highest positive performance (0.9) and the lowest negative performance \((-0.1);\) this indicates the superior overall performance \((\lambda _{a}=0.8)\) of the leader during the AI blockchain robotic colon surgery. The worst overall performance (0.22) is allotted to the surgeon, who is required to be removed from the surgery team by the leader physician. The outcomes are validated by a comparative analysis with respect to the classical bipolar fuzzy graph and bipolar fuzzy hypergraph, and NLP (natural language processing) approaches.

Graph theoretic techniques have been widely applied to model many types of links in social systems. Also, algebraic hypercompositional structure theory has demonstrated its systematic application in some problems. Influenced by these mathematical notions, a novel semihypergroup-based graph (SBG) of $G=⟨H,E⟩$ is constructed through the fundamental relation ${\gamma }_n$ on $H,$ where semihypergroup H is appointed as the set of vertices and E is addressed as the set of edges on SBG. Indeed, two arbitrary vertices x and y are adjacent if $x{\gamma }_{n}y.$ The connectivity of graph G is characterized by $x{\gamma }^{*}y,$ whereby the connected components SBG of G would be exactly the elements of the fundamental group $H/{\gamma }^{*}.$ Based on SBG, some fundamental characteristics of the graph such as complete, regular, Eulerian, isomorphism, and Cartesian products are discussed along with illustrative examples to clarify the relevance between semihypergroup H and its corresponding graph. Furthermore, the notions of geometric space, block, polygonal, and connected components are introduced in terms of the developed SBG. To formulate the links among individuals/countries in the wake of the COVID (coronavirus disease) pandemic, a theoretical SBG methodology is presented to analyze and simplify such social systems. Finally, the developed SBG is used to model the trend diffusion of the viral disease COVID-n in social systems (i.e., countries and individuals).

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 developedn-ary relation andn-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, then-ary relation represents the hypergraph pattern, while then-ary fuzzy relation refers to the generalized fuzzy hypergraph model. Fundamental characteristics ofn-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 betweent-cut and Cartesian product. Based on then-ary fuzzy relation, then-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 introducedt-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 fuzzyn-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.