Type‐3 fuzzy logic has been recently used in many control methods. The type‐3 fuzzy controller enhances the handling of uncertainty and improves robustness by integrating fuzzy sets with fuzzy membership functions. The latest approaches using type‐3 fuzzy logic in the field of control are studied and evaluated. An overview of developments in control methods based on type‐3 fuzzy logic is also provided. It is shown that type‐3 fuzzy system has many advantages compared to type‐1 and type‐2 fuzzy. The advantages and challenges of using type‐3 fuzzy logic are identified and discussed. The studies are classified according to the type of control approach, as well as by the type of control applications. Finally, the main achievements, open challenges, and future directions and impacts are identified, to provide important guidance for interested researchers.

For sustainable growth, investments in renewable energy must be maximized. Maximizing investments in renewable energy opens the door to a more successful and environmentally friendly future. Analyzing technological viability, cost‐effectiveness, regulatory compliance, and environmental impact are all part of this optimization process. This paper delves into a sophisticated methodology designed to tackle uncertainties in decision‐making by leveraging the innovative concept of Pythagorean hesitant fuzzy sets (PHFSs). We defined aggregation operations and distance measures for PHFS. After that, we introduced Measurement of Alternatives and Ranking According to the Compromise Solution (MARCOS), a novel methodology under PHFS, it is a robust tool acknowledged for navigating complex decision scenarios with multiple criteria. Following that, we showcased a case study on enhancing renewable energy investments through an AI‐based strategy for sustainable development, utilizing the newly developed MARCOS algorithm. The study highlights the significance of its adaptability and efficiency in practical applications. Furthermore, we compared this methodology with the Technique for Establishing Order Performance by Similarity to the Ideal Solution (TOPSIS), offering insights into their respective strengths. This offers a concrete demonstration of its real‐world utility and potential impact in decision‐making scenarios. Finally, in the last, we conclude the whole study.

The need to address the impediments to teaching numeracy in early childhood education necessitates a comprehensive approach, as an evident lack of exploration of impediments and their intertwined relationships exists in the domain literature. Thus, this work advances such agenda by utilizing the decision‐making trial and evaluation laboratory (DEMATEL) approach with q‐rung orthopair fuzzy sets (q‐ROFSs), referred to as q‐ROF‐DEMATEL. Unlike other fuzzy set extensions, q‐ROFS offers a larger decision space, providing the capability to handle information with greater ambiguity. The proposed q‐ROF‐DEMATEL is applied to identify the critical factors impeding effective instruction of numeracy skills to early childhood learners. The findings suggest that the prominent impediments include inadequate teaching time, lack of teaching knowledge, and underestimation of learners’ knowledge. Moreover, among the identified impediments, the lack of teaching knowledge emerges as the key impediment, while language barriers, inadequate teaching time, and lack of educational resources are identified as minor key impediments. These findings could guide decision makers in academic institutions to allocate resources effectively, pool human resources strategically, and develop appropriate strategies to augment teaching numeracy. Investing in professional development opportunities, incorporating visual representations and culturally relevant materials, and seeking community partnerships for resources are some recommended initiatives to address these challenges. Insights for future work were outlined.

The domain of decision‐making theory has made significant progress, especially within the industrial and management fields. Diverse decision‐making challenges such as multicriteria decision‐making (MCDM), multiattribute decision‐making (MADM), and multiattribute group decision‐making (MAGDM) have been thoroughly examined, equipping decision‐makers with effective strategies for tackling these issues. In the context of the automotive industry, a specific hurdle emerges when identifying the most suitable site for establishing a warehouse to store goods destined for multiple destinations. This article addresses a scenario amid uncertainty, leveraging substantial data. Neutrosophic sets (NSs) emerge as a comprehensive tool for effectively managing the imprecision inherent in such data. Among these sets, single‐valued neutrosophic sets (SVNSs) stand out due to their adeptness in handling inconsistent or incomplete data. The octagonal single‐valued neutrosophic numbers (OSVNNs) has a new tool for representing the uncertainty information in a simplified manner. Octagonal structure allows for representing different distinctions of truth, neutrality, and falsity of any complex situation and it is an efficient tool to compare different options based on their level of ambiguity. They have a wide range of applications in various fields, becoming increasingly important in addressing many difficult and uncertain issues. The article aims to propose a new ranking function for OSVNNs to convert the OSVNN data into precise values, drawing from the existing mean interval method (MIM). The conventional decision‐making approaches such as weighted sum model (WSM), weighted product model (WPM), technique for order of preference by similarity to ideal solution (TOPSIS), and VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) are employed to obtain the optimal warehouse location using OSVN application. Furthermore, it demonstrates the application along with the proposed ranking function using the software MATLAB to determine the most favorable alternatives. Finally, sensitivity analyses are performed to assess how different scenarios could impact the optimal location selection for automotive logistics.

In this paper, several results and theorems about the high-order strongly generalized Hukuhara differentiability of function defined via the fuzzy Riemann improper integral (in the sense of Wu) have been established. Then, some properties dealing with the partial derivatives of fuzzy Laplace transform for a fuzzy function of two real variables have been proved. Afterwards, an algorithm of fuzzy Laplace transform for solving second-order fuzzy partial differential equations has been proposed. Finally, two numerical examples, including the heat equation under fuzzy initial conditions, have been studied to justify the efficiency of the algorithm.

Analyzing the stability of many control systems required solving a couple of crisp Sylvester matrix equations (CSMEs) simultaneously. However, there are some situations in which the crisp Sylvester matrix equations are not well equipped to deal with the uncertainty problem during the stability analysis of control systems. This paper constructs analytical and numerical methods for solving a couple of trapezoidal fully fuzzy Sylvester matrix equations (CTrFFSMEs) to overcome the drawbacks of the existing crisp methods. In developing these new methods, fuzzy arithmetic multiplication is applied on the CTrFFSME to transform it into an equivalent system of four CSMEs. Then, the fuzzy solution is obtained analytically by the fuzzy matrix vectorization method and numerically by gradient and least square methods. The analytical method can obtain the exact solution; however, it is limited to small-sized systems while the numerical methods can approximate the solution for large dimensional systems up to 100 × 100 with a very small error bound for any initial value. In addition, the proposed methods are applied to other fuzzy systems such as Sylvester and Lyapunov matrix equations. The proposed methods are illustrated by solving numerical examples with different size systems.

In this paper, we introduce the concept of relative fuzzy annihilator ideals in C-algebras and investigate some its properties. We characterize relative fuzzy annihilators in terms of fuzzy points. It is proved that the class of fuzzy ideals of C-algebras forms Heything algebra. We observe that the class of all fuzzy annihilator ideals can be made as a complete Boolean algebra. Moreover, we study the concept of fuzzy annihilator preserving homomorphism. We provide a sufficient condition for a homomorphism to be a fuzzy annihilator preserving.

Today, regarding the rapid growth of Information and Communications Technology (ICT), e-commerce, and the subsequent expansion of electronic banking, the banking market structure is also expected to dramatically be changed. This paper aims to explore the main effect of electronic banking on the structure of the Iranian banking industry by investigating the banking market concentration degree. To accomplish this aim, an intelligent hybrid model is developed based on multilayer perceptron neural network and fuzzy regression of the effects of banking on the relative electronic share of banks. In the developed method, the neural network parameters such as weights and errors have been considered as the fuzzy parameters to model it under uncertainty. Ultimately, the descriptive statistics are utilized to evaluate how the difference in relative size of banks concerning e-banking has changed, in addition to exploring the main effect of e-banking on the bank’s contribution described as a neural network-fuzzy regression model. Moreover, it shows how the concentration degree in the Iranian banking sector has been reduced. The implemented analysis of the reasons for this decrease reveals that the share of banks has decreased due to an increase in the share of the small banks. Furthermore, model estimation confirms that there exists a positive relationship between banks’ share and the use of electronic banking. Besides, the small banks have strongly been shown to utilize the e-banking so that it would lead to an increase in their share and a decrease in the concentration degree. As such, it can be concluded that e-banking has reduced the concentration degree in Iran. The descriptive statistics are employed to prove it.

In todayʼs world where technology is rapidly evolving, hotels need to be the best in all conditions to be one step ahead of other competitors. Digital marketing and hotel website solutions play a lead role in this competition. Therefore, hotel websites need to be innovative, user-friendly, and descriptive. The main purpose of the study is to evaluate and rank potential hotel websites and digital solutions provider firms. Since there are various potentially competing quantitative and qualitative criteria to take into consideration in the decision-making process, a multicriteria decision-making (MCDM) method is needed. As the MCDM method, fuzzy best-worst method (FBWM) is integrated with the Fuzzy Technique for Order Preference by Similarity to Ideal Solution (F-TOPSIS). In this integration, FBWM is applied to determine fuzzy evaluation criteria weights and then F-TOPSIS is implemented to rank alternatives utilizing the obtained fuzzy weights. A case study is presented, where 4 alternative hotel websites and digital solutions provider firms for Paloma Hotels in Turkey are evaluated based on 9 criteria by 3 hotel managers.