Dual Maclaurin Symmetric Mean Research Articles

Q-Rung orthopair fuzzy 2-tuple linguistic WASPAS algorithm for patients’ prioritization based on prioritized Maclaurin symmetric mean aggregation operators

Due to the fuzziness of the medical field, q-rung orthopair fuzzy 2-tuple linguistic (q-RF2L) set is the privileged way to aid medical professionals in conveying their assessments in the patient prioritization problem. The theme of the present study is to put forward a novel approach centered around the merging of prioritized averaging (PA) and the Maclaurin symmetric mean (MSM) operator within q-RF2L context. According to the prioritization of the professionals and the correlation among the defined criteria, we apply both PA and MSM to assess priority degrees and relationships, respectively. Keeping the pluses of the PA and MSM operators in mind, we introduce two aggregation operators (AOs), namely q-RF2L prioritized Maclaurin symmetric mean and q-RF2L prioritized dual Maclaurin symmetric mean operators. Meanwhile, some essential features and remarks of the proposed AOs are discussed at length. Based on the formulated AOs, we extend the weighted aggregated sum product assessment methodology to cope with q-RF2L decision-making problems. Ultimately, to illustrate the practicality and effectiveness of the stated methodology, a real-world example of patients’ prioritization problem is addressed, and an in-depth analysis with prevailing methods is performed.

Partitioned dual Maclaurin symmetric mean operators based on picture fuzzy sets and their applications in multi-attribute decision-making problems

The partitioned Dual Maclaurin symmetric mean (PDMSM) operator has the supremacy that can justify the interrelationship of distinct characteristics and there are a lot of exploration consequences for it. However, it has not been employed to manage “multi-attribute decision-making” (MADM) problems represented by picture fuzzy numbers. The basic inspiration of this identification is to develop the novel theory of picture fuzzy PDMSM operator, and weighted picture fuzzy PDMSM operator and to identify their important results (Idempotency, Monotonicity, and Boundedness). Further, to identify the best decision, every expert realized that they needed the best way to find the beneficial optimal using the proper decision-making procedure, for this, we diagnosed the MADM tool in the consideration of deliberated approaches based on PF information. Finally, to drive the characteristics of the invented work, several examples are utilized to test the manifest of the comparative analysis with various more existing theories, which is a fascinating and meaningful technique to deeply explain the features and exhibited of the proposed approaches.

Multi-attribute decision-making based on q-rung dual hesitant power dual Maclaurin symmetric mean operator and a new ranking method

Multi-attribute decision-making based on q-rung dual hesitant power dual Maclaurin symmetric mean operator and a new ranking method

A novel linguistic decision making approach based on attribute correlation and EDAS method

One of characteristics of large-scale linguistic decision making problems is that decision information with respect to decision making attributes is derived from multi-sources information. In addition, the number of decision makers, alternatives or criteria of decision making problems in the context of big data are increasingly large. Correlation analysis between decision making attributes has become an important issue of large-scale linguistic decision making problems. In the paper, we concentrate on correlation analysis between decision making attributes to deal with large-scale decision making problems with linguistic intuitionistic fuzzy values. Firstly, we proposed a new similarity measure between two linguistic intuitionistic fuzzy sets to formally define correlation between decision making attributes. Then we propose linguistic intuitionistic fuzzy reducible weighted Maclaurin symmetric mean (LIFRWMSM) operator and linguistic intuitionistic fuzzy reducible weighted dual Maclaurin symmetric mean (LIFRWDMSM) operator to aggregate linguistic intuitionistic fuzzy value decision information of correlational decision making attributes, and analyze several important properties of the two operator. Inspired by evaluation based on distance from average solution (EDAS) method, we design a solution scheme and decision steps to deal with large-scale linguistic intuitionistic fuzzy decision making problems. To show the effectiveness and usefulness of the proposed decision method, we employ the choice of buying a house and the selection of travel destination to demonstrate our method and make comparative analysis with others aggregation operators or methods.

An Approach for the Assessment of Multi-National Companies Using a Multi-Attribute Decision Making Process Based on Interval Valued Spherical Fuzzy Maclaurin Symmetric Mean Operators

Many fuzzy concepts have been researched and described with uncertain information. Collecting data under uncertain information is a difficult task, especially when there is a difference between the opinions of experts. To deal with such situations, different types of operators have been introduced. This paper aims to develop the Maclaurin symmetric mean (MSM) operator for the information in the shape of the interval-valued spherical fuzzy set (IVSFS). In this article, a family of aggregation operators (AOs) is proposed which consists of interval valued spherical fuzzy Maclaurin symmetric mean operator (IVSFMSM), interval valued spherical fuzzy weighted Maclaurin symmetric mean (IVSFWMSM), interval valued spherical fuzzy dual Maclaurin symmetric mean (IVSFDMSM), and interval valued spherical fuzzy dual weighted Maclaurin symmetric mean (IVSFDWMSM) operators. In this paper, we studied an elucidative example to discuss the evaluation of multi-national companies for the application of the proposed operator. Then the obtained results from the proposed operators are compared. The results obtained are graphed and tabulated for a better understanding.

Interval-Valued Picture Fuzzy Maclaurin Symmetric Mean Operator with application in Multiple Attribute Decision-Making

A lot of fuzzy models have been planned and researched to review the information under uncertainty and ambiguity. Among these, the model of the interval-valued picture fuzzy set (IVPFS) is very important which can explain the information by four possibilities in the opinion of experts using a membership degree (MD), non-membership degree (NMD), abstinence degree (AD), and a refusal degree (RD) in the form of intervals. The gathering of data is difficult all the time, particularly when the difference of opinions is connected. This article aims to explore the idea of a Maclaurin symmetric mean (MSM) operator in the framework of IVPFS. In this article, we have studied MSM in the framework of IVPFSs and discussed their application in picking the most suitable company benefit plan (CBP) using interval-valued picture fuzzy (IVPF) data. The proposed operators IVPF MSM (IVPFMSM), IVPF weighted MSM (IVPFWMSM), IVPF dual MSM (IVPFDMSM), and IVPF dual weighted MSM (IVPFDWMSM) operators are found trustworthy with the basic properties. Finally, to show the proposed method's importance and significance, a numerical example has been provided and results have been compared with some existing operators.

A New Approach to Decision-Making Problem under Complex Pythagorean Fuzzy Information

In daily life, decision-making (DM) problem is a complicated work related to uncertainties and vagueness. To overcome these imprecisions, many fuzzy sets and theories have been presented by different scholars. Probabilistic models are the communal models proposed for the management of uncertainties. On the other hand, if these uncertainties are not probabilistic in nature, then other models such as fuzzy linguistic and fuzzy logic are developed. Here, a new approach known as the complex Pythagorean fuzzy Maclaurin symmetric mean (CPFMSM) operator is used to handle these uncertainties in DM issues. This complex Pythagorean fuzzy set (CPFS) is a modified form of the Pythagorean fuzzy set (PFS) and of the complex intuitionistic fuzzy set (CIFS). The aggregation operators have the ability to combine different sources of information. Therefore, an aggregation operator known as the MSM operator is utilized under the complex Pythagorean fuzzy (CPF) environment to extend the theory and applications of traditional MSM. For this purpose, we devised new operators known as CPFMSM and CPF dual Maclaurin symmetric mean (CPFDMSM) to aggregate CPF data. To evaluate an emergency program, the MAGDM approach is used, which is based on the newly introduced operators. Furthermore, the viability and applicability of the propounded method are certified by a detailed analysis with the other approaches researched in the past.

A Novel MAGDM Approach Based on Cubic q -Rung Orthopair Fuzzy Power Generalized Maclaurin Symmetric Mean Operator

The cubic q -rung orthopair fuzzy set (Cq-ROFS) is a basic simplification of several fuzzy notions, including fuzzy set (FS), interval valued FS (INVFS), intuitionistic FS (INTFS), q -rung orthopair FS (q-ROFS), and INV q -rung orthopair FS (INVq-ROFS). By the degrees of INVq-ROFS and q-ROFS, Cq-ROFS exposes fuzzy judgement, and this is one of the advanced mathematical tools to handle more complicated assessment information in multiple attribute group decision-making (MAGDM) problems. In this article, firstly, encouraged from power average (PA) operator, generalized MSM operator, and generalized dual MSM operator, two novel aggregation operators (AOs) such as cubic q -rung orthopair fuzzy power generalized Maclaurin symmetric mean (Cq-ROFPWGMSM) operator and cubic q -rung orthopair fuzzy power generalized dual Maclaurin symmetric mean (Cq-ROFPWGDMSM) operator are initiated by merging PA operator with GMSM and GDMSM operators and some core characteristics of these AOs are investigated. Furthermore, some core cases with respect to different general parameters values are also investigated and found that some aggregation operators are special cases of the initiated AOs. Secondly, the weighted form of these newly initiated aggregation operators is also offered. Thirdly, two MAGDM models are offered based on Cq-OFPGWMSM and Cq-ROFPGWDMSM operators. Lastly, a numerical example about the selection of the best assistant professor of the year is taken as an application to show the effectiveness and capability of the initiated approaches. There is also a comparison with existing decision-making models.

Modified EDAS Method for MAGDM Based on MSM Operators with 2-Tuple Linguistic T -Spherical Fuzzy Sets

The coronavirus (COVID-19) pandemic, which began in China and is fast spreading around the world, has increased the number of cases and deaths. Governments have suffered substantial damage and losses not only in the health sector but also in a variety of other areas. In this situation, it is critical to determine the most crucial vaccine that doctors and specialists should implement. In order to evaluate the many vaccines to control the COVID-19 epidemic, a decision problem based on the decisions of many experts, with some contradicting and multiple criteria, should be taken into account. This decision process is characterized as a multiattribute group decision-making (MAGDM) problem that includes uncertainty in this study. T -spherical fuzzy sets are utilized for this, allowing decision-experts to make evaluations over a larger area and better deal with complicated data. The T -spherical fuzzy set is a useful tool for dealing with uncertainty and ambiguity, especially where additional answers of the type “yes,” “no,” “abstain,” and “refusal” are required, and the 2-tuple linguistic terms are useful for the qualitative evaluation of uncertain data. From the perspective of the uncertainty surrounding the problems of MAGDM, we propose the notion of 2-tuple linguistic T -spherical fuzzy numbers (2TL T -SFNs) generated with the integration of T -spherical fuzzy numbers and 2-tuple linguistic terms. Then, the assessment based on distance from average solution (EDAS) for the ranking of alternatives based on the 2TL T -SFNs is investigated as a new decision-making strategy. This study provides the following significant contributions: (1) the procedure for constructing a 2TL T -SFNs is described, together with their aggregation operators, ranking criteria, relevant attributes, and some operational laws. (2) The traditional Maclaurin symmetric mean (MSM) operator is useful for modeling attribute interrelationships and aggregating 2TL T -SF information to tackle the MAGDM problems. A few recent MSM and dual MSM operators are being built to evaluate the 2TL T -SF information. Thus, 2-tuple linguistic T -spherical fuzzy Maclaurin symmetric mean (2TL T -SFMSM) operator, 2-tuple linguistic T -spherical fuzzy weighted Maclaurin symmetric mean (2TL T -SFWMSM) operator, 2-tuple linguistic T -spherical fuzzy dual Maclaurin symmetric mean (2TL T -SFDMSM) operator, and 2-tuple linguistic T -spherical fuzzy weighted dual Maclaurin symmetric mean (2TL T -SFWDMSM) operator are proposed. (3) We incorporate the 2TL T -SFNs into the EDAS approach and develop a new 2TL T -SF-EDAS method for solving the MAGDM problems based on the proposed aggregation operators in a 2TL T -SF environment. A case study for the selection of an optimal vaccine to control the outbreak of the COVID-19 epidemic is also presented to show the validity of the proposed methodology. Furthermore, the comparative analysis with existing approaches shows the advantages and superiority of the proposed framework.

Models for MAGDM with dual hesitant q-rung orthopair fuzzy 2-tuple linguistic MSM operators and their application to COVID-19 pandemic.

In this article, we introduce dual hesitant -rung orthopair fuzzy 2-tuple linguistic set (DHq-ROFTLS), a new strategy for dealing with uncertainty that incorporates a 2-tuple linguistic term into dual hesitant -rung orthopair fuzzy set (DHq-ROFS). DHq-ROFTLS is a better way to deal with uncertain and imprecise information in the decision-making environment. We elaborate the operational rules, based on which, the DHq-ROFTL weighted averaging (DHq-ROFTLWA) operator and the DHq-ROFTL weighted geometric (DHq-ROFTLWG) operator are presented to fuse the DHq-ROFTL numbers (DHq-ROFTLNs). As Maclaurin symmetric mean (MSM) aggregation operator is a useful tool to model the interrelationship between multi-input arguments, we generalize the traditional MSM to aggregate DHq-ROFTL information. Firstly, the DHq-ROFTL Maclaurin symmetric mean (DHq-ROFTLMSM) and the DHq-ROFTL weighted Maclaurin symmetric mean (DHq-ROFTLWMSM) operators are proposed along with some of their desirable properties and some special cases. Further, the DHq-ROFTL dual Maclaurin symmetric mean (DHq-ROFTLDMSM) and weighted dual Maclaurin symmetric mean (DHq-ROFTLWDMSM) operators with some properties and cases are presented. Moreover, the assessment and prioritizing of the most important aspects in multiple attribute group decision-making (MAGDM) problems is analysed by an extended novel approach based on the proposed aggregation operators under DHq-ROFTL framework. At long last, a numerical model is provided for the selection of adequate medication to control COVID-19 outbreaks to demonstrate the use of the generated technique and exhibit its adequacy. Finally, to analyse the advantages of the proposed method, a comparison analysis is conducted and the superiorities are illustrated.

Analysis of Maclaurin Symmetric Mean Operators for Managing Complex Interval-Valued q-Rung Orthopair Fuzzy Setting and Their Applications

Risk is demonstrated as unknowns that have measurable possibilities, while complication requires unknown with no significant possibilities of the outcome. These notions are associated but are not identical. Ambiguity and risk are closely concerned notions in decisionmaking strategies using fuzzy set theory. Similarly, Maclaurin symmetric mean (MSM) is also massive beneficial and valuable for using to accumulate the family of attributes into a singleton set. To enhance the superiority of the research work, in this scenario, we used the informative idea of a complex interval-valued q-rung orthopair fuzzy (CIVq-ROF) setting and took a valuable tool of MSM to present the CIVq-ROF MSM (CIVq-ROFMSM), CIVq-ROF-weighted MSM (CIVq-ROFWMSM), CIVq-ROF dual MSM (CIVq-ROFDMSM), and CIVq-ROF-weighted dual MSM (CIVq-ROFWDMSM) operators. To verify the supremacy of the invented works for the different values of parameters, several specific cases are also explored. Finally, with the help of multi-attribute decision-making (MADM) skills, we identified a beneficial optimal in the presence of the source of descriptions in the form of invented operators using the decision making process. Comparison of the invented approaches with many existing scenarios is also simplified at the end of this analysis, which shows the dominancy and competency of the diagnosed approaches.

An integrated approach for service quality evaluation of online health communities based on q-rung orthopair fuzzy linguistic aggregation operators

Online health communities (OHCs) have emerged as a significant platform for people communicating health information and self-healthcare management. In recent, the researches focusing on its performance measurement and the service quality evaluation have drawn intensive attention. Although some qualitative methods have made evaluation and analyses for the OHCs performance, the studies based on fuzzy multi-attribute decision making theory are rarely developed in the service quality evaluation of OHCs. In view of the complexity and uncertainty of evaluation mission, this paper develops an integrated evaluation approach of the OHC service quality based on the q-rung orthopair fuzzy linguistic aggregation operators. Firstly, we propose the cross-entropy of q-rung orthopair fuzzy numbers, which is applied in solving the optimal weight of indicators by a linear programming model. Next, the q-rung orthopair fuzzy linguistic power average (q-ROFLPA) and q-rung orthopair fuzzy linguistic partitioned dual Maclaurin symmetric mean (q-ROFLPDMSM) operators are developed for aggregating the assessment information and ranking the OHCs. Based on the proposed aggregation operators, the evaluation indicator system and an evaluation framework are constructed to accomplish the service quality evaluation of OHCs. Finally, a practical evaluation case of OHCs is provided to demonstrate the reliability and advantages of the proposed approach.

Complex intuitionistic fuzzy Maclaurin symmetric mean operators and its application to emergency program selection

Due to the indeterminacy and uncertainty of the decision-makers (DM) in the complex decision making problems of daily life, evaluation and aggregation of the information usually becomes a complicated task. In literature many theories and fuzzy sets (FS) are presented for the evaluation of these decision tasks, but most of these theories and fuzzy sets have failed to explain the uncertainty and vagueness in the decision making issues. Therefore, we use complex intuitionistic fuzzy set (CIFS) instead of fuzzy set and intuitionistic fuzzy set (IFS). A new type of aggregation operation is also developed by the use of complex intuitionistic fuzzy numbers (CIFNs), their accuracy and the score functions are also discussed in detail. Moreover, we utilized the Maclaurin symmetric mean (MSM) operator, which have the ability to capture the relationship among multi-input arguments, as a result, CIF Maclarurin symmetric mean (CIFMSM) operator and CIF dual Maclaurin symmetric mean (CIFDMSM) operator are presented and their characteristics are discussed in detail. On the basis of these operators, a MAGDM method is presented for the solution of group decision making problems. Finally, the validation of the propounded approach is proved by evaluating a numerical example, and by the comparison with the previously researched results.

Multiple Attribute Decision-Making Method Based upon Intuitionistic Fuzzy Partitioned Dual Maclaurin Symmetric Mean Operators

We propound the idea of the partitioned dual Maclaurin symmetric mean (PDMSM) operator stimulated by the partitioned Maclaurin symmetric mean, suppose that we can partition overall attributes into some portions and the attributes are interrelated in the same portion, but the attributes are not interrelated in different portions. We can deal with decision-making issues using PDMSM operator in the intuitionistic fuzzy environment. We also analysis features and peculiar instance of the PDMSM operator. And, we extend the PDMSM operator to introduce the intuitionistic fuzzy partitioned dual Maclaurin symmetric mean operator and the weighted intuitionistic fuzzy partitioned dual Maclaurin symmetric mean operator. Then, we analysis several characteristics and peculiar instances of the developed operators. A new multiple attribute decision-making (MADM) approach grounded on the established weighted intuitionistic fuzzy partitioned dual Maclaurin symmetric mean operator is propounded; the MADM method is to choose the optimal alternative from several alternatives. Finally, we demonstrate the designed method is more general and effective than existing methods through comparative analysis.

Redefined “Maclaurin Symmetric Mean Aggregation Operators Based on Cubic Pythagorean Linguistic Fuzzy Numbers”

In this study, we highlight the errors in Sections 2.3, 2.4, 3, and 4 in the article by Fahmi et al. (J Ambient Intell Human Comput (2020). https://doi.org/10.1007/s12652-020-02272-9) by counter definitions and theorems. We find that the definition of cubic Pythagorean fuzzy set (CPFS) (Definition 2.3.1) and operational laws (Definition 2.3.2) violates the rules to consider the membership and nonmembership functions, and then, we redefined the corrected definition and their operations for CPFS. Furthermore, we redefine the concept of cubic Pythagorean linguistic fuzzy set (CPLFS) and their basic operational laws. In addition, we find that Sections 3 and 4 (consist of a list of Maclaurin symmetric mean (MSM) and dual MSM aggregation operators) are invalid, and then, we redefined the list of updated MSM and dual MSM aggregation operators in correct way. Finally, we established the numerical application of the proposed improved algorithm using cubic Pythagorean linguistic fuzzy information to show the applicability and effectiveness of the proposed technique.

Medical Waste Treatment Station Selection Based on Linguistic q-Rung Orthopair Fuzzy Numbers

During the COVID-19 outbreak, the use of single-use medical supplies increased significantly. It is essential to select suitable sites for establishing medical waste treatment stations. It is a big challenge to solve the medical waste treatment station selection problem due to some conflicting factors. This paper proposes a multi-attribute decision-making (MADM) method based on the partitioned Maclaurin symmetric mean (PMSM) operator. For the medical waste treatment station selection problem, the factors or attributes (these two terms can be interchanged.) in the same clusters are closely related, and the attributes in different clusters have no relationships. The partitioned Maclaurin symmetric mean function (PMSMF) can handle these complex attribute relationships. Hence, we extend the PMSM operator to process the linguistic q-rung orthopair fuzzy numbers (Lq-ROFNs) and propose the linguistic q-rung orthopair fuzzy partitioned Maclaurin symmetric mean (Lq-ROFPMSM) operator and its weighted form (Lq-ROFWPMSM). To reduce the negative impact of unreasonable data on the final output results, we propose the linguistic q-rung orthopair fuzzy partitioned dual Maclaurin symmetric mean (Lq-ROFPDMSM) operator and its weighted form (Lq-ROFWPDMSM). We also discuss the characteristics and typical examples of the above operators. A novel MADM method uses the Lq-ROFWPMSM operator and the Lq-ROFWPDMSM operator to solve the medical waste treatment station selection problem. Finally, the usability and superiority of the proposed method are verified by comparing it with previous methods.

Maclaurin symmetric mean aggregation operators based on cubic Pythagorean linguistic fuzzy number

The Maclaurin symmetric mean (MSM) and dual Maclaurin symmetric mean (DMSM) operators are two aggregation operators to aggregate the cubic Pythagorean linguistic fuzzy number. The cubic Pythagorean linguistic fuzzy structure is more real to designate fuzzy data in real decision-making problems. The cubic Pythagorean linguistic fuzzy number is more superior and difficult information in the environment of the fuzzy set theory. We describe the score and accuracy function of CPLFN. We define some aggregation operators, including the CPLFAA, CGPLFAA, CPLFGA, CPLFMSM, and CPLFWMSM operators. We present some operators, with the CPLFDWMSMA, CPLFDOWMSMA, CPLFDHWMSMA, CPLFDWMSMG, CPLFDOWMSMG and CPLFDHWMSMG operators. Moreover, some properties and special cases of our proposed methods are also introduced. Then we present multi-attributive group decision-making based on proposed methods. Further, a numerical example is provided to illustrate the flexibility and accuracy of the proposed operators. Last, the proposed methods are compared with existing methods to examine the best developing skill initiatives.

Single-valued neutrosophic linguistic reducible weighted MSM for tourism mobile e-commerce service quality evaluation

The tourism mobile e-commerce service quality evaluation (TMESQE) is of great concern to enterprises for enriching the service content of the enterprise and improving its market competitiveness. The key issue arises tremendous vagueness and reciprocity for TMESQE. The Maclaurin symmetric mean (MSM), as a vital information fusion tool, can capture the reciprocity among multiple given argument more effectually. Amount of weighted MSMs have been presented for dealing various neutrosophic information integration issues because the arguments are hourly interoperable. However, these kinds of weighted MSM (WMSM) operators are out of the reducibility or idempotency. To solve two above issues, we introduce the single-valued neutrosophic linguistic reducible WMSM (SVNLRWMSM) operator and the single-valued neutrosophic linguistic reducible weighted dual MSM (SVNLRWDMSM) operator. In the meantime, certain interesting properties and some special cases of developed operators are explored in detail. Whereafter, we develop two multiple attribute decision making (MADM) algorithms based on SVNLRWMSM and SVNLRWDMSM for dealing the TMESQE issue, along with the sensitivity analysis of various parameter values on final ordering. Conclusively, a comparison with some existing algorithms has been conducted for showing their availability.

Maclaurin symmetric mean operators and their applications in the environment of complex q-rung orthopair fuzzy sets

The Maclaurin symmetric mean (MSM) and dual Maclaurin symmetric mean (DMSM) operators are two aggregation operators to aggregate the q-rung orthopair fuzzy numbers (q-ROFNs) into a single element. The complex q-rung orthopair fuzzy framework is more effective to describe fuzzy information in real decision-making problems. The complex q-rung orthopair fuzzy sets (Cq-ROFSs) are more superior to the complex intuitionistic fuzzy sets (CIFSs) and complex pythagorean fuzzy sets (CPFSs) to cope with uncertain and difficult information in the environment of fuzzy set theory. Thus, this manuscript proposes some complex q-rung orthopair fuzzy Maclaurin symmetric mean (Cq-ROFMSM), complex q-rung orthopair fuzzy weighted Maclaurin symmetric mean (Cq-ROFWMSM), complex q-rung orthopair fuzzy dual Maclaurin symmetric mean (Cq-ROFDMSM) and complex q-rung orthopair fuzzy weighted dual Maclaurin symmetric mean (Cq-ROFWDMSM) operators. Moreover, some properties and special cases of our proposed methods are also introduced. Then we present a multi-attributive group decision-making based on proposed methods. Further, a numerical example is provided to illustrate the flexibility and accuracy of the proposed operators. Last, the proposed methods are compared with existing methods to examine the best emerging technology enterprises.

A method to multi-attribute decision-making based on interval-valued q-rung dual hesitant linguistic Maclaurin symmetric mean operators

The aim of this paper is to propose a new multi-attribute decision-making (MADM) method to rank all feasible alternatives in complex decision-making scenarios and determine the optimal one. To this end, we first propose the notion of interval-valued q-rung dual hesitant linguistic sets (IVq-RDHLSs) by combining interval-valued q-rung dual hesitant fuzzy (IVq-RDHF) sets with linguistic terms set. The proposed IVq-RDHLSs utilize IVq-RDHF membership and non-membership degrees to assess linguistic terms, so that they can fully express decision-makers’ evaluation information. Additionally, some related concepts such as the operational rules, score and accuracy functions, and ranking method of IVq-RDHLSs are presented. Considering the good performance of the classical Maclaurin symmetric mean (MSM) in integrating fuzzy information, we further generalize MSM into IVq-RDHLSs to propose the interval-valued q-rung dual hesitant linguistic MSM operator, the interval-valued q-rung dual hesitant linguistic dual MSM operator, as well as their weighted forms. Afterwards, we study the applications of IVq-RDHLSs and their aggregation operators in decision-making and propose a new MADM method. Some real decision-making problems in daily life are employed to prove the rightness of the proposed method. We also attempt to demonstrate the advantages and superiorities of our proposed method through comparing with some other methods in this paper.