The primary objective of this paper is to develop a new method for root-finding by combining forward and finite-difference techniques in order to provide an efficient, derivative-free algorithm with a lower processing cost per iteration. This will be accomplished by combining forward and finite-difference techniques. We also detail the convergence criterion that was devised for the root-finding approach, and we show that the method that was recommended is quintic-order convergent. We addressed a few engineering issues in order to illustrate the validity and application of the developed root-finding algorithm. The quantitative results justified the constructed root-finding algorithm’s robust performance in comparison to other quintic-order methods that can be found in the literature. For the graphical analysis, we make use of the newly discovered method to plot some novel polynomiographs that are attractive to the eye, and then we evaluate these new plots in relation to previously established quintic-order root-finding strategies. The graphic analysis demonstrates that the newly created method for root-finding has better convergence with the larger area than the other comparable methods do.

More recently, type-3 (T3) fuzzy logic systems (FLSs) with better learning ability and uncertainty modeling have been presented. On other hand, the proportional-integral-derivative (PID) is commonly employed in most industrial control systems, because of its simplicity and efficiency. The measurement errors, nonlinearities, and uncertainties degrade the performance of conventional PIDs. In this study, for the first time, a new T3-FLS-based PID scheme with deep learning approach is introduced. In addition to rules, the parameters of fuzzy sets are also tuned such that a fast regulation efficiency is obtained. Unlike the most conventional approaches, the suggested tuning approach is done in an online scheme. Also, a nonsingleton fuzzification is suggested to reduce the effect of sensor errors. The proposed scheme is examined on a case-study microgrid (MG), and its good frequency stabilization performance is demonstrated in various hard conditions such as variable load, unknown dynamics, and variation in renewable energy (RE) sources.

In the ever-evolving vibrant landscape of our times, it is crucial that a peaceful environment is ensured taking into account all the likely ecological parameters along with humidity and temperature while conserving energy. Thus, besides mechanical and electric control systems, it has become vital to ensure that artificial intelligence (AI) is assimilated and deployed into the systems so as to raise the well-being of the environment. By disseminating intelligence across the building by utilizing the new internet of things (IoT) technology, along with control formats, local open standard data, AI algorithms, and cloud-based predictive analytics, the heating, ventilation, and air conditioning (HVAC) mechanism renders the capability to acclimatize to use patterns, alterations in use patterns, and equipment breakdown. By tracing human activity coupled with analysis of noise, energy, and temperature in the building, its occupants and facility managers can obtain vital insights for planning, optimum use of space, and behavioral changes, in turn ensuring more content and safer inhabitants and considerably more efficient structures. Moreover, fuzzy modeling shows its applicability factor with the execution of human rationale and reasoning with if-then rules as attained from the systems input-output info for model setup and training. Additionally, it presents advantages pertaining to predictive functions for tackling nonlinearity and uncertainty as well as studying the capability of the models recommended. Thus, the multi-dimensional model recommended in this study outlines a system architecture as an implementation methodology and how it harmonizes prevailing systems while offering comprehensive knowledge to HVAC systems for the accomplishment of lower energy consumption and inhabitant safety and well-being on the basis of the fuzzy modeling. With tolerance for CO₂ discharges moving towards zero, the recommended multi-dimensional model provides substantial advantages for the HVAC sector for meeting the essential objectives while taking into account enhanced sustainability in vibrant and nonlinear environments for enhancing the accuracy and fairness of the assessment outcomes.

Players in the Small and Medium System (SME) collaboration gamification system need suitable partner references to support the goals of their activities. This study aims to build an intelligent system gamification mechanics model to provide the proper partner reference for players. The following steps are carried out sequentially in carrying out this research. First, analyze needs for a recommendation model that supports partner reference. Second, design an intelligent system formula using the Fuzzy‐Analytical Hierarchy Process (Fuzzy‐AHP) and K‐Means algorithms to obtain partner reference recommendation patterns and segmentation of similarity of interests between partners. Third, compile the scenario of recommendation model mechanics which involves actors and activities involved in the model. Fourth, design use cases and activity diagrams to translate scenarios in the form of program flow. Fifth, code programs related to use cases and activity diagrams. The sixth is to conduct experiment with the prototype results to test all the functions of the proposed model. Fuzzy‐AHP produces a weight for each tested data which can be claimed as a ranking, with the highest weight value being 9,980. K‐Means produces 3 clusters in which, based on this experimental data, the third cluster has the most members. Both models are realized in the dashboard, and referring to experiments from 63 respondents, the model shows its performance by displaying SME rankings and clusters according to the data and criteria being tested. Intelligent system algorithms are to develop models of gamification mechanics, primarily to support player decisions in determining more effective game steps. This model can work well if sufficient data requirements support it. Therefore, the proposed mechanics depends on game activities, and more data are available to be extracted and produce more precise recommendations.

Any company must constantly innovate if they want to maintain its market share in the present cutthroat and unstable industry. Innovation has a big influence on consumer behavior, yet it goes against the principles of sustainability. The issue of sustainability has become crucial to their company’s growth. In order to evaluate a business firm’s sustainability performance statistically, a new and effective fuzzy logic tool is created. Evolution and assessment are performed by a novel interval type‐2 fuzzy logic inference system. The judgment of the inference system is carried out on the basis of type‐2 fuzzy logic (T2FL), principal component analysis (PCA), and statistical data analysis. The main input variables include corporate environmental performance (CEP) and corporate financial performance (CFP). The suggested approach can effectively examine a corporation’s sustainable performance, according to experimental findings. A unique approach that makes use of language variables and if‐then logic to assist quantitative business sustainability events is the link between CEP and CFP. The recommended test will provide senior administrative leaders with useful information to supervise natural concerns correctly and gauge their commitment to company success.

Fuzzy and anti fuzzy normal subgroups are the current instrument for dealing with ambiguity in various decision‐making challenges. This article discusses γ‐anti fuzzy normal subgroups and γ‐fuzzy normal subgroups. Set‐theoretic properties of union and intersection are examined and it is observed that union and intersection of γ‐anti fuzzy normal subgroups are γ‐anti fuzzy normal subgroups. Employee selection impacts the input quality of employees and hence plays an important part in human resource management. The cost of a group is established in proportion to the fuzzy multisets of a fuzzy multigroup. It was a good idea to introduce anti‐intuitionistic fuzzy sets and anti‐intuitionistic fuzzy subgroups, as well as to demonstrate some of their algebraic features. Product of γ‐anti fuzzy normal subgroups and γ‐fuzzy normal subgroups is defined, the product’s algebraic nature is analyzed, and the findings are supported by presenting γ‐anti typical sections with blurring and γ‐ordinary parts with the weirdness of well‐defined and well‐established groups of genetic codes.