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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]

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]

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]

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 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]

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]

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]

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]

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]

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]

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]

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 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, 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]

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]

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]

In this paper, we extend the Bonferroni mean (BM) operator with the picture fuzzy numbers (PFNs) to propose novel picture fuzzy aggregation operators and demonstrate their application to multicriteria decision making (MCDM). On the basis of the algebraic operational rules of PFNs and BM, we introduce some aggregation operators: the picture fuzzy Bonferroni mean, the picture fuzzy normalized weighted Bonferroni mean, and the picture fuzzy ordered weighted Bonferroni mean. Then, a new picture fuzzy MCDM method is proposed with the help of the proposed operators. Lastly, a practical application of proposed model is given to verify the developed model and related results of the proposed model is compared with the results of the existing models to indicate its applicability. [ABSTRACT FROM AUTHOR]

The probabilistic linguistic term set is a flexible and efficient tool to represent the cognitive complex information of experts. It has attracted many scholars' attention since it was proposed. Information fusion over the cognitive complex information is a significant issue for decision‐making problems. Over the past years, more than 40 aggregation operators have been proposed to fuse the probabilistic linguistic term sets. The aim of this paper is to survey the existing probabilistic linguistic aggregation operators from the perspectives of principles, definitions, classifications, and applications. To do so, first, we summarize the present normalization techniques and operations of probabilistic linguistic term sets. Afterward, this study classifies the existing probabilistic linguistic aggregation operators into 12 kinds. Then, the application areas of these probabilistic linguistic aggregation operators are outlined. Future research directions with interests are proposed to tackle present challenges. [ABSTRACT FROM AUTHOR]

Pythagorean fuzzy sets, as an extension of intuitionistic fuzzy sets to deal with uncertainty, have attracted much attention since their introduction, in both theory and application aspects. In this paper, we investigate multiple attribute decision‐making (MADM) problems with Pythagorean linguistic information based on some new aggregation operators. To begin with, we present some new Pythagorean fuzzy linguistic Muirhead mean (PFLMM) operators to deal with MADM problems with Pythagorean fuzzy linguistic information, including the PFLMM operator, the Pythagorean fuzzy linguistic‐weighted Muirhead mean operator, the Pythagorean fuzzy linguistic dual Muirhead mean operator and the Pythagorean fuzzy linguistic dual‐weighted Muirhead mean operator. The main advantages of these aggregation operators are that they can capture the interrelationships of multiple attributes among any number of attributes by a parameter vector P and make the information aggregation process more flexible by the parameter vector P. In addition, some of the properties of these new aggregation operators are proved and some special cases are discussed where the parameter vector takes some different values. Moreover, we present two new methods to solve MADM problems with Pythagorean fuzzy linguistic information. Finally, an illustrative example is provided to show the feasibility and validity of the new methods, to investigate the influences of parameter vector P on decision‐making results, and also to analyze the advantages of the proposed methods by comparing them with the other existing methods. [ABSTRACT FROM AUTHOR]

The linguistic intuitionistic fuzzy sets (LIFSs) and linguistic Pythagorean fuzzy sets (LPFSs) are two linguistic orthopair fuzzy sets whose membership grades are pairs of linguistic terms from the predefined linguistic term sets (LTSs). One linguistic term indicates the membership degree (MD), while the other one gives the nonmembership degree (NMD). In each LIFS, the sum of the subscripts of MD and NMD is less than the cardinality of LTS. In the LPFSs, the sum of the squares of the subscripts of MD and NMD is less than the square of the cardinality of LTS. In this paper, we propose a general form of these two linguistic orthopair fuzzy sets, which can be named linguistic q‐rung orthopair fuzzy sets. We devise the operational laws, based on which, the linguistic q‐rung orthopair fuzzy weighted averaging (LqROFWA) operator and linguistic q‐rung orthopair fuzzy weighted geometric (LqROFWG) operator are developed to aggregate the linguistic q‐rung orthopair fuzzy numbers (LqROFNs). Then, the novel interactional operational laws that consider the interactions between the MD and NMD from different LqROFNs are given. The partitioned geometric Heronian mean (PGHM) operator can effectively solve the decision‐making problems in which the attributes grouped into the same clusters have interrelationships and the attributes belonging to different clusters have no interrelationship. Based on these novel operational laws and PGHM operator, the linguistic q‐rung orthopair fuzzy interactional PGHM (LqROFIPGHM) operator and linguistic q‐rung orthopair fuzzy interactional weighted PGHM (LqROFIWPGHM) operator are proposed and their properties are discussed. Based on the LqROFIWPGHM operator, an efficient multiattribute group decision‐making model is given to deal with the linguistic q‐rung orthopair fuzzy information. Finally, the superiorities of the interactional operational laws and LqROFIWPGHM operator are tested using some illustrative examples. [ABSTRACT FROM AUTHOR]

The power Bonferroni mean (PBM) operator can relieve the influence of unreasonable aggregation values and also capture the interrelationship among the input arguments, which is an important generalization of power average operator and Bonferroni mean operator, and Pythagorean fuzzy set is an effective mathematical method to handle imprecise and uncertain information. In this paper, we extend PBM operator to integrate Pythagorean fuzzy numbers (PFNs) based on the interaction operational laws of PFNs, and propose Pythagorean fuzzy interaction PBM operator and weighted Pythagorean fuzzy interaction PBM operator. These new Pythagorean fuzzy interaction PBM operators can capture the interactions between the membership and nonmembership function of PFNs and retain the main merits of the PBM operator. Then, we analyze some desirable properties and particular cases of the presented operators. Further, a new multiple attribute decision making method based on the proposed method has been presented. Finally, a numerical example concerning the evaluation of online payment service providers is provided to illustrate the validity and merits of the new method by comparing it with the existing methods. [ABSTRACT FROM AUTHOR]

Multiple‐attribute group decision making (MAGDM) under linguistic environment is an important part of modern decision sciences, and information aggregation operator plays an import role in solving MAGDM problems. In this paper, an approach for solving MAGDM problem with q‐rung orthopair fuzzy 2‐tuple linguistic information is developed. First, the q‐rung orthopair fuzzy 2‐tuple linguistic weighted averaging (q‐ROFTLWA) operator and the q‐rung orthopair fuzzy 2‐tuple linguistic weighted geometric (q‐ROFTLWG) operator are presented. Furthermore, the q‐rung orthopair fuzzy 2‐tuple linguistic Muirhead mean (q‐ROFTLMM) operator and the q‐rung orthopair fuzzy 2‐tuple linguistic dual Muirhead mean (q‐ROFTLDMM) operator are proposed on the basis of Muirhead mean (MM) operator and dual Muirhead mean (DMM) operator. Then, an approach is developed to deal with MAGDM problem under q‐rung orthopair fuzzy 2‐tuple linguistic environment based on the proposed operators. Finally, a numerical example for selecting desirable emergency alternative(s) in the process of designing emergency preplan is given to illustrate the application of the developed method and demonstrate its effectiveness. [ABSTRACT FROM AUTHOR]

The concept of q‐rung orthopair fuzzy set (q‐ROFS) is the extension of intuitionistic fuzzy set (IFS) in which the sum of the qth power of the support for and the qth power of the support against is bounded by one. Therefore, the q‐ROFSs are an important way to express uncertain information in broader space, and they are superior to the IFSs and the Pythagorean fuzzy sets. In this paper, the familiarity degree of the experts with the evaluated objects is incorporated to the initial assessments under q‐rung orthopair fuzzy environment. For this, some aggregation operators are proposed to combine these two types of information. Their some important properties are also well proved. Furthermore, these developed operators are utilized in a multicriteria decision‐making approach and demonstrated with a real life problem of customers' choice. Then, the experimental results are compared with other existing methods to show its superiority over recent research works. [ABSTRACT FROM AUTHOR]

In this paper, a new tool, called q‐rung orthopair uncertain linguistic numbers (q‐ROULNs), is developed and a new multiattribute group decision making (MAGDM) method for q‐ROULNs is proposed. First, the concept of q‐rung orthopair uncertain linguistic sets (q‐ROULSs) is introduced, and some operational laws, expected function, accuracy function, and distance measure of q‐ROULSs are defined. Further, to effectively aggregate q‐ROULNs, we take advantage of partitioned Heronian mean operator and power average operator and propose the q‐rung orthopair uncertain linguistic power partitioned Heronian mean operator and its weighted form. The proposed operators not only deal with this situations where attributes are divided into several parts and attributes in the same part are interrelated each other, whereas attributes in different parts have no relationship, but also reduce the negative influence of unreasonable attribute values provided by decision makers on final results. Some desirable properties and special cases of the proposed operators are also investigated. Finally, a MAGDM method based on the proposed operators is developed and a numerical instance as well as comparative analysis is conducted to illustrate the effectiveness and advantages of the proposed method. [ABSTRACT FROM AUTHOR]

In the real decision making, q‐rung orthopair fuzzy sets (q‐ROFSs) as a novel effective tool can depict and handle uncertain information in a broader perspective. Considering the interrelationships among the criteria, this paper extends Choquet integral to the q‐rung orthopair fuzzy environment and further investigates its application in multicriteria two‐sided matching decision making. To determine the fuzzy measures used in Choquet integral, we first define a pair of q‐rung orthopair fuzzy entropy and cross‐entropy. Then, by utilizing λ‐fuzzy measure theory, we propose an entropy‐based method to calculate the fuzzy measures upon criteria. Furthermore, we discuss q‐rung orthopair fuzzy Choquet integral operator and its properties. Thus, with the aid of q‐rung orthopair fuzzy Choquet integral, we consider the preference heterogeneity of the matching subjects and further explore the corresponding generalized model and approach for the two‐sided matching. Finally, a simulated example of loan market matching is given to illustrate the validity and applicability of our proposed approach. [ABSTRACT FROM AUTHOR]

The operations of t‐norm (TN) and t‐conorm (TCN), developed by Dombi, are generally known as Dombi operations, which have an advantage of flexibility within the working behavior of parameter. In this paper, we use Dombi operations to construct a few Q‐rung orthopair fuzzy Dombi aggregation operators: Q‐rung orthopair fuzzy Dombi weighted average operator, Q‐rung orthopair fuzzy Dombi order weighted average operator, Q‐rung orthopair fuzzy Dombi hybrid weighted average operator, Q‐rung orthopair fuzzy Dombi weighted geometric operator, Q‐rung orthopair fuzzy Dombi order weighted geometric operator, and Q‐rung orthopair fuzzy Dombi hybrid weighted geometric operator. The different features of these proposed operators are reviewed. At that point, we have used these operators to build up a model to solve the multiple‐attribute decision making issues under Q‐rung orthopair fuzzy environment. Ultimately, a realistic instance is stated to substantiate the created model and to exhibit its applicability and viability. [ABSTRACT FROM AUTHOR]

The variance is a statistical measure frequently used for analysis of dispersion in the data. This paper presents new types of variances that use Bonferroni means and ordered weighted averages in the aggregation process of the variance. The main advantage of this approach is that we can underestimate or overestimate the variance according to the attitudinal character of the decision‐maker. The work considers several particular cases including the minimum and the maximum variance and presents some numerical examples. The article also develops some extensions and generalizations by using induced aggregation operators and generalized and quasi‐arithmetic means. These approaches provide a more general framework that can consider a lot of other particular cases and a complex attitudinal character that could be affected by a wide range of variables. The study ends with an application of the new approach in a business decision‐making problem regarding strategic analysis in enterprise risk management. [ABSTRACT FROM AUTHOR]

To the problem of multi‐attribute decision making with fuzzy numbers, this paper proposes a new type of operator called the density‐clusters ordered weighted averaging (OWA) operator based on generalized trapezoidal fuzzy (GTF) numbers. This operator is abbreviated as the GTF‐DOWA operator. A primary characteristic of the GTF‐DOWA operator is that it considers the implicit structure of the GTF numbers to be aggregated by grouping the numbers to various local clusters. We discuss the grouping methods of the GTF numbers using the centroids of the numbers. The cluster weights are determined by the combined consideration of the decision maker's attitude and the scale of each local cluster. In addition, we discuss the primary properties of the GTF‐DOWA operator. Finally, a numerical example regarding the selection of optimal alternative is provided. The aggregations of the GTF‐DOWA operator are compared with those of the weighted arithmetic averaging (WAA) operator and the OWA operator based on GTF numbers to illustrate the validity of the GTF‐DOWA operator. [ABSTRACT FROM AUTHOR]

Multiple attribute linguistic group decision making (MALGDM) is one of the important research topics in decision‐making theory. The material supplier grading involves multiple attributes and forms a typical MALGDM problem. In this paper, based on interval‐valued Pythagorean uncertain linguistic Euclidean distance (IVPUL‐Euclidean distance) and IVPUL aggregation operators, we develop a new outranking sorting approach, which can cope with MALGDM problems in IVPUL environment. The proposed IVPUL‐Euclidean distance defines a novel outranking relation, and it introduces three parameters that can adjust outranking sorting result according to various decision‐making situations. Meanwhile, the IVPUL aggregation operators are introduced to aggregate the IVPUL information. Eventually, we give a numerical example concerning the comprehensive assessment of material supplier to illustrate validity and applicability of the proposed approach and compare the proposed method with different generalized aggregation operators to perform its flexibility. [ABSTRACT FROM AUTHOR]

Weighted power means with weights and exponents serving as their parameters are generalizations of arithmetic means. Taking into account decision makers' flexibility in decision making, each attribute value is usually expressed by a q‐rung orthopair fuzzy value (q‐ROFV, q≥1), where the former indicates the support for membership, the latter support against membership, and the sum of their qth powers is bounded by one. In this paper, we propose the weighted power means of q‐rung orthopair fuzzy values to enrich and flourish aggregations on q‐ROFVs. First, the q‐rung orthopair fuzzy weighted power mean operator is presented, and its boundedness is precisely characterized in terms of the power exponent. Then, the q‐rung orthopair fuzzy ordered weighted power mean operator is introduced, and some of its fundamental properties are investigated in detail. Finally, a novel multiattribute decision making method is explored based on developed operators under the q‐rung orthopair fuzzy environment. A numerical example is given to illustrate the feasibility and validity of the proposed approach, and it is shown that the power exponent is an index suggesting the degree of the optimism of decision makers. [ABSTRACT FROM AUTHOR]

In this paper, according to the Maclaurin symmetric mean (MSM) operator, the dual MSM (DMSM) operator and the q‐rung interval‐valued orthopair fuzzy set (q‐RIVOFS), we develop some novel MSM operators under the q‐rung interval‐valued orthopair fuzzy environment, such as, the q‐rung interval‐valued orthopair fuzzy MSM operator, the q‐rung interval‐valued orthopair fuzzy weighted MSM (q‐RIVOFWMSM) operator, the q‐rung interval‐valued orthopair fuzzy DMSM operator, and the q‐rung interval‐valued orthopair fuzzy weighted DMSM operator. In addition, some precious properties and numerical examples of these new operators are given in detail. These new operators have the advantages of considering the interrelationship of arguments and can deal with multiple attribute group decision‐making problems with q‐rung interval‐valued orthopair fuzzy information. Finally, a reality example for green suppliers selection in green supply chain management is provided to demonstrate the proposed approach and to verify its rationality and scientific. [ABSTRACT FROM AUTHOR]

q‐Rung orthopair fuzzy sets (q‐ROFSs), originally presented by Yager, are a powerful fuzzy information representation model, which generalize the classical intuitionistic fuzzy sets and Pythagorean fuzzy sets and provide more freedom and choice for decision makers (DMs) by allowing the sum of the qth power of the membership and the qth power of the nonmembership to be less than or equal to 1. In this paper, a new class of fuzzy sets called q‐rung orthopair uncertain linguistic sets (q‐ROULSs) based on the q‐ROFSs and uncertain linguistic variables (ULVs) is proposed, and this can describe the qualitative assessment of DMs and provide them more freedom in reflecting their belief about allowable membership grades. On the basis of the proposed operational rules and comparison method of q‐ROULSs, several q‐rung orthopair uncertain linguistic aggregation operators are developed, including the q‐rung orthopair uncertain linguistic weighted arithmetic average operator, the q‐rung orthopair uncertain linguistic ordered weighted average operator, the q‐rung orthopair uncertain linguistic hybrid weighted average operator, the q‐rung orthopair uncertain linguistic weighted geometric average operator, the q‐rung orthopair uncertain linguistic ordered weighted geometric operator, and the q‐rung orthopair uncertain linguistic hybrid weighted geometric operator. Then, some desirable properties and special cases of these new operators are also investigated and studied, in particular, some existing intuitionistic fuzzy aggregation operators and Pythagorean fuzzy aggregation operators are proved to be special cases of these new operators. Furthermore, based on these proposed operators, we develop an approach to solve the multiple attribute group decision making problems, in which the evaluation information is expressed as q‐rung orthopair ULVs. Finally, we provide several examples to illustrate the specific decision‐making steps and explain the validity and feasibility of two methods by comparing with other methods. [ABSTRACT FROM AUTHOR]

Pythagorean fuzzy sets (PFSs) accommodate more uncertainties than Lx the intuitionistic fuzzy sets and hence its applications are more extensive. Under the PFS, the objective of this paper is to develop some new operational laws and their corresponding weighted geometric aggregation operators. For it, we define some new neutral multiplication and power operational laws by including the feature of the probability sum and the interaction coefficient into the analysis to get a neutral or a fair treatment to the membership and nonmembership functions of PFSs. Associated with these operational laws, we define some novel Pythagorean fuzzy weighted, ordered weighted, and hybrid neutral geometric operators for Pythagorean fuzzy information, which can neutrally treat the membership and nonmembership degrees. The desirable relations and the characteristics of the proposed operators are studied in details. Furthermore, a multiple attribute group decision‐making approach based on the proposed operators under the Pythagorean fuzzy environment is developed. Finally, an illustrative example is provided to show the practicality and the feasibility of the developed approach. [ABSTRACT FROM AUTHOR]

Multicriteria decision‐making problems have been applied to many applications for its practicality. Nevertheless, when the evaluated satisfactions are more complex, such as interval‐valued distributions, how to reasonably obtain the aggregation results of alternatives is still an open issue. In this paper, an interval‐valued exceedance method is proposed to solve such a question based on the Golden Rule representative value and probabilistic exceedance method. Due to good performance of expressing uncertain information, the Golden Rule representative value method is used to order interval‐valued satisfactions after an effective normalization process. In addition, a quantifier‐based ordered weighted averaging operator is also introduced to consider the preferences of decision makers. A realistic application of supplier selection is shown to illustrate the practicality of the proposed method. [ABSTRACT FROM AUTHOR]

A q‐rung orthopair uncertain linguistic set can be served as an extension of an uncertain linguistic set (ULS) and a q‐rung orthopair fuzzy set, which can also be treated as a generalized form of the existing intuitionistic ULS and Pythagorean ULS. The new linguistic set uses the uncertain linguistic variable to express the qualitative evaluation information and allows decision makers to provide their true views freely in a larger membership grade space. In this paper, we investigate the Bonferroni mean under the q‐rung orthopair uncertain linguistic environment, then we propose the q‐rung orthopair uncertain linguistic Bonferroni mean and its weighted form. Furthermore, considering the specific partition pattern among the attributes, the q‐rung orthopair uncertain linguistic partitioned Bonferroni mean and its weighted form are developed. Meanwhile, we discuss several representative cases and attractive properties of our proposed operators in depth. Subsequently, a novel multi‐attribute decision‐making method is developed based on the above‐mentioned aggregation operators. In the end, a comprehensible case is performed to analyze the superiority of the developed method by comparing with other typical studies. [ABSTRACT FROM AUTHOR]

In Artificial Intelligence, 171(2-3):161-184, 2007. Luo and Jennings identify and analyze the complete spectrum of compromise aggregation operators that can be used to model the various attitudes that decision-making agents can have toward risk in aggregation. In this paper, we extend these operators to deal with aggregation when the ratings have different degrees of importance. Specifically, we generalize the method of weighted uninorms to handle this issue. We choose this approach because uninorm compromise operators are a kind of common ones, and their weighted counterparts, which are widely accepted, can cover other common operators, such as weighted t-norms and t-conorms, as special cases. As per the analysis of weighted uninorms, we identify common properties that the weighting operators of the various compromise operators should satisfy, and in so doing, we introduce the concept of a general weighting operator for compromise operators and reveal the different properties that a specific type of weighting operator should obey. This, in turn, defines the concepts of the various weighting operators of the various compromise operators. We then go onto discuss the construction issue of weighting operators associated with the various compromise operators. [ABSTRACT FROM AUTHOR]

One of the most common techniques to find the adequate weights in ordered weighted averaging (OWA) operators is based on the orness concept, where the weights are determined by maximizing the entropy (variation) for a fixed orness value. But such an entropy represents a dispersion measure for nominal variables, while weights in an OWA operator are essentially ordinal rather than nominal. Hence, in this paper, we propose a novel way to determine OWA weights based upon ordinal dispersion measures instead of an standard entropy measure. From this approach, we find an explicit formula for the weights, and we illustrate differences by means some multicriteria decision‐making examples. [ABSTRACT FROM AUTHOR]

In this paper, a novel approach is developed to deal with multiple‐attribute group decision‐making (MAGDM) problem under q‐rung orthopair fuzzy environment. Firstly, some operators have been proposed to aggregate q‐rung orthopair fuzzy information, such as the q‐rung orthopair fuzzy generalized power averaging (q‐ROFGPA) operator, the q‐rung orthopair fuzzy generalized power weighted averaging (q‐ROFGPWA) operator, the q‐rung orthopair fuzzy generalized power geometric (q‐ROFGPG) operator, and the q‐rung orthopair fuzzy generalized power weighted geometric (q‐ROFGPWG) operator. In addition, some desirable properties and special cases of these operators are discussed. Second, a novel approach is developed to solve MAGDM problem under the q‐rung orthopair fuzzy environment based on the proposed q‐ROFGPWA and q‐ROFGPWG operators. Finally, a practical example is given to illustrate the application of the proposed method, and further the sensitivity analysis and comparative analysis are carried out. [ABSTRACT FROM AUTHOR]