Cybersecurity tools are essential components in maintaining the security and integrity of information technology infrastructures. These tools shape themselves to prevent, detect, and respond to various security breaches, confirming the protection, confidentiality, and accessibility of data. Different tools are designed for specific functions in cybersecurity, such as safeguarding endpoints, overseeing network security, and examining risks and vulnerabilities. Each tool serves a distinct purpose in protecting systems and data. However, despite the availability of several tools, there is a lot of uncertainty and ambiguity when choosing the most effective cybersecurity tool. Therefore, the selection of a suitable cybersecurity tool is a multicriteria decision‐making (MCDM) problem. First, this manuscript develops the concept of a set termed as ( p , q )‐fractional fuzzy sets, which is more flexible than the other extensions of fuzzy sets. After that, we develop a set of geometric fusing operators based on Aczel–Alsina t‐norms in the framework of ( p , q )‐fractional fuzzy sets, and some well‐known properties are also discussed. Furthermore, we introduced an innovative decision‐making model in the context of ( p , q )‐fractional fuzzy Aczel–Alsina geometric operators to select the most suitable cybersecurity tool for an organization. We also employed the anticipated model to tackle the challenges of pattern recognition within a ( p , q )‐fractional fuzzy setting, resulting in impressive outcomes. In the end, we conducted a comparison between the inferred work and the existing research to confirm the superiority and advantages of the deduced work. The outcomes of the comparison indicate that the suggested method is suitable and dependable for the decision‐support model.

Artificial neural network (ANN) also known simply as a neural network , is a branch of machine learning(ML), that is developed based on neuronal organization discovered by connectionism in the biological neural network in animal intelligence. In this manuscript, we invent the theory of pq-rung orthopair fuzzy linguistic (pq-ROFL) set and their valuable properties. Moreover, we expose the theory of pq-ROFL Muirhead mean (pq-ROFLMM), pq-ROFL weighted Muirhead mean (pq-ROFLWMM), pq-ROFL dual Muirhead mean (pq-ROFLDMM), and pq-ROFL dual weighted Muirhead mean (pq-ROFLDWMM) operators. Some effective and reliable properties of the invented theory are also derived. Additionally, we also evaluate the unkhnown weight vector of criteria by using analytical hierarchy process (AHP). Moreover, we discovered the best type of artificial neural network under the consideration of derived operators for pq-ROFL information. Finally, we illustrate some numerical examples in the environment of multi-attribute decision-making (MADM) and try to compare the proposed results with some prevailing results to show the reliability and supremacy of the invented approaches.

In decision support systems, linguistic fuzzy information played an important role and the linguistic fuzzy aggregation operators (AOs) worked in group decision support systems. Recently, we proposed the linguistic picture fuzzy (LPF) sets, which is the extension of the linguistic intuitionist fuzzy sets, to reflect the ambiguity and vagueness of knowledge in decision-making (DM) problem. The goal of this research work is to define a new family of LPF AOs through the use of Dombi operations and Heronian mean (HM) operator. In addition to fusing individual attribute values, the evolved operators are good ability to handle the common association between the attributes, making them more appropriate to effectively solve difficult multi-attribute DM (MADM) problems. Therefore, we developed an approach for MADM problem based on LPF Dombi HM operators and solved an emergency programme selection problem. The comparison section provides the effectiveness, reliability and practicality.

The main aim of the proposed work is to develop the new technique based on decision-theoretical rough sets (DTRSs) and their applications in three-way decision-making problems. This study first develop a fractional fuzzy set (FFS) and their operations, the FFS is a more generalized and accurate tool for describing uncertainty in real-life data information. A new form of decision technique for dealing with the issue of choice based on DTRSs is included in the three-way decisions. The loss function of DTRSs is being used in the proposed decision method model. Initially, the idea of fractional fuzzy α-covering (FF α-covering), fractional fuzzy α–neighborhood (FF α–neighborhood) was introduced. Under the fractional fuzzy state, we integrated the loss function of DTRSs with covering-based fractional fuzzy rough sets. Furthermore, we proposed and established performance characteristics for a new fractional fuzzy α-covering decision-theoretical rough sets model (FFCDTRSs). Then, according to the level of fractional fuzzy numbers (FFN's) positive and negative membership and related three-way decision-making, four methods to solve the expected loss expressed in the form of (FFNs) are described. We have developed a multicriteria decision algorithm (MCDM) based on FFCDTRS. Then an example is used to prove the feasibility of the four methods to solve the MCDM problem. Finally, the results of four distinct decision procedures with various loss functions are compared. The proposed three-way decision-making models are more accurate as compared with particular fuzzy sets.

The emergency response to the health care management in the hospital do not have enough systems for providing medical service to the COVID19 patients (e.g., scheduled or nonemergency). Therefore, in this paper, we developed an emergency decision support model for consideration of patients care and admission scheduling (PCAS). The complex decision support model assigns a set of patients into a number of restricted resources like rooms, time slots, and beds depending on satisfying a number of predefined constraints such as disease severity, waiting time, and disease types. This is a crucial issue with multi-criteria decision making (MCDM). In this paper, we first begin an assessment into the admission and care to tackle this issue and collect four factors effecting the admission and care of COVID-19 patients that form a system of criteria. While there is a lot of vague and uncertain data that can be effectively depicted for these indicators by the spherical hesitant fuzzy set, then, we implement a strong MCDM method based on list of aggregation operators to address the patients' hospital admission and care. Last of all, a numerical real-life application about PCAS is provided to demonstrate the validity of the proposed approaches along with relevant discussions, the merits of proposed approaches are also analyzed by validity test. The proposed methodology has been shown to help hospitals manage the admissions and care of COVID-19 patients in a flexible manner.

In multiattribute group decision-making (MAGDM), experts often articulate their preference information to support decision-making by applying the multigranular linguistic model. Thus, the present work aims to introduce a novel MAGDM model to manage multigranular generalized orthopair 2-tuple linguistic information (GO2TLI). To begin with, a generalized orthopair 2-tuple linguistic model is put forward with the attempt of taking advantages of both q-rung orthopair fuzzy set (q-ROFS) and the 2-tuple linguistic model, while a transformation approach is supplied to tackle the consistency of multigranular GO2TLI. In addition, the Archimedean Copula as well as the Co-Copula operators are extended to handle GO2TLI along with their operational laws, to comprehensively model the relationship among attributes and experts. The Banzhaf Choquet-Copula aggregation operators on the generalized orthopair 2-tuple linguistic (GO2TLBCCA) are introduced, also some of its properties discussed. Third, the algorithms for regulating and determining the fuzzy measure (FM) of attributes and experts sets are proposed, followed by the corresponding decision-making approaches based upon the proposed GO2TLBCCA. The proposed MAGDM model can not only accommodate effectively the FMs of attribute (and expert) sets which are given subjectively, but also effectively address some multigranular GO2TLI as well as the partially unknown or completely unknown weights of attribute and expert sets. Finally, a case study is provided to demonstrate the validity of the proposed approach along with relevant discussions, the merits of the proposed approach are also analyzed by comparing with some extant decision methods.

Significant emergency measures should be taken until an emergency event occurs. It is understood that the emergency is characterized by limited time and information, harmfulness and uncertainty, and decision-makers are always critically bound by uncertainty and risk. This paper introduces many novel approaches to addressing the emergency situation of COVID-19 under spherical fuzzy environment. Fundamentally, the paper includes six main sections to achieve appropriate and accurate measures to address the situation of emergency decision-making. As the spherical fuzzy set (FS) is a generalized framework of fuzzy structure to handle more uncertainty and ambiguity in decision-making problems (DMPs). First, we discuss basic algebraic operational laws (AOLs) under spherical FS. In addition, elaborate on the deficiency of existing AOLs and present three cases to address the validity of the proposed novel AOLs under spherical fuzzy settings. Second, we present a list of Einstein aggregation operators (AgOp) based on the Einstein norm to aggregate uncertain information in DMPs. Thirdly, we are introducing two techniques to demonstrate the unknown weight of the criteria. Fourthly, we develop extended TOPSIS and Gray relational analysis approaches based on AgOp with unknown weight information of the criteria. In fifth, we design three algorithms to address the uncertainty and ambiguity information in emergency DMPs. Finally, the numerical case study of the novel carnivorous (COVID-19) situation is provided as an application for emergency decision-making based on the proposed three algorithms. Results explore the effectiveness of our proposed methodologies and provide accurate emergency measures to address the global uncertainty of COVID-19.

There has been a quick development in construction activities during the last couple of decades attributable to a general improvement in all features of humankind. Because of innovative progressions and regularly expanding human progress, there is a diligent requirement of power. Close by the ordinary energy sources, renewable energy sources have likewise lead significantly to the rising power requirement. All over the world in the past, a number of small hydropower plants (SHPPs) have been developed, as a renewable energy source. Generally, these SHPPs are being manufactured and worked by the private designers consenting to the administration rules. So as to help a designer in choosing the most productive and doable SHPP for development and consequent activity, the concept of the intuitionistic cubic fuzzy set (ICFS) theory is established and a few important operations for ICFSs are characterized, and also a strategy dependent on intuitionistic cubic fuzzy Hamacher hybrid averaging (ICFHHA) operator, intuitionistic cubic fuzzy Hamacher order weighted averaging (ICFHOWA) operator, and intuitionistic cubic fuzzy Hamacher weighted averaging (ICFHWA) operators is utilized in the present paper. The financial criteria and technobusiness, as assumed for examining the practicality of the candidate SHPPs, are presented qualitatively utilizing intuitionistic cubic fuzzy numbers (ICFNs). Further study their fundamental properties and the relationship among these aggregation operators. Developed group decision-making (DM) algorithm under intuitionistic cubic fuzzy (ICF) environment. An interpretative case for the analysis of SHPP for construction is given to demonstrate the feasibility and practicality of the mentioned new techniques. Further validate its effectiveness and benefits via a comparative analysis with pre-existing aggregation operators, and the outcomes demonstrate that the proposed SHPP determination model has some special favorable circumstances, which is progressively practical and adaptable for SHPP choice under a complex and uncertain environment.

Spherical fuzzy sets (SFSs) are a new extension of Cuong's picture fuzzy sets (PFSs). In SFSs, membership degrees satisfy the condition instead of as is in PFSs. In the present work, we extend different strict archimedean triangular norm and conorm to aggregate spherical fuzzy information. Firstly, we define the SFS and discuss some operational rules. Generalized spherical aggregation operators for spherical fuzzy numbers utilizing these strict Archimedean t-norm and t-conorm are proposed. Finally, based on these operators, a decision-making method has been established for ranking the alternatives by utilizing a spherical fuzzy environment. The suggested technique has been demonstrated with a descriptive example for viewing their effectiveness as well as reliability. A test checking the reliability and validity has also been conducted for viewing the supremacy of the suggested technique.

Pythagorean fuzzy set (PFS) is a powerful tool to deal with the imprecision and vagueness. Many aggregation operators have been proposed by many researchers based on PFSs. But the existing methods are under the hypothesis that the decision-makers (DMs) and the attributes are at the same priority level. However, in real group decision-making problems, the attribute and DMs may have different priority level. Therefore, in this paper, we introduce multiattribute group decision-making (MAGDM) based on PFSs where there exists a prioritization relationship over the attributes and DMs. First we develop Pythagorean fuzzy Einstein prioritized weighted average operator and Pythagorean fuzzy Einstein prioritized weighted geometric operator. We study some of its desirable properties such as idempotency, boundary, and monotonicity in detail. Moreover we propose a MAGDM approach based on the developed operators under Pythagorean fuzzy environment. Finally, an illustrative example is provided to illustrate the practicality of the proposed approach.

In this paper, the concept of multiple-attribute group decision-making (MAGDM) problems with interval-valued Pythagorean fuzzy information is developed, in which the attribute values are interval-valued Pythagorean fuzzy numbers and the information about the attribute weight is incomplete. Since the concept of interval-valued Pythagorean fuzzy sets is the generalization of interval-valued intuitionistic fuzzy set. Thus, due the this motivation in this paper, the concept of interval-valued Pythagorean fuzzy Choquet integral average (IVPFCIA) operator is introduced by generalizing the concept of interval-valued intuitionistic fuzzy Choquet integral average operator. To illustrate the developed operator, a numerical example is also investigated. Extended the concept of traditional GRA method, a new extension of GRA method based on interval-valued Pythagorean fuzzy information is introduced. First, utilize IVPFCIA operator to aggregate all the interval-valued Pythagorean fuzzy decision matrices. Then, an optimization model based on the basic ideal of traditional grey relational analysis (GRA) method is established, to get the weight vector of the attributes. Based on the traditional GRA method, calculation steps for solving interval-valued Pythagorean fuzzy MAGDM problems with incompletely known weight information are given. The degree of grey relation between every alternative and positive-ideal solution and negative-ideal solution is calculated. To determine the ranking order of all alternatives, a relative relational degree is defined by calculating the degree of grey relation to both the positive-ideal solution and negative ideal solution simultaneously. Finally, to illustrate the developed approach a numerical example is to demonstrate its practicality and effectiveness.