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This study addresses the problem of fractional-order nonlinear containment control of heterogeneous multi-agent systems within a leader–follower framework, focusing on the impact of False Data Injection (FDI) attacks. By employing adaptive mechanisms and fuzzy logic, the suggested method enhances system resilience, ensuring reliable coordination and stability even in the presence of deceptive disturbances. To deal with these uncertainties, our controller makes use of interval type-II (IT2) fuzzy sets, and we create matrix equalities and inequalities to account for the asymmetry of Laplace matrices. Also, we use the Lyapunov functions for the stability analysis of our system. Lastly, we explain the numerical simulations for the effectiveness of our theoretical results, and these simulated examples are used to verify the effectiveness of our approach and designed model. [ABSTRACT FROM AUTHOR]

Chemical engineers can model numerous interactions in a process using incidence graphs. They are used to methodically map out a whole network of interconnected processes and controllers to describe each component's impact on the others. It makes it easier to visualize potential process paths or a series of impacts. A Pythagorean fuzzy set is an effective tool to overcome ambiguity and vagueness. In this paper, we introduce the concept of Pythagorean fuzzy incidence graphs. We discuss the incidence path and characterize the strongest incidence path in Pythagorean fuzzy incidence graphs. Furthermore, we propose the idea of Pythagorean fuzzy incidence cycles and Pythagorean fuzzy incidence trees in Pythagorean fuzzy incidence graphs and give some essential results. We illustrate the notions of Pythagorean fuzzy incidence cut vertices, Pythagorean fuzzy incidence bridges, and Pythagorean fuzzy incidence cut pairs. We also establish some results about Pythagorean fuzzy incidence cut pairs. Moreover, we study the types of incidence pairs and determine some crucial results concerning strong incidence pairs in the Pythagorean fuzzy incidence graph. We also obtain the characterization of Pythagorean fuzzy incidence cut pairs using ff-strong incidence pairs and find the relation between Pythagorean fuzzy incidence trees and 1-strong incidence pairs. Finally, we provide the application of Pythagorean fuzzy incidence graphs in the illegal wildlife trade. [ABSTRACT FROM AUTHOR]

Multi-criteria group decision-making (MCGDM) approaches have a substantial effect on decision-making in a range of critical sectors, including science, business, and real-life research. These strategies also efficiently assist researchers in resolving challenges that may arise throughout their study activity. The current work's major purpose is to research and develop the combinative distance-based assessment (CODAS) approach by employing -tuple linguistic -rung picture fuzzy sets ( TL -RPFSs) as a background. The CODAS technique computes the distances from the negative ideal solutions and ranks the alternatives in increasing order. To compute the normal weights of attributes, the entropy weighting information process is used. Furthermore, two aggregation operators, namely the -tuple linguistic -rung picture fuzzy Einstein weighted average and the -tuple linguistic -rung picture fuzzy Einstein order weighted average, are introduced. Our inspiration for employing the notion of TL -RPFSs is the ability of -RPFSs to support a wide range of information and the significant qualities of -tuple linguistic term sets to handle qualitative data. Congested transportation networks may be made more efficient by leveraging digital transformation. Real-time traffic management is one solution to the problem of road congestion. As a result of connected autonomous vehicle (CAV) advances, the benefits of real-time traffic management systems have grown dramatically. CAVs can help manage traffic by acting as enforcers. To complement the extended approach, the proposed technique is used to select the best alternative for a real-time traffic management system. The performance of the suggested technique is validated using scenario analysis. The results show that the suggested strategy is efficient and relevant to real-world situations. [ABSTRACT FROM AUTHOR]

Many real-world decision-making issues frequently involve competing sets of criteria, uncertainty, and inaccurate information. Some of these require the involvement of a group of decision-makers, where it is necessary to reduce the various available individual preferences to a single collective preference. To enhance the effectiveness of multi-criteria decisions, multi-criteria decision-making is a popular decision-making technique that makes the procedure more precise, reasonable, and effcient. The "Technique for Order Preference by Similarity to Ideal Solution (TOPSIS)" and "Elimination and Choice Transforming Reality (ELECTRE)" are prominent ranking methods and widely used in the multi-criteria decision-making to solve complicated decision-making problems. In this study, two m-polar fuzzy set-based ranking methods are proposed by extending the ELECTRE-I and TOPSIS approaches equipped with cubic m-polar fuzzy (CmPF) sets, where the experts provide assessment results on feasible alternatives through a CmPF decision matrix. The first proposed method, CmPF-TOPSIS, focuses on the alternative that is closest to a CmPF positive ideal solution and farthest away from the CmPF negative ideal solution. The Euclidean and normalized Euclidean distances are used to determine the proximity of an alternative to ideal solutions. In contrast, the second developed method is CmPF-ELECTRE-I which uses an outranking directed decision graph to determine the optimal alternative, which entirely depends on the CmPF concordance and discordance sets. Furthermore, a practical case study is carried out in the diagnosis of impulse control disorders to illustrate the feasibility and applicability of the proposed methods. Finally, a comparative analysis is performed to demonstrate the veracity, superiority, and effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

In this paper, we used the permutation group together with the concept of cordiality in graph theory to introduce a new method of labeling. This construed permuted cordial labeling can be applied to all paths, cycles, fans and wheel graphs. Moreover, some other properties are investigated and show that the union of any two paths and the union of any two cycles are permuted cordial graphs. In addition, we investigated the permuted cordiality for the union of any path with cycle. [ABSTRACT FROM AUTHOR]

In recent years, network security has become a major concern. Using the Internet to store and analyze data has become an integral aspect of the production and operation of many new and traditional enterprises. However, many enterprises lack the necessary resources to secure information security, and selecting the best network security service provider has become a real issue for many enterprises. This research introduces a novel decision-making method utilizing the 2-tuple linguistic complex q-rung orthopair fuzzy numbers (2TLCq-ROFNs) to tackle this issue. We propose the 2TLCq-ROF concept by combining the complex q-rung orthopair fuzzy set with 2-tuple linguistic terms, including the fundamental definition, operational rules, scoring, and accuracy functions. Aggregation operators are the fundamental mathematical approach used to combine various inputs into a single output. Taking into account the interaction between the attributes, we develop the 2TLCq-ROF Hamacher (2TLCq-ROFH) operators by using the innovative operational rules. These operators include the 2TLCq-ROFH weighted average (2TLCq-ROFHWA), 2TLCq-ROFH ordered weighted average (2TLCq-ROFHOWA), 2TLCq-ROFH hybrid average (2TLCq-ROFHHA), 2TLCq-ROFH weighted geometric (2TLCq-ROFHWG), 2TLCq-ROFH ordered weighted geometric (2TLCq-ROFHOWG), and 2TLCq-ROFH hybrid geometric (2TLCq-ROFHHG) operators. In addition, we talk about the properties of 2TLCq-ROFH operators such as idempotency, commutativity, monotonicity, and boundedness and also examine their spatial cases. To tackle the problems of the 2TLCq-ROF multiattribute group decision-making (MAGDM) environment, we develop a novel approach according to the COPRAS (complex proportional assessment) model. Finally, to validate the feasibility of the given strategy, we employ a quantitative example related to select the best network security service provider. In comparison with existing approaches, the developed decision-making algorithm is most extensively used and reduces the loss of information. [ABSTRACT FROM AUTHOR]

Aggregation is a very efficient indispensable tool in which several input values are transformed into a single output value that further supports dealing with different decision-making situations. Additionally, note that the theory of m-polar fuzzy (mF) sets is proposed to tackle multipolar information in decision-making problems. To date, several aggregation tools have been widely investigated to tackle multiple criteria decision-making (MCDM) problems in an m-polar fuzzy environment, including m-polar fuzzy Dombi and Hamacher aggregation operators (AOs). However, the aggregation tool to deal with m-polar information under Yager's operations (that is, Yager's t-norm and t-conorm) is missing in the literature. Due to these reasons, this study is devoted to investigating some novel averaging and geometric AOs in an mF information environment through the use of Yager's operations. Our proposed AOs are named as the mF Yager weighted averaging (mFYWA) operator, mF Yager ordered weighted averaging operator, mF Yager hybrid averaging operator, mF Yager weighted geometric (mFYWG) operator, mF Yager ordered weighted geometric operator and mF Yager hybrid geometric operator. The initiated averaging and geometric AOs are explained via illustrative examples and some of their basic properties, including boundedness, monotonicity, idempotency and commutativity are also studied. Further, to deal with different MCDM situations containing mF information, an innovative algorithm for MCDM is established under the under the condition of mFYWA and mFYWG operators. After that, a real-life application (that is, selecting a suitable site for an oil refinery) is explored under the conditions of developed AOs. Moreover, the initiated mF Yager AOs are compared with existing mF Hamacher and Dombi AOs through a numerical example. Finally, the effectiveness and reliability of the presented AOs are checked with the help of some existing validity tests.

The need for multi-attribute decision-making brings more and more complexity, and this type of decision-making extends to an ever wider range of areas of life. A recent model that captures many components of decision-making frameworks is the complex $ q $-rung picture fuzzy set (C$ q $-RPFS), a generalization of complex fuzzy sets and $ q $-rung picture fuzzy sets. From a different standpoint, linguistic terms are very useful to evaluate qualitative information without specialized knowledge. Inspired by the ease of use of the linguistic evaluations by means of 2-tuple linguistic term sets, and the broad scope of applications of C$ q $-RPFSs, in this paper we introduce the novel structure called 2-tuple linguistic complex $ q $-rung picture fuzzy sets (2TLC$ q $-RPFSs). We argue that this model prevails to represent the two-dimensional information over the boundary of C$ q $-RPFSs, thanks to the additional features of 2-tuple linguistic terms. Subsequently, some 2TLC$ q $-RPF aggregation operators are proposed. Fundamental cases include the 2TLC$ q $-RPF weighted averaging/geometric operators. Other sophisticated aggregation operators that we propose are based on the Hamacher operator. In addition, we investigate some essential properties of the new operators. These tools are the building blocks of a multi-attribute decision making strategy for problems posed in the 2TLC$ q $-RPFS setting. Furthermore, a numerical instance that selects an optimal machine is given to guarantee the applicability and effectiveness of the proposed approach. Finally, we conduct a comparison with other existing approaches.

In this article, we introduce the 2-tuple linguistic bipolar fuzzy set (2TLBFS), a new strategy for dealing with uncertainty that incorporates a 2-tuple linguistic term into bipolar fuzzy set. The 2TLBFS is a better way to deal with uncertain and imprecise information in the decision-making environment. We elaborate the operational rules, based on which, the 2-tuple linguistic bipolar fuzzy weighted averaging (2TLBFWA) operator and the 2-tuple linguistic bipolar fuzzy weighted geometric (2TLBFWG) operator are presented to fuse the 2TLBF numbers (2TLBFNs). The Heronian mean (HM) operator, which can reflect the internal correlation between attributes and their influence on decision results, is integrated into the 2TLBF environment to analyze the effect of the correlation between decision factors on decision results. Initially, the generalized 2-tuple linguistic bipolar fuzzy Heronian mean (G2TLBFHM) operator and generalized 2-tuple linguistic bipolar fuzzy weighted Heronian mean (G2TLBFWHM) operator are proposed and properties are explained. Further, 2-tuple linguistic bipolar fuzzy geometric Heronian mean (2TLBFGHM) operator and 2-tuple linguistic bipolar weighted geometric Heronian mean (2TLBFWGHM) operator are proposed along with some of their desirable properties. Then, an approach to multi-attribute group decision-making (MAGDM) based on the proposed aggregation operators under the 2TLBF framework is developed. At last, a numerical illustration is provided for the selection of the best photovoltaic cell to demonstrate the use of the generated technique and exhibit its adequacy.