In recent decades, there has been a massive growth towards the prime interest of the hydrogen energy industry in automobile transportation fuel. Hydrogen is the most plentiful component and a perfect carrier of energy. Generally, evaluating a suitable hydrogen power plant site is a complex selection of multi-criteria decision-making (MCDM) problem concerning proper location assessment based on numerous essential criteria, the decision-makers expert opinion, and other qualitative/quantitative aspects. This paper presents the novel single-valued neutrosophic (SVN) multi-attribute decision-making method to help decision-makers choose the optimal hydrogen power plant site. At first, novel operating laws based on sine trigonometric function for single-valued neutrosophic sets (SVNSs) are introduced. The well-known sine trigonometry function preserves the periodicity and symmetric in nature about the origin, and therefore it satisfies the decision-maker preferences over the multi-time phase parameters. In conjunction with these properties and laws, we define several new aggregation operators (AOs), called SVN weighted averaging and geometric operators, to aggregate SVNSs. Subsequently, on the basis of the proposed AOs, we introduce decision-making technique for addressing multi-attribute decision-making (MADM) problems and provide a numerical illustration of the hydrogen power plant selection problem for validation. A detailed comparative analysis, including a sensitivity analysis, was carried out to improve the understanding and clarity of the proposed methodologies in view of the existing literature on MADM problems.

In this study, we solve the fractional advection–dispersion equation (FADE) by applying the Laplace transform decomposition method (LTDM) and the variational iteration transform method (VITM). The Atangana–Baleanu (AB) sense is used to describe the fractional derivative. This equation is utilized to determine solute transport in groundwater and soils. The FADE is converted into a system of non-linear algebraic equations whose solution leads to the approximate solution for this equation using the techniques presented. The proposed approximate method’s convergence is examined. The suggested method’s applicability is demonstrated by testing it on several illustrative examples. The series solutions to the specified issues are obtained, and they contain components that converge more quickly to the precise solutions. The actual and estimated results are demonstrated in graphs and tables to be quite similar, demonstrating the usefulness of the proposed strategy. The innovation of the current work is in the application of an effective method that requires less calculation and achieves a greater level of accuracy. Furthermore, the proposed approaches may be implemented to prove their utility in tackling fractional-order problems in science and engineering.

The fuzzy set has its own limitations due to the membership function only. The fuzzy set does not describe the negative aspects of an object. The Fermatean fuzzy set covers the negative aspects of an object. The complex Fermatean fuzzy set is the most effective tool for handling ambiguous and uncertain information. The aim of this research work is to develop new techniques for complex decision-making based on complex Fermatean fuzzy numbers. First, we construct different aggregation operators for complex Fermatean fuzzy numbers, using Einstein t-norms. We define a series of aggregation operators named complex Fermatean fuzzy Einstein weighted average aggregation (CFFEWAA), complex Fermatean fuzzy Einstein ordered weighted average aggregation (CFFEOWAA), and complex Fermatean fuzzy Einstein hybrid average aggregation (CFFEHAA). The fundamental properties of the proposed aggregation operators are discussed here. The proposed aggregation operators are applied to the decision-making technique with the help of the score functions. We also construct different algorithms based on different aggregation operators. The extended TOPSIS method is described for the decision-making problem. We apply the proposed extended TOPSIS method to MAGDM problem “selection of an English language instructor”. We also compare the proposed models with the existing models.

To finding appropriate recycling methods for plastic materials is a critical research issue and the effectiveness of a new method is being tested in this problem. Decision-making under conditions of ambiguity can be difficult due to the lack of understanding and incomplete information. The objective of this study is to enhance the process of selecting the most suitable recycling method. To address uncertainty in group decision-making, this essay proposes using MAGDM approaches with 2-tuple linguistic confidence level complex q-rung orthopair fuzzy sets (2TLCLCq-ROFSs). The CODAS method is extended to 2TLCLCq-ROFSs to tackle MAGDM issues. The 2TLCLCq-ROFSs is an innovative fuzzy framework that confirms positive and negative degrees on the unit circle of the complex plane to resolve ambiguity and vague data effectively. Using the innovative concept of a 2-tuple linguistic Cq-ROFS with confidence level , we presented a novel decision-making approach in this study (2TLCLCq-ROFSs). Additionally,we also perform a comparative sensitivity analysis to examine the results of CODAS method and compare it by some existing MCDM methods. These analyses show that the proposed method is efficient, and the results are also shown graphically in this work.

Branded apps offer both an essential tool for businesses and consumers to interact in real-time and share marketing messages as well as an innovative approach to business that promotes value co-creation. In order to explore the impact of branded apps on customers, this study provides a Three-way decision (TWDs) technique with decision-theoretic rough sets (DTRSs) for selecting branded apps under spherical double hierarchy linguistic term sets (SDHLTSs) information. SDHLTSs is a combination of the first hierarchy linguistic term and the second hierarchy linguistic term that can more flexibly describe ambiguity and uncertainty in decision-making (DM) problems. To aggregate the SDHLTSs, we propose a series of aggregation operators and fundamental operational laws for SDHLTSs. A grey relational analysis is considered to evaluate a conditional probability, which improves decision-making. A step-wise algorithm of the TWDs method based on decision-theoretic rough sets (DTRSs) is given for SDHLTSs. Further, a proposed aggregation operator is used to compute the loss function, and the decision’s results are decided by the minimum-loss principle. Finally, a real-world case study of the brand experience of a branded app is considered to demonstrate the efficiency of the proposed methods.