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Advancement in mobile phone (MP) technology has revolutionized the lifestyle. In recent years, we observed that MP technology had been involved in almost all aspects of life, such as communication purposes, e-commerce, mobile baking, and social media connectivity. So, it becomes a hot research topic to select the best MP that fulfills the desired feathers requirement. In this paper, the expert's familiarity with the examined objects is factored into the initial judgments under the T-spherical fuzzy sets (T-SFSs) environment. The T-SFS is the extension of the picture fuzzy (PF) set (PFS), which gives wider scope for finding the most precise options than existing fuzzy frameworks. The multiattribute decision-making (MADM) is a common and valuable method for aggregating information. For MADM, various aggregation operators (AOs) have been created over the years. The article introduces the newly proposed approach T-spherical fuzzy (T-SF) confidence level weighted averaging T − SFWA c and T-SF confidence level weighted geometric T − SFWG c . Also, some desired properties of AOs are discussed, and the T-SF entropy measure is introduced for selecting the weight criteria. A MADM framework is introduced, on the behalf of proposed operators. The proposed MADM framework is applied to solve the real-life example of consumers' preferences to show effectiveness and practicality. Lastly, the developed framework is set side by side with other prevailing approaches to demonstrate the superiority and significance of other existing AOs. [ABSTRACT FROM AUTHOR]

In the creation of better multiple attribute decision‐making (MADM) patterns to address the ambiguity in the expanding sophisticated of expert systems, the hypothesis of interval‐valued intuitionistic fuzzy sets has proven to be an effective and advantageous technique. We employ Aczel–Alsina operations to remedy the MADM issue, wherein all data supplied by decision‐makers is conveyed as interval‐valued intuitionistic fuzzy (IVIF) decision matrices with all components described by an IVIF number (IVIFN). This allows us to satisfy much more demands from fuzzy decision‐making concerns (IVIFN). In the framework of IVIFNs, we primarily describe several novel Aczel–Alsina operations. On the basis of these operations, we construct several novel IVIF aggregation operators, such as the IVIF Aczel–Alsina weighted averaging operator, the IVIF Aczel–Alsina order weighted averaging operator, and IVIF Aczel–Alsina hybrid averaging operator. We built up several features of such operators. We recommend an MADM technique dependent on the advanced IVIF aggregation operators. To demonstrate the effectiveness of the developed technique, we present an overview of research scientist selection. The experimental results show the viability and benefits of the created strategy by contrasting it with the different strategies. This paper reveals that some existing IVIF aggregation operators are particular instances of the operators induced in this paper. [ABSTRACT FROM AUTHOR]

The aim of the paper is to present the concept of a multiplicative preference relation (MPR) with the features of the single‐valued neutrosophic (SVN) set and named as SVN multiplicative preference relation (SVNMPR). The SVN set (SVNS) handles uncertainties more broadly than the intuitionistic fuzzy set by considering the three independent degree systems with a scale rating of 0–1 and is symmetrical about 0.5. However, for asymmetrical distribution, Saaty discusses the 1–9 scale to display the information. Driven by the advantages of the scale of 1–9 and the independence nature of degrees in SVNS, in this paper, we introduce the concept of SVNMPR with ratings values as SVN numbers with range 1∕q−q with q>1. The main advantages of the proposed relation are the asymmetric and nonuniform distributions of about 1. To complete address this, we divide the stated work into three parts. First, an idea of SVNMPR is added wherein pairwise evaluation values are represented the usage of SVN numbers over a scale of 1∕q−q with q>1. Also, we outline the idea of the SVN multiplicative preference set (SVNMPS). Second, to rank the proposed SVNMPS, we define a new ranking method with improved score functions by adding the expert's attitude to the analysis. The relationship between the proposed and the existing functions is also derived. Third, we are defining some new operation laws for SVNMPS to preserve the closeness property. On the basis of these laws, we define a number of operators to aggregate the different pairs of the SVNMPSs and to derive a number of relations and inequalities. Finally, a group decision‐making approach is established and the practicality of it is demonstrated with a numerical example and compared with a number of existing approaches. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Induced aggregation operators are more suitable for aggregating the individual preference relations into a collective fuzzy preference relation. Therefore, in this paper, we introduce the notion of some new types of induced aggregation operators, based on the Aczel-Alsina operations. We construct some induced interval-valued intuitionistic trapezoidal fuzzy Aczel-Alsina ordered weighted averaging/geometric (I-IVITrFAAOWA/G) operator, induced interval-valued intuitionistic trapezoidal fuzzy Aczel-Alsina hybrid averaging/geometric (I-IVITrFAAHA/G) operator. Moreover, some dominant properties of these developed operators are studied in detail. Based on these proposed approaches, a model is a build up for multicriteria decision making (MCDM), and their stepwise algorithm is being presented. Finally, in utilizing the developed approach, an illustrative example is solved with the help of proposed operators. In the end, we utilize an applicable example for supplier selection to prove the proposed methods and compare the result with existing methods, which shows the superiority, competence, and ability of the developed model. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In the aggregation of uncertain information, it is very important to consider the interrelationship of the input information. Hamy mean (HM) is one of the fine tools to deal with such scenarios. This paper aims to extend the idea of the HM operator and dual HM (DHM) operator in the framework of complex intuitionistic fuzzy sets (CIFSs). The main benefit of using the frame of complex intuitionistic fuzzy CIF information is that it handles two possibilities of the truth degree (TD) and falsity degree (FD) of the uncertain information. We proposed four types of HM operators: CIF Hamy mean (CIFHM), CIF weighted Hamy mean (CIFWHM), CIF dual Hamy mean (CIFDHM), and CIF weighted dual Hamy mean (CIFWDHM) operators. The validity of the proposed HM operators is numerically established. The proposed HM operators are utilized to assess a multiattribute decision-making (MADM) problem where the case study of tourism destination places is discussed. For this purpose, a MADM algorithm involving the proposed HM operators is proposed and applied to the numerical example. The effectiveness and flexibility of the proposed method are also discussed, and the sensitivity of the involved parameters is studied. The conclusive remarks, after a comparative study, show that the results obtained in the frame of CIFSs improve the accuracy of the results by using the proposed HM operators. [ABSTRACT FROM AUTHOR]

The neutrosophic cubic hesitant fuzzy set can efficiently handle the complex information in a decision-making problem because it combines the advantages of the neutrosophic cubic set and the hesitant fuzzy set. The algebraic operations based on Dombi norms and co-norms are more flexible than the usual algebraic operations as they involve an operational parameter. First, this paper establishes Dombi algebraic operational laws, score functions, and similarity measures in neutrosophic cubic hesitant fuzzy sets. Then, we proposed Dombi exponential operational laws in which the exponents are neutrosophic cubic hesitant fuzzy values and bases are positive real numbers. To use neutrosophic cubic hesitant fuzzy sets in decision-making, we are developing Dombi exponential aggregation operators in the current study. In the end, we present applications of exponential aggregation operators in multiattribute decision-making problems. [ABSTRACT FROM AUTHOR]

The intuitionistic fuzzy hypersoft set (IFHSS) is the most generalized form of the intuitionistic fuzzy soft set used to resolve uncertain and vague data in the decision-making process, considering the parameters' multi-sub-attributes. Aggregation operators execute a dynamic role in assessing the two prospect sequences and eliminating anxieties from this perception. This paper prolongs the IFHSS to interval-valued IFHSS (IVIFHSS), which proficiently contracts with hesitant and unclear data. It is the most potent technique for incorporating insecure data into decision-making (DM). The main objective of this research is to develop the algebraic operational laws for IVIFHSS. Furthermore, using the algebraic operational law, some aggregation operators (AOs) for IVIFHSS have been presented, such as interval-valued intuitionistic fuzzy hypersoft weighted average (IVIFHSWA) and interval-valued intuitionistic fuzzy hypersoft weighted geometric (IVIFHSWG) operators with their essential properties. Multi-criteria group decision-making (MCGDM) technique is vigorous for material selection. However, conventional methods of MCGDM regularly provide inconsistent results. Based on the expected AOs, industrial enterprises propose a robust MCGDM material selection method to meet this shortfall. The real-world application of the planned MCGDM method for cryogenic storing vessel material selection (MS) is presented. The implication is that the designed model is more efficient and consistent in handling information based on IVIFHSS. [ABSTRACT FROM AUTHOR]

This paper proposes an extended VlseKriterijuska Optimizacija I Komoromisno Resenje (VIKOR) method based on the particle swarm optimization (PSO) algorithm for solving multicriteria group decision‐making problems with probabilistic linguistic information. First, we define the novel operations of probabilistic linguistic term sets and then prove the corresponding properties. Second, we apply a modified PSO algorithm to the consensus reaching process to improve the collective consensus level. In the context of probabilistic linguistic information, each participant can be recognized as a particle moving towards the best position. The consensus level can be regarded as the objective function that is used to construct the fitness function. In the update function, the trust relationship and the similarity measure between experts are exploited to determine the adjustment coefficient. The new consensus model based on PSO can ensure that the ultimate evaluation achieves a high level of consensus. Afterward, we propose the extended VIKOR method to obtain the optimal solution, which not only avoids the loss of decision information, but also considers the separation of each alternative from the positive ideal solution and the negative ideal solution when criteria are interactive. The advantages of the proposed method are highlighted through a numerical example. Finally, we perform a comparative analysis and a sensitivity analysis to reveal the effectiveness and applicability of the method. [ABSTRACT FROM AUTHOR]

This paper develops a novel group decision-making (GDM) approach for solving multiple-criteria group decision-making (MCGDM) problems with uncertainty. The hesitant fuzzy linguistic term sets (HFLTSs) are applied to elicit the decision makers' linguistic preferences due to their distinguished efficiency and flexibility in representing uncertainty. However, the existing context-free grammar for linguistic description cannot allow generating the linguistic expressions completely free to limit the richness of HFLTSs, and the related methods for dealing with HFLTSs also have limitations in aggregating HFLTSs with different lengths and types. Therefore, this paper proposes extended context-free grammar and a novel GDM approach for HFLTSs, considering the advantages of the rough set theory and OWA operators. The rough set theory can manage the uncertainty existing in the fuzzy representation and deal with HFLTSs represented by the 2-tuple fuzzy linguistic model to get rough number sets. The OWA operator can aggregate these sets with different numbers of elements into an interval simply and objectively. Then, an extended VIKOR method based on the proposed GDM approach for HFLTSs is presented to solve the MCGDM problems. Finally, two examples are given to illustrate the applicability and validity of the developed GDM approach and the hesitant VIKOR method through sensitivity and comparison analysis with other existing approaches. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new type of fuzzy set, called Pythagorean linguistic sets (PLSs), to address the preferred and nonpreferred degrees of linguistic variables. Moreover, it allows decision makers to offer effectively handle uncertain information more flexible than intuitionistic linguistic sets (ILSs) when one compares two alternatives in the process of decision making. Some of the fundamental operational laws, score, accuracy, and aggregation operators are defined, and their properties are investigated. Preference relation (PR) is a useful and efficient tool for decision making that only requires the decision makers to compare two alternatives at one time. Taking the advantages of PLSs and PRs, this paper also introduces Pythagorean linguistic preference relations (PLPRs) and studies their application. We propose an approach for group decision making using group recommendations based on consistency matrices and feedback mechanism. First, the proposed method constructs the collective consistency matrix, the weight collective PRs, and the group collective PRs. Then, it constructs a consensus relation for each expert and determines the group consensus degree (GCD) for all experts. If the GCD is smaller than a predefined threshold value, then a feedback mechanism is activated to update the PLPRs. Finally, after the GCD is greater than or equal to the predefined threshold value, we calculate the arithmetic mathematical average values of the updated group collective PR to select the most appropriate alternative. [ABSTRACT FROM AUTHOR]

The objective of this paper is to present novel algorithms for solving the multiple attribute decision-making problems under the possibility intuitionistic fuzzy soft set (PIFSS) information. The prominent characteristics of the PIFSS are that it considers the membership and nonmembership degrees of each object during evaluation and their corresponding possibility degree. Keeping these features, this paper presents some new operation laws, score function, and comparison laws between the pairs of the PIFSSs. Further, we define COmplex PRoportional ASsessment (COPRAS) and weighted averaging and geometric aggregation operators to aggregate the PIFSS information into a single one. Later, we develop two algorithms based on COPRAS and aggregation operators to solve decision-making problems. In these approaches, the experts and the weights of the parameters are determined with the help of entropy and the distance measure to remove the ambiguity in the information. Finally, a numerical example is given to demonstrate the presented approaches. [ABSTRACT FROM AUTHOR]

Pythagorean hesitant fuzzy sets are widely watched because of their excellent ability to deal with uncertainty, imprecise and vague information. This paper extends Pythagorean hesitant fuzzy environments to interval-valued Pythagorean hesitant fuzzy environments and proposes the concept of interval-valued Pythagorean hesitant fuzzy set (IVPHFS), which allows the membership of each object to be a set of several pairs of possible interval-valued Pythagorean fuzzy elements. Furthermore, we develop a series of aggregation operators for interval-valued Pythagorean hesitant fuzzy information and apply them to multiattribute group decision-making (MAGDM) problems. Then, some desired operational laws and properties of IVPHFSs are studied. Especially, considering an interval-valued Pythagorean fuzzy element (IVPHFE) is formed by several pairs of interval values, this paper proposes the concepts of score function and accuracy function in the form of two interval numbers which can retain interval-valued Pythagorean fuzzy information as much as possible. Then, the relationship among these operators is discussed by comparing the interval numbers. Eventually, an illustrative example fully shows the feasibility, practicality, and effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

Cognitive information can be described by Z-number fully and effectively. However, many problems of Z-number need to be further studied. In this paper, two hidden probability models for calculating Z-number are established to provide more intuitive and abundant information. Next, the dominance degree relationship of Z-number is developed and subdivided. Furthermore, combined with the hidden probability of calculation, three different measurements of dominance degree are defined from three levels of geometry, algebra, and cross entropy based on the outranking relationship. The influencing factors are analyzed for different combinations of two probability models and three dominance degree measures. A multiattribute decision model is established on the basis of new grey association analysis and QUALIFLEX method. Finally, a decision example is given to verify the effectiveness and feasibility of the method. And sensitivity analysis is made to determine the impact of parameters and hidden probability on the decision model. [ABSTRACT FROM AUTHOR]

The interval‐valued q‐rung orthopair fuzzy set (IVq‐ROFS) provides an extension of Yager's q‐rung orthopair fuzzy set (q‐ROFS), where membership and nonmembership degrees are subsets of the closed interval [0,1]. In such a situation, it is more superior for decision makers to provide their judgments by intervals instead of crisp numbers due to the uncertainty and vagueness in real life. In this paper, we study the calculus theories of IVq‐ROFS from the microscopic. In particular, we first introduce the elementary arithmetic of interval‐valued q‐rung orthopair fuzzy values (IVq‐ROFVs), including addition, multiplication, and their inverse. They are the basis for analysis and calculation throughout the work. In addition, we discuss and prove in detail the operation properties and aggregation operators of IVq‐ROFVs. Then, we introduce the concept of interval‐valued q‐rung orthopair fuzzy functions (IVq‐ROFFs), which is the main research object of this paper. After that, we further discuss the continuity, derivatives and differentials of IVq‐ROFFs. We also find that the derivatives of IVq‐ROFFs are closely related to elasticity, which is an important concept in economics. Finally, we provide some application examples to verify the feasibility and effectiveness of the derived results. [ABSTRACT FROM AUTHOR]

A Pythagorean fuzzy set, an extension of intuitionistic fuzzy sets, is very helpful in representing vague information that occurs in real world scenarios. The Dombi operators with operational parameters, have excellent flexibility. Due to the flexible nature of these Dombi operational parameters, this research paper introduces some new aggregation operators under Pythagorean fuzzy environment, including Pythagorean Dombi fuzzy weighted arithmetic averaging (PDFWAA) operator, Pythagorean Dombi fuzzy weighted geometric averaging (PDFWGA) operator, Pythagorean Dombi fuzzy ordered weighted arithmetic averaging operator and Pythagorean Dombi fuzzy ordered weighted geometric averaging operator. Further, this paper presents several advantageous characteristics, including idempotency, monotonicity, boundedness, reducibility and commutativity of preceding operators. By utilizing PDFWAA and PDFWGA operators, this article describes a multicriteria decision‐making (MCDM) technique for solving MCDM problems. Finally, a numerical example related to selection of a leading textile industry is presented to illustrate the applicability of our proposed technique. [ABSTRACT FROM AUTHOR]

In an information age, people often need to face a lot of decision-making information when making decisions. Some indicators are on the high side and others are on the low side which is a common phenomenon in decision-making. So, it is difficult to make a correct and rational judgment. Long-term research has proved that information aggregation operator is an effective tool to solve this kind of problem. Bonferroni mean (BM) is an important information aggregation tool which has the main feature of capturing the interrelationships among aggregated arguments. Because the existing geometric Bonferroni mean (GBM) cannot reflect the two-layer average calculation and the weighted GBM do not feature reducibility, this paper develops the intuitionistic fuzzy normalized weighted optimized GBM (IFNWOGBM) and the generalized intuitionistic fuzzy normalized weighted optimized GBM (GIFNWOGBM) and also studies their desirable properties and special cases. In the end, based on the IFNWOGBM and GIFNWOGBM, a method to multiple attribute decision-making (MADM) problem is proposed. In order to verify the effectiveness of the method, it is used to select the location of the library. [ABSTRACT FROM AUTHOR]

The objectives of this paper are to define novel aggregation operators (AOs) for aggregating different complex spherical fuzzy numbers (CSFNs) under the influence of their membership grades. The uncertainties included in the information are dealt with in contemporary studies of the fuzzy set and its extensions by membership grades, which are a subset of real numbers that lose some relevant information and hence alter the decision results. The conversion to these complex spherical fuzzy sets addresses the classes' uncertainty, whose ranges differ from the specific subset of the complex subset of the unit disk. For this purpose, we defined new CSF power AOs. Some of the desirable properties of these operators have also been investigated. A multiattribute group decision-making (MAGDM) approach is implemented in the structure developed by the CSFNs on the basis of these operators. A numerical example concerning the selection of the best alternatives is given to demonstrate the effectiveness of the defined method and is tested by comparing its results with the various methods. [ABSTRACT FROM AUTHOR]

In this paper, some fundamental theories of the Pythagorean interval 2-tuple linguistic numbers (PI2TLNs) combined with the EDAS (evaluation based on distance from average solution) method are proposed. Firstly, we introduced the original concepts of Pythagorean interval 2-tuple linguistic sets (PI2TLSs), and two aggregation operators of PI2TLN were also introduced. Then, the steps of the EDAS method were described briefly. Moreover, the PI2TLN-EDAS model was provided to address the multiattribute group decision-making (MAGDM) problem, and calculation steps were deduced in detail. The effectiveness of the method was illustrated by taking the ship navigation environment safety assessment as an example. Finally, we conducted comparative analysis between PI2TLN-EDAS method and Pythagorean interval 2-tuple linguistic weighted averaging (PI2TLWA) operator/Pythagorean interval 2-tuple linguistic weighted geometric (PI2TLWG) operator. [ABSTRACT FROM AUTHOR]

This paper describes the new intuitionistic fuzzy aggregation operators in consequence of Aczel–Alsina operations that possess certain advantages in cases of solving real life problems. We first present some new operations of intuitionistic fuzzy sets (IFSs), for example, Aczel–Alsina sum, Aczel–Alsina product, and Aczel–Alsina scalar multiplication. At that point, we create some IF aggregation operators, for example, the IF Aczel–Alsina weighted averaging operator, the IF Aczel–Alsina ordered weighted averaging operator and IF Aczel–Alsina hybrid averaging operator. We set up different properties of these operators. It is demonstrated that suggested averaging operators have the properties of idempotency, boundary, monotonicity, and commutativity. Then, we design new techniques dependent on these operators to fix multiattribute decision making issues. We present an example of human resource selection to elaborate on the performance of our proposed approach. The outcome shows the practicality and viability of the new technique. Eventually, an organized comparison between the prevailing techniques and the suggested technique has been given. [ABSTRACT FROM AUTHOR]

The concept of granulized Z‐numbers improves information utilization and manages the degree of uncertainty in decision‐making. In this paper, a novel scoring method, namely, ordered weighted averaging‐based expected granulized Z‐number, a new aggregation operator, named, granulized Z‐number‐based ordered weighted averaging operator, and a novel fuzzy risk assessment scheme is proposed. The proposed scoring method is used to order the granulized Z‐numbers and takes care of the possibilistic as well as probabilistic information contained in the granulized Z‐numbers. The maximum entropy principle‐based nonlinear optimization model is formulated to capture the aforesaid probabilistic information during the scoring process. Based on the proposed scoring and ordering method, the granulized Z‐number‐based ordered weighted averaging operator is developed, which judiciously integrates the benefits of the granulized Z‐numbers and the ordered weighted averaging operator to provide an improved aggregation of the decision‐making information collected from multiple sources (experts). The required properties are also proved. Finally, the novel fuzzy risk assessment scheme is developed using the granulized Z‐number‐based ordered weighted averaging operator, the average linkage‐based ordered weighted averaged similarity measure between two granulized Z‐numbers, and the basic operations of logical gates of a fault tree. This scheme provides the system‐level failure probability in an easy‐to‐understand form with reliability. A case study is also presented to demonstrate the usability and feasibility of the proposed models and schemes. [ABSTRACT FROM AUTHOR]

In the process of talent selection and evaluation, it is important to know the personality traits, ability, knowledge level, and development potential of the candidates. However, the above evaluation indicators are difficult to describe with precise values, and personnel evaluation often needs to be done through group decision making (GDM). In this paper, we establish a GDM method under the interval‐valued intuitionistic fuzzy (IVIF) environment based on Dombi aggregation operations, which are the extension of existing operations. First, IVIF operations are introduced. Second, a series of IVIF Dombi aggregation operators are proposed, such as IVIF Dombi weighted averaging operator, IVIF Dombi‐ordered weighted averaging (IIFDOWA) operator, IVIF Dombi geometric weighted geometric (IIFDWG) operator, and IVIF Dombi‐ordered weighted geometric (IIFDOWG). The desirable properties of these proposed aggregation operators are well studied. Finally, the GDM method based on these Dombi aggregation operators under the IVIF environment is presented; the case study about personnel evaluation based on the proposed method is presented to show its validity and rationality. The comparison with other methods is presented to show the difference and advantage of the GDM method proposed in this paper. [ABSTRACT FROM AUTHOR]

The q‐rung orthopair fuzzy set (q‐ROFS) that the sum of the qth power of the membership degree and the qth power of the nonmembership degree is restricted to one is a generalization of fuzzy set (FS). Recently, many researchers have given a series of aggregation operators to fuse q‐rung orthopair fuzzy discrete information. Subsequently, although some scholars have also focused on studying q‐rung orthopair fuzzy continuous information and give its continuity, derivative, differential, and integral, those studies are only considered from the perspective of multivariable fuzzy functions. Thus, the main aim of the paper is to study the q‐rung orthopair fuzzy continuous single variable information. In this paper, we first define the concept of q‐rung orthopair single variable fuzzy function (q‐ROSVFF) to describe the fuzzy continuous information, and give its domain to make sure that this kind of function is meaningful. Afterward, we propose the limits, continuities, and infinitesimal of q‐ROSVFFs, and offer the relationship between the limit of q‐ROSVFF and that of q‐ROSVFF infinitesimal. On the basis of the definition of derivative in mathematical analysis, we define the subtraction and division derivatives and basic operational rules, and offer the simpler proofs for the derivatives of q‐ROSVFFs. What is more, we propose the subtraction and division differential invariances, and give the approximate calculation formulas of q‐ROSVFFs when the value of independent variable is changed small enough. In the real situation, fundamental functions cannot be used to express more complicated functions, thus we define the compound q‐ROSVFFs and give their chain rules of subtraction and division derivatives. Finally, we use numerical examples by simulation to verify the feasibility and veracity of the approximate calculation on q‐ROSVFFs. [ABSTRACT FROM AUTHOR]

The study presents a novel conception of aggregation operators (AOs) based on bipolar neutrosophic sets by using Hamacher operations and their application in modeling real-life multicriteria decision-making problems. The neutrosophic set represents incomplete, inconsistent, and indeterminate information effectively. For better understanding in this paper, we have explained all essential definitions and their respective derived neutrosophic sets (NSs) and generalization bipolar neutrosophic sets (BNSs). The primary focus of our work is Hamacher aggregation operators like BN Hamacher weighted geometric (BNHWG), BN Hamacher ordered weighted geometric (BNHOWG), and BN Hamacher hybrid geometric (BNHHG) and their required properties. The proposed scheme provides decision-makers with a comprehensive view of the complexities and vagueness in multicriteria decision-making. As compared to existing methods, these techniques provide comprehensive, increasingly exact, and precise results. Finally, we applied different types of newly introduced AOs and numerical representation on a practical example to demonstrate the effectiveness of the proposed method. Our proposed model and its application have shown improved utility and applicability in the complex decision-making process. [ABSTRACT FROM AUTHOR]

Industrial control system (ICS) attacks are usually targeted attacks that use the ICS entry approach to get a foothold within a system and move laterally throughout the organization. In recent decades, powerful attacks such as Stuxnet, Duqu, Flame, and Havex have served as wake-up calls for industrial units. All organizations are faced with the rise of security challenges in technological innovations. This paper aims to develop aggregation operators that can be used to address the decision-making problems based on a spherical fuzzy rough environment. Meanwhile, some interesting properties of idempotence, boundedness, and monotonicity for the proposed operators are analyzed. Moreover, we use this newly constructed framework to select ICS security suppliers and validate its acceptability. Furthermore, a different test has been performed based on a new operator to strengthen the suggested approach. Additionally, comparative analysis based on the novel extended TOPSIS method is presented to demonstrate the superiority of the proposed technique. The results show that the conventional approach has a larger area for information representation, better adaptability to the evaluation environment, and higher reliability of the evaluation results. [ABSTRACT FROM AUTHOR]

In recent years, q-rung orthopair fuzzy sets have been appeared to deal with an increase in the value of q > 1 , which allows obtaining membership and nonmembership grades from a larger area. Practically, it covers those membership and nonmembership grades, which are not in the range of intuitionistic fuzzy sets. The hybrid form of q-rung orthopair fuzzy sets with soft sets have emerged as a useful framework in fuzzy mathematics and decision-makings. In this paper, we presented group generalized q-rung orthopair fuzzy soft sets (GGq-ROFSSs) by using the combination of q-rung orthopair fuzzy soft sets and q-rung orthopair fuzzy sets. We investigated some basic operations on GGq-ROFSSs. Notably, we initiated new averaging and geometric aggregation operators on GGq-ROFSSs and investigated their underlying properties. A multicriteria decision-making (MCDM) framework is presented and validated through a numerical example. Finally, we showed the interconnection of our methodology with other existing methods. [ABSTRACT FROM AUTHOR]

This paper proposes an approach to linguistic three‐way decision making problem with double hierarchy linguistic term evaluation information. Double hierarchy linguistic term set consists of the first hierarchy and second hierarchy linguistic term set, which can describe uncertainty and fuzziness more flexibly. First, the Hamacher operational rules, score function and distance measure of double hierarchy linguistic elements are defined. Next, we construct the double hierarchy linguistic decision‐theoretic rough set model. And the conditional probability is calculated based on the double hierarchy linguistic term environment with grey relational analysis, which makes the process of decisions more rational. Then the loss functions are aggregated by the double hierarchy linguistic Hamacher weighted averaging operator, which takes into account different decision attitudes of decision makers. And the results of decision are deduced by the minimum‐loss principle. Finally, a case study about the selection of cooperation companies during the COVID‐19 is used to demonstrate the practicability of our proposed method. [ABSTRACT FROM AUTHOR]

Uncertainty modeling can be done by different theories, such as probability theory, fuzzy sets theory, vague sets theory, and so forth. Each of them may be appropriate for special cases and circumstances, based on the nature and type of the existing problem. In this paper, generalized hesitant fuzzy numbers (GHFNs), as a generalization of hesitant fuzzy sets in which decision‐maker is hesitant between a finite set of real values with a finite set of hesitation degrees, will be introduced. Some usage and needful concepts, such as mean value, score function, and variance, of GHFNs will be proposed. These concepts will be applied to compare any two given GHFNs. Also, arithmetic operations, generalized hesitant fuzzy weighted arithmetic averaging operator, generalized hesitant fuzzy weighted geometric averaging operator, generalized hesitant fuzzy ordered weighted averaging operator, and generalized hesitant fuzzy ordered weighted geometric averaging operator of GHFNs will be defined. In the following, an uncertain multiattribute group decision‐making problem will be modeled and solved via these new concepts. The proposed concepts will be illustrated by a numerical example, where the credibility of its results will be checked by test criteria and studied comparatively. [ABSTRACT FROM AUTHOR]

In this paper, we develop a multicriteria group decision‐making methodology with probabilistic linguistic q‐rung orthopair fuzzy sets (PLqROFSs). The benefit of choosing PLqROFSs is that they consider the simultaneous occurrence of stochastic and nonstochastic uncertainty and so are superior to probabilistic hesitant fuzzy sets, linguistic intuitionistic fuzzy sets, and linguistic Pythagorean fuzzy sets. To develop the methodology, we first propose two types of operators, namely, probabilistic linguistic q‐rung orthopair fuzzy weighted Generalized Dombi operator which gives the flexibility of choosing the parameter values and probabilistic linguistic q‐rung orthopair fuzzy weighted Generalized Dombi Bonferroni mean operator which can consider the interrelationships between criteria. Since both the subjective and objective weights of experts are hardly considered in the current PLqROFSs‐based research, so in our proposed methodology, we deploy the thought of consistency and similarity between the experts to calculate the subjective and objective weights, respectively, of the experts and as a result the evaluation results do not get malformed. For measuring the weights of criteria, the gray correlation coefficient of the assessment value of criteria is used to reflect the similarity between the criteria and its reference value. To exhibit the applicability of the proposed operators, we provide a case study on biomass feedstock selection. Moreover, to make sure that our model is stable, we have investigated a sensitivity analysis of parameters. At the end, we make a comparison of our approach to different existing schemes. [ABSTRACT FROM AUTHOR]

Interval numbers multiple attribute decision‐making (MADM) is an important branch of uncertainty decision theory, and the decision result largely depends on the selection of the aggregation operator. In this paper, we analyze the ordered weighted average (OWA) operator, which is an averaging aggregation operator. The OWA operator provides an aggregation method between the minimum and maximum operators. Moreover, we further analyze some of extensions about OWA operator, and pay special attention to the Bonferroni means and OWA (BON‐OWA) operator. Note that the BON‐OWA operator only aggregate the input arguments which are exact numbers. Under normal circumstances, decision makers is difficult to provide a clear evaluation value for attribute and most of them are described by vague information. When the decision information is an interval numbers, the BON‐OWA operator cannot describe decision result accurately. Under these environments, we proposed the interval numbers BON‐OWA (IBr,q‐OWA) operator to deal with the vague decision information in this paper. Then we consider their main properties, such as idempotence, monotonicity, and boundedness and prove them. Besides, a wide range of special aggregation operators are found in changing parameter values, such as the square mean and max operator, and so on. We also compare the ranking method of the interval numbers based on Boolean matrix. As a result, the combination of IBr,q‐OWA operator makes the decision result more scientific. Finally, a new approach for decision‐making problem is developed based on the IBr,q‐OWA operator, which shows the effectiveness in practical examples. [ABSTRACT FROM AUTHOR]

To evaluate objects under uncertainty, many fuzzy frameworks have been designed and investigated so far. Among them, the frame of picture fuzzy set (PFS) is of considerable significance which can describe the four possible aspects of expert's opinion using a degree of membership (DM), degree of nonmembership (DNM), degree of abstinence (DA), and degree of refusal (DR) in a certain range. Aggregation of information is always challenging especially when the input arguments are interrelated. To deal with such cases, the goal of this study is to develop the notion of the Maclaurin symmetric mean (MSM) operator as it aggregates information under uncertain environments and considers the relationship of the input arguments, which make it unique. In this paper, we studied the theory of MSM operators in the layout of PFSs and discussed their applications in the selection of the most suitable enterprise resource management (ERP) scheme for engineering purposes. We developed picture fuzzy MSM (PFMSM) operators and investigated their validity. We developed the multiattribute decision-making (MADM) algorithm based on the PFMSM operators to examine the performance of the ERP systems using picture fuzzy information. A numerical example to evaluate the performance of ERP systems is studied, and the effects of the associated parameters are discussed. The proposed aggregated results using PFMSM operators are found to be reliable as it takes into account the interrelationship of the input information, unlike traditional aggregation operators. A comparative study of the proposed PFMSM operators is also studied. [ABSTRACT FROM AUTHOR]

This paper extends q‐rung orthopair fuzzy numbers into q‐rung orthopair trapezoidal fuzzy numbers to solve a multiattribute group decision‐making problem. The decision‐makers (DMs) provide some of their assessments in hesitant form, along with hesitancy weights. The basic operations laws, Hamming distance, weighted similarity measure, value and ambiguity indexes, weighted average aggregation operator, and weighted geometric aggregation operator, with their properties, are discussed for these extended fuzzy numbers. The value and ambiguity indexes are used in the Shannon entropy to evaluate the weights of the DMs and attributes'. These weights are then used to aggregate the DMs' assessments in the TOPSIS approach to obtain a weighted similarity measure from both the alternatives' positive and negative ideal solutions. The proposed approach's effectiveness is demonstrated by solving a waste disposal site selection problem. The approach is further validated through the basic properties of multiattribute decision making, comparative analyses, and comparing simulation results with an existing approach. [ABSTRACT FROM AUTHOR]

In this paper, we examine the multicriteria decision-making (MCDM) difficulties for Pythagorean fuzzy hypersoft sets (PFHSSs). The PFHSSs are a suitable extension of the Pythagorean fuzzy soft sets (PFSSs) which deliberates the parametrization of multi-subattributes of considered parameters. It is a most substantial notion for describing fuzzy information in the decision-making (DM) procedure to accommodate more vagueness comparative to existing PFSSs and intuitionistic fuzzy hypersoft sets (IFHSSs). The core objective of this study is to plan some innovative operational laws considering the interaction for Pythagorean fuzzy hypersoft numbers (PFHSNs). Also, based on settled interaction operational laws, two aggregation operators (AOs) i.e., Pythagorean fuzzy hypersoft interaction weighted average (PFHSIWA) and Pythagorean fuzzy hypersoft interaction weighted geometric (PFHSIWG) operators for PFHSSs operators have been presented with their fundamental properties. Furthermore, an MCDM technique has been established using planned interaction AOs. To ensure the strength and practicality of the developed MCDM method, a mathematical illustration has been presented. The usefulness, influence, and versatility of the developed method have been demonstrated via comparative analysis with the help of some conventional studies. [ABSTRACT FROM AUTHOR]

For the application of probabilistic linguistic term sets (PLTSs) in multicriteria group decision making (MCGDM), this paper aims to develop an approach to solve the preference problem. First, a belief interval interpretation of PLTSs is presented, which makes it possible to represent the mathematical operations on PLTSs as the operations on belief intervals. This can reduce the uncertainty degree of information caused by the differentiated knowledge and cognitions of decision makers. Then, two methods of belief interval measure are proposed. One is the distance measure, which is utilized to obtain the criteria weights of each decision maker, so as to recognize the preferences for criteria. The other is the probability degree, which is used to get the partial order relation for alternatives of each decision maker, and to recognize the preferences for alternatives. Next, employing Dempster's rule of combination and graph theory, a visual algorithm is constructed to solve the MCGDM preference problem in the application of PLTSs. Finally, an illustrative example for the selection of emergency materials deployment scheme and the comparative analyses are shown to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In view of the decision‐making problem that the alternatives actively participate in the decision‐making process and present competitive behavior, this paper proposes a new type of aggregation operator called the competitive behavior induced ordered weighted averaging (CB‐IOWA) operator. The primary characteristic of the CB‐IOWA operator is that the alternative is permitted to highlight its competitive advantage through the order‐inducing variables and the weighting vector. A method is introduced to determine the final weighting vector based on the weights provided by different alternatives that can reflect their competitive advantages. The final weights are calculated by maximizing the closeness degree between the final weights and the ones provided the alternatives. The main properties of the CB‐IOWA operator are discussed, such as commutativity, boundness, and monotonicity under certain condition. Finally, an application example regarding the competitive development of the economy‐environment of four cities in China is provided to illustrate the usage of the CB‐IOWA operator. The validity of the operator is checked by comparison with the weighted arithmetic averaging operator representing noncompetitive behavior. [ABSTRACT FROM AUTHOR]

Many aggregation operators in multiattribute decisions assume that attributes are independent of each other; this leads to an unreasonable situation in information aggregation and decision-making. Heronian mean is the aggregation operator that can embody the interaction between attributes. In this paper, we merge the linguistic neutrosophic cubic number (LNCN) and the Heronian mean operator together to develop a LNCN generalized weighted Heronian mean (LNCNGWHM) operator and a LNCN three-parameter weighted Heronian mean (LNCNTPWHM) operator and then discuss their properties. Further, two multiattribute decision methods based on the proposed LNCNGWHM or LNCNTPWHM operator are introduced under LNCN environment. Finally, an example is used to indicate the effectiveness of the developed methods. [ABSTRACT FROM AUTHOR]

This paper proposes an approach to linguistic multiple attribute decision-making problems with interactive unbalanced linguistic assessment information by unbalanced linguistic generalized Heronian mean aggregation operators. First, some generalized Heronian mean aggregation operators with unbalanced linguistic information are proposed, involving the unbalanced linguistic generalized arithmetic Heronian mean operator and the unbalanced linguistic generalized geometric Heronian mean operator. For the situation that the input arguments have different degrees of importance, the unbalanced linguistic generalized weighted arithmetic Heronian mean operator and the unbalanced linguistic generalized weighted geometric Heronian mean operator are developed. Then we investigate their properties and some particular cases. Finally, the effectiveness and universality of the developed approach are illustrated by a low-carbon tourist instance and comparison analysis. A sensitivity analysis is performed as well to test the robustness of proposed methods. [ABSTRACT FROM AUTHOR]

In the multiple attribute linguistic group decision making analysis with interval-valued intuitionistic fuzzy linguistic information, seeking highly efficient aggregation method and order relation play a crucial role. In this paper, we redefine an interval-valued intuitionistic fuzzy linguistic variable that considers principal component and propose generalized interval-valued intuitionistic fuzzy linguistic induced hybrid aggregation (GIVIFLIHA) operator with entropic order-inducing variable and interval-valued intuitionistic fuzzy linguistic technique for order preference by similarity to an ideal solution (TOPSIS) order relation based on interval-valued intuitionistic fuzzy linguistic distance measure. Then, some primary properties of the GIVIFLIHA operator are discussed, and a linguistic group decision-making approach based on GIVIFLIHA operator and interval-valued intuitionistic fuzzy linguistic TOPSIS order relation is proposed. Finally, a numerical example concerning the investment strategy is given to illustrate the validity and applicability of the proposed method, and then the method is compared with the existing method to further illustrate its flexibility. [ABSTRACT FROM AUTHOR]

In this paper, we utilize power aggregation operators to develop some Pythagorean fuzzy power aggregation operators: Pythagorean fuzzy power average operator, Pythagorean fuzzy power geometric operator, Pythagorean fuzzy power weighted average operator, Pythagorean fuzzy power weighted geometric operator, Pythagorean fuzzy power ordered weighted average operator, Pythagorean fuzzy power ordered weighted geometric operator, Pythagorean fuzzy power hybrid average operator, and Pythagorean fuzzy power hybrid geometric operator. The prominent characteristic of these proposed operators are studied. Then, we have utilized these operators to develop some approaches to solve the Pythagorean fuzzy multiple attribute decision-making problems. Finally, a practical example is given to verify the developed approach and to demonstrate its practicality and effectiveness. [ABSTRACT FROM AUTHOR]

In this paper, Bonferroni mean (BM) and Dombi t‐conorms and t‐norms (Dt‐CN&t‐Ns) are combined under dual hesitant q‐rung orthopair fuzzy (DHq‐ROF) environment to produce DHq‐ROF‐Dombi BM, weighted Dombi BM, Dombi geometric BM, and Dombi weighted geometric BM aggregation operators (AOs). Using these operators, the decision making processes would become more flexible and also would possess the capabilities of capturing interrelationships among input arguments under imprecise decision making environments. Apart from those, a large number of AOs either already developed or not yet developed may also be derived from the proposed AOs. In the process of developing the AOs, some operational laws of DHq‐ROF numbers based on Dt‐CN&t‐Ns are defined first. Several important properties of the developed operators are discussed. The proposed AOs are used to frame a new methodology to solve multicriteria group decision making problems under DHq‐ROF contexts. Several illustrative examples are solved to demonstrate effectiveness and benefits of the developed method. Sensitivity analysis is performed to show the variations of ranking values with the change of different parameters in the decision making contexts. Finally, the introduced method is compared with several existing techniques to establish superiority and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, based on power aggregation (PA) operators, neutrality average and neutrality geometric aggregation operators are proposed. Furthermore, a general score function for q‐rung orthopair fuzzy sets (q‐ROFSs) is proposed. PA can reduce the impact of excessively high or excessively low arguments. It also emphasizes the interrelationship between attributes on the decision matrix. PA and neutrality aggregations (NAs) were hybrid with more fair and neutral decisions of the DMs evaluations. Also, neutrality aggregation operator provides reliable results by taking into account neutrality among decision‐makers. On the one hand, through its dynamic structure, q‐ROFSs provide a wider evaluation for decision‐makers (DMs). q‐ROFSs include many fuzzy sets with varying q≥1 parameters. One of the most important parts of multi‐attribute group decision‐making problems is that DMs do not take into account their bias. On the other hand, the NA operator evaluates the decisions of the DMs from a neutral attitude perspective. The power neutrality aggregation operator proposed in this study produces more objective results. The proposed operator is more consistent with the advantages of both operators and it deals with the attitude of DMs more objectively. Validity tests are applied to the proposed methods. Also, the superior aspects of the proposed methods are demonstrated by numerical examples. As a result of validity tests and comparisons with other studies in the literature, it is seen that the proposed methods give effective results. [ABSTRACT FROM AUTHOR]

In this paper we propose a new induced ordered weighted averaging (IOWA) operator for expert opinions aggregation, namely, the average‐induced OWA (AIOWA) operator. The AIOWA operator defines the order‐induced variable as the similarity of each individual expert's opinion with respect to the average opinion of the group, as the average opinion is notably an important piece of information of the group opinion and often used as an approximate estimate of the group opinion with equal weights. The new operator facilitates to capture the distribution characteristics of the opinion data with respect to the consensus and constructs a nonlinear aggregation of individual opinions. Further, we extend the new operator to the situation where the experts' opinions are represented by probability density functions (PDFs). Last, we incorporate the entropy‐orness optimization model into the proposed aggregation operator. The new operator makes the aggregation process more flexible in terms of application problems. Two case studies are conducted to show the effectiveness of the proposed operators. The result is promising. [ABSTRACT FROM AUTHOR]

Probabilistic linguistic term sets (PLTSs) have many applications in the field of group decision making (GDM) because it includes both linguistic evaluation and probabilistic distribution when expressing preference information. However, the difference of information credibility in PLTSs is ignored, resulting in an inaccurate representation of decision information and unreasonable probability calculation. In this paper, we first consider the credibility of the information and propose the concept of Z‐uncertain probabilistic linguistic variables (Z‐UPLVs). Subsequently, the operational rules, normalization, distance and similarity measures, and comparison method of Z‐UPLVs are introduced. Then, a probability calculation method based on credibility, an extended TOPSIS method, and some operators are proposed, which can be applied to emergency decision making in the Z‐uncertain probabilistic linguistic (Z‐UPL) environment. Finally, an emergency decision‐making case of COVID‐19 patients and comparative analysis illustrate the necessity and effectiveness of this method. [ABSTRACT FROM AUTHOR]

Information fusion is an important part of multiple-attribute decision-making, and aggregation operator is an important tool of decision information fusion. Integration operators in a variety of fuzzy information environments have a slight lack of consideration for the correlation between variables. Archimedean copula provides information fusion patterns that rely on the intrinsic relevance of information. This paper extends the Archimedean copula to the aggregation of hesitant fuzzy information. Firstly, the Archimedean copula is used to generate the operation rules of the hesitant fuzzy elements. Secondly, the hesitant fuzzy copula Bonferroni mean operator and hesitant fuzzy weighted copula Bonferroni mean operator are propounded, and several properties are proved in detail. Furthermore, a decision-making method based on the operators is proposed, and the specific decision steps are given. Finally, an example is presented to illustrate the practical advantages of the method, and the sensitivity analysis of the decision results with the change of parameters is carried out. [ABSTRACT FROM AUTHOR]

This paper clarifies, how a preference aggregation problem can be solved using the prioritized aggregation operators (PAO), where, a given group of candidates should be aggregated based upon their satisfaction for a collection of ranked places. The comparison results show that the proposed method can accurate aggregate a preference ranking system with less computation and without the need to solve any mathematical model. Also, a metasearch application shows the usefulness of applying the PAO for a preference aggregation. © 2010 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

The probabilistic hesitant fuzzy preference relations (PHFPRs) provide the decision makers with an efficient means to express the preference information on pairwise comparisons over alternatives. In this paper, we propose an automatic consistency improving model for PHFPRs. First, we propose a novel normalization algorithm to normalize probabilistic hesitant fuzzy elements (PHFEs) by using probability splitting idea and develop novel operational laws. Then, we define the consistency index to compute the degree of deviation between the PHFPRs and their multiplicative consistent PHFPRs. We also develop a novel consistency threshold estimation method for obtaining the threshold of consistency index and then put forward an automatic consistency improving algorithm for repairing inconsistent PHFPRs. Moreover, two probabilistic hesitant fuzzy aggregation operators are put forward to aggregate preference values in acceptably multiplicative consistent PHFPRs for obtaining the ranking orders of alternatives. Finally, an illustrative example is given to show the implementation process of our proposed automatic consistency improving model and also we compare our proposed model with the existing studies. [ABSTRACT FROM AUTHOR]

This paper investigates the geometric aggregation operators for aggregating the interval-valued complex fuzzy sets (IVCFSs) whose membership grades are a special set of complex numbers. We develop some geometric aggregation operators under the interval-valued complex fuzzy environment, namely, interval-valued complex fuzzy geometric (IVCFG), interval-valued complex fuzzy weighted geometric (IVCFWG), and interval-valued complex fuzzy ordered weighted geometric (IVCFOWG) operators. Then, we investigate the rotational and reflectional invariances of these operators. Further, a decision-making approach based on these operators is presented under the interval-valued complex fuzzy environment and an example is illustrated to demonstrate the efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

Data Envelopment Analysis is one of the paramount mathematical methods to compute the general performance of organizations, which utilizes similar sources to produce similar outputs. Original DEA schemes involve crisp information of inputs and outputs that may not always be accessible in real-world applications. Nevertheless, in some cases, the values of the data are information with indeterminacy, impreciseness, vagueness, inconsistent, and incompleteness. Furthermore, the conventional DEA models have been originally formulated solely for desirable outputs. However, undesirable outputs may additionally be present in the manufacturing system, which wishes to be minimized. To tackle the mentioned issues and in order to obtain a reliable measurement that keeps original advantage of DEA and considers the influence of undesirable factors under the indeterminate environments, this paper presents a neutrosophic DEA model with undesirable outputs. The recommended technique is based on the aggregation operator and has a simple construction. Finally, an example is given to illustrate the new model and ranking approach in details. [ABSTRACT FROM AUTHOR]

In the process of decision making (DM), to have more freedom in expressing DM experts' belief about membership and nonmembership grade, Yager presented the q‐rung orthopair fuzzy sets (q‐ROFSs) as an extension of fuzzy sets. Recently, for aggregating discrete and continuous q‐ROF information, many scholars provided various aggregation operators. However, there are still some kinds of continuous q‐ROF information cannot be aggregated through existing aggregation operators. In this paper, we present two novel kinds of line integrals under the q‐rung orthopair fuzzy environment (q‐ROFE), which supply a wider range on method choice for multiple attribute decision making (MADM) concerning discrete or continuous q‐ROF information. We first construct the first form of line integral under the q‐ROFE and study their properties, we prove the specific condition mean valued theorem but negate the general condition for it. Besides, several inequalities with regard to it are also provided. After that, we give two characterization forms of the second form of line integral under the q‐ROFE, we study the relationship between two kinds of line integrals. What is more important, we show the Green formula under q‐ROFE, which connect the existing q‐rung orthopair fuzzy integration theory. Afterward, we provide two kinds of aggregation operators on the basis of two line integrals, respectively. As their applications, we give two novel MADM methods based on two kinds of line integral aggregation operators. And some examples are shown to demonstrate the aggregation process of line integral operators. We not only stress their availabilities and superiorities on aggregating continuous q‐ROF information, but also comparing with other existing aggregation methods for emphasizing the novel methods' abilities when deal with abnormal q‐ROF information. [ABSTRACT FROM AUTHOR]