Maclaurin Symmetric Mean Operator Research Articles

Linguistic neutrosophic partitioned Maclaurin symmetric mean operators based on clustering algorithm and their application to multi-criteria group decision-making

Linguistic neutrosophic number (LNN) can describe evaluation information by three linguistic variables indicating truth-membership, indeterminacy-membership and falsity-membership respectively, which is an effective tool to represent uncertainty, the partitioned Maclaurin symmetric mean (PMSM) operator can reflect the interrelationships among criteria where there are interrelationships among criteria in the same partition, but the criteria in different partitions are irrelevant, so, in this paper, we extend the PMSM operator to LNNs, define linguistic neutrosophic partitioned Maclaurin symmetric mean operator and linguistic neutrosophic weighted partitioned Maclaurin symmetric mean (LNWPMSM) operator, and discuss the properties and theorems of the proposed operators. Then we propose a clustering algorithm for linguistic neutrosophic sets based on the similarity measure to give some objective and reasonable partitions among criteria, and based on the LNWPMSM operator and the objective partition structure of the criteria, a novel multi-criteria group decision-making method is developed for linguistic neutrosophic environment. Finally, one practical example is presented to illustrate the applicability of the proposed method, and a comparison analysis is to show the advantages of the proposed method compared with the existing methods.

A Novel Decision-Making Method Based on Probabilistic Linguistic Information

The Maclaurin symmetric mean (MSM) operator has the characteristic of capturing the interrelationship among multi-input arguments, the probabilistic linguistic terms set (PLTS) can reflect the different degrees of importance or weights of all possible evaluation values, and the improved operational laws of probabilistic linguistic information (PLI) can not only avoid the operational values out of bounds for the linguistic terms set (LTS) but also keep the probability information complete after operations; hence, it is very meaningful to extend the MSM operator to PLTS based on the operational laws. To fully take advantage of the MSM operator and the improved operational laws of PLI, the MSM operator is extended to PLI. At the same time, two new aggregated operators are proposed, including the probabilistic linguistic MSM (PLMSM) operator and the weighted probabilistic linguistic MSM (WPLMSM) operator. Simultaneously, the properties and the special cases of these operators are discussed. Further, based on the proposed WPLMSM operator, a novel approach for multiple attribute decision-making (MADM) problems with PLI is proposed. With a given numerical example, the feasibility of the proposed method is proven, and a comparison with the existing methods can show the advantages of the new method in this paper. The developed method adopts the new operational rules with the accurate operations, and it can overcome some existing weaknesses and capture the interrelationship among the multi-input PLTSs, which easily express the qualitative information given by the decision-makers’ cognition.

Some Maclaurin Symmetric Mean Aggregation Operators Based on Cloud Model and Their Application to Decision-Making

The cloud model (CM) is an important tool to describe qualitative concept by the quantitative method, and the Maclaurin symmetric mean (MSM) can capture the interrelationship among the multi-inputs and it can generalize most of existing operators. In this paper, we firstly convert the uncertain linguistic variables (ULVs), which are easily used to express the qualitative information, to CM. Then, we combine the MSM with the CM, and propose the cloud MSM (CMSM) operator and cloud weighted MSM (CWMSM) operator. In addition, we explore some of their desirable features and develop a new approach to deal with some multi-attribute group decision-making (MAGDM) problems under the uncertain environment based on the proposed operators. Finally, by comparing with other approaches, an illustrative example is arranged to demonstrate the usability of the proposed method.

Multi-attribute decision making method based on generalized maclaurin symmetric mean aggregation operators for probabilistic linguistic information

The generalized Maclaurin symmetric mean (GMSM) operator not only can consider the interrelationship among the multi-input arguments, but also can be flexibly converted to many existing operators by adjusting the parameters. The probabilistic linguistic terms set (PLTS) can give different important degrees of all given evaluation values, and provide more accurate information for the decision making. In order to fully take the advantages of the GMSM operator and probabilistic linguistic information (PLI), in this paper, we extend the GMSM operator to PLI, and four new aggregated operators are proposed, including the probabilistic linguistic GMSM (PLGMSM) operator, the probabilistic linguistic geometric MSM (PLGeoMSM) operator, the weighted probabilistic linguistic GMSM (WPLGMSM) operator and the weighted probabilistic linguistic geometric MSM (WPLGeoMSM) operator. In the Meanwhile, we discuss their properties and special cases. Further, based on proposed WPLGMSM operator and the WPLGeoMSM operator, a novel approach for multi-attribute group decision making (MAGDM) problems with PLI is proposed. Finally, a numerical example is given to illustrate the feasibility and superiority of the proposed method.

Maclaurin symmetric mean aggregation operators based on t-norm operations for the dual hesitant fuzzy soft set

The objective of this paper is to present a Maclaurin symmetric mean (MSM) operator to aggregate dual hesitant fuzzy (DHF) soft numbers. The salient feature of MSM operators is that it can reflect the interrelationship between the multi-input arguments. Under DHF soft set environment, we develop some aggregation operators named as DHF soft MSM averaging (DHFSMSMA) operator, the weighted DHF soft MSM averaging (WDHFSMSMA) operator, DHF soft MSM geometric (DHFSMSMG) operator, and the weighted DHF soft MSM geometric (WDHFSMSMG) operator. Further, some properties and the special cases of these operators are discussed. Then, by utilizing these operators, we develop an approach for solving the multicriteria decision-making problem and illustrate it with a numerical example. Finally, a comparison analysis has been done to analyze the advantages of the proposed operators.

Multiple Attribute Decision-Making Methods with Unbalanced Linguistic Variables Based on Maclaurin Symmetric Mean Operators

In this paper, we firstly introduced the unbalanced linguistic term sets, the linguistic transforming methodology, the Maclaurin symmetric mean (MSM) operator and dual MSM (DMSM) operator. Then, we proposed the closed operational rules of unbalanced linguistic variables, and several new MSM aggregation operators, including unbalanced linguistic MSM (ULMSM) operator, weighted unbalanced linguistic MSM (WULMSM) operator, unbalanced linguistic DMSM (ULDMSM) operator and weighted unbalanced linguistic DMSM (WULDMSM) operator. Further, we proposed two multiple attribute decision-making (MADM) methods under unbalanced linguistic environments based on the WULMSM operator and WULDMSM operator, respectively. Finally, a numerical example is used to show the applicability and effectiveness of the proposed MADM methods and to reveal their advantages by comparing with the existing methods.

Multiple-Attribute Group Decision-Making Based on q-Rung Orthopair Fuzzy Power Maclaurin Symmetric Mean Operators

To be able to describe more complex fuzzy uncertainty information effectively, the concept of q-rung orthopair fuzzy sets (q-ROFSs) was first proposed by Yager. The q-ROFSs can dynamically adjust the range of indication of decision information by changing a parameter q based on the different hesitation degree from the decision-makers, where q ≥ 1, so they outperform the traditional intuitionistic fuzzy sets and Pythagorean fuzzy sets. In real decision-making problems, there is often an interaction phenomenon between attributes. For aggregating these complex fuzzy information, the Maclaurin symmetric mean (MSM) operator is more superior by considering interrelationships among attributes. In addition, the power average (PA) operator can reduce the effects of extreme evaluating data from some experts with prejudice. In this paper, we introduce the PA operator and the MSM operator based on q-rung orthopair fuzzy numbers (q-ROFNs). Then, we put forward the q-rung orthopair fuzzy power MSM (q-ROFPMSM) operator and the q-rung orthopair fuzzy power weighed MSM (q-ROFPWMSM) operator of q-ROFNs and present some of their properties. Finally, we present a novel multiple-attribute group decision-making (MAGDM) method based on the q-ROFPWA and the q-ROFPWMSM operators. The experimental results show that the novel MAGDM method outperforms the existing MAGDM methods for dealing with MAGDM problems.

Interval Neutrosophic Reducible Weighted Maclaurin Symmetric Means With Internet of Medical Things (IoMt) Industry Evaluation

The Internet of Medical Things (IoMT) is a global infrastructure composing of plentiful applications and medical devices that are interconnected by ICT. In considering the problem of the IoMT industry evaluation, the requisite issue that concerns strong interaction and incertitude. The Maclaurin symmetric mean (MSM), as a resultful information concordant instrument, can capture the interrelation among multiple arguments more efficiently. The abundance of the weighted MSMs has been presented to manage the different uncertain information aggregation issues by reason that the attribute variables are frequently diverse. However, these existing weighted form of MSM operators fail to possess the fundamental properties of idempotency and reducibility. To solve the above issues, we explore the interval neutrosophic reducible weighted MSM (INRWMSM) operator and the interval neutrosophic reducible weighted dual MSM (INRWDMSM) operator. Moreover, momentous properties and some special cases of the INRWMSM and INRWDMSM operators are discussed in detail. Whereafter, we propose some multiple attribute decision making (MADM) algorithms based on INRWMSM and INRWDMSM. The availability of proposed algorithms is stated by an IoMT evaluation issue. Finally, a comparison of the developed with the existing interval neutrosophic decision making algorithms has been formed for showing their validity.

Neutrosophic Reducible Weighted Maclaurin Symmetric Mean for Undergraduate Teaching Audit and Evaluation

The undergraduate teaching audit and evaluation (UTAE) is critically important for the university to promote the establishment of a quality assurance system and improve the quality of teaching. In considering the case of UTAE, the essential question arises strong ambiguity and interaction. The Maclaurin symmetric mean (MSM), as a significant information integration tool, can seize the interrelation among multiple input values more effectively. A series of weighted MSMs have been developed to cope with diverse neutrosophic information aggregation issues by reason that the attribute variables are frequently desparate. Nevertheless, these weighted form of MSM operators is not idempotent. Moreover, the weight MSM cannot degrade into the MSM when their weights information is equivalent. In other words, it signifies without the reducibility. To resolve two issues, we develop the single-valued neutrosophic reducible weighted MSM (SVNRWMSM) operator and the single-valued neutrosophic reducible weighted dual MSM (SVNRWDMSM) operator. Meanwhile, certain interesting properties and some special cases of the SVNRWMSM and SVNRWDMSM operators are explored in detail. Afterward, we develop two multiple attribute decision-making methods based on SVNRWMSM and SVNRWDMSM. The validity of algorithms is illustrated by an undergraduate teaching evaluation issue, along with the sensitivity analysis of diverse parameter values on the ranking. Finally, a comparison of the developed with the existing single-valued neutrosophic decision-making algorithms has been executed for displaying their efficiency.

A Method of Multiple Attribute Group Decision Making Based on 2-Tuple Linguistic Dependent Maclaurin Symmetric Mean Operators

Aiming at multiple attribute group decision making (MAGDM) problems, especially the attribute values of 2-tuple linguistic numbers and the interrelationships between each attribute needing to be considered, this paper proposes a new method of analysis. Firstly, we developed a few new aggregation operators, like the 2-tuple linguistic dependent weighted Maclaurin symmetric mean (2TLDWMSM) operator, the 2-tuple linguistic dependent weighted generalized Maclaurin symmetric mean (2TLDWGMSM) operator, and the 2-tuple linguistic dependent weighted geometric Maclaurin symmetric mean (2TLDWGeoMSM) operator. In the above operators, Maclaurin symmetric mean (MSM) operators can take the relationships between each attribute into account and dependent operators can mitigate the unfair parameters’ impact on the overall outcome, in which those ‘‘incorrect’’ and ‘‘prejudiced’’ parameters are distributed with low weights. Next, a method used by the 2TLDWMSM, 2TLDWGMSM, and 2TLDWGeoMSM operators for MAGDM is introduced. Finally, there is an explanative example to confirm the proposed approach and explain its availability and usefulness.

Hesitant Pythagorean fuzzy Maclaurin symmetric mean operators and its applications to multiattribute decision-making process

Hesitant Pythagorean fuzzy (HPF) sets can easily express the uncertain information while Maclaurin symmetric mean (MSM) operator, can capture the interrelationship among the multiattributes, and are suitable for aggregating the information into a single number. By taking the advantages of both, in this paper, we extend the traditional MSM to HPF environment. For this, we develop the HPFMSM operator for aggregating the HPF information. The desirable characteristics, such as idempotency, monotonicity, and boundedness, are studied. Then, we discussed some special cases with respect to the parameter value of the HPFMSM operators and showed that it generalizes the various existing operators. Furthermore, we studied the weighted HPFMSM operator to aggregate the HPF information with different preferences to the input arguments. On the basis of these operators, we solved the multiattribute decision-making problems with HPF information. The practicality and effectiveness of the developed approach are demonstrated through a numerical example.

Some q-rung orthopair fuzzy maclaurin symmetric mean operators and their applications to potential evaluation of emerging technology commercialization

Some q-rung orthopair fuzzy maclaurin symmetric mean operators and their applications to potential evaluation of emerging technology commercialization

A New Decision-Making Method Based on Interval-Valued Linguistic Intuitionistic Fuzzy Information

In real decision-making, because of the particularity of human cognition activity, it is difficult to depict the decision information by exact numbers, especially, for complex decision information, how to express and aggregate them is an important work for solving these decision-making problems. In order to express the complex fuzzy information accurately, we proposed the concept of interval-valued linguistic intuitionistic fuzzy numbers (IVLIFNs), where their membership function and non-membership function are represented by interval-valued linguistic terms, and then we developed the operational rules, score function, accuracy function, and comparison method of them. Considering that the Maclaurin symmetric mean (MSM) operator has a good characteristic in dealing with the interrelationships among multi-parameters, and it also is a generalization of arithmetic aggregation operator, Bonferroni mean (BM) operator, and geometric aggregation operator, we further proposed the interval-valued linguistic intuitionistic fuzzy MSM (IVLIFMSM) operator, the weighted interval-valued linguistic intuitionistic fuzzy MSM (WIVLIFMSM) operator, and proved some related properties of them. We gave an illustrative example to demonstrate the steps and the effectiveness of the proposed method by the comparison with existing methods. IVLIFNs can more conveniently express the complex fuzzy information in qualitative environment by considering the cognition of decision-makers, and the proposed method can consider the interrelationship among multiple input arguments, so it can make the decision-making results more reasonable. In a word, the proposed method is more scientific and flexible in solving multiple attribute decision-making (MADM) problems than some existing methods.

Approaches to Multiple Attribute Decision Making with Interval-Valued 2-Tuple Linguistic Pythagorean Fuzzy Information

The Maclaurin symmetric mean (MSM) operator is a classical mean type aggregation operator used in modern information fusion theory, which is suitable to aggregate numerical values. The prominent characteristic of the MSM operator is that it can capture the interrelationship among multi-input arguments. Motivated by the ideal characteristic of the MSM operator, in this paper, we expand the MSM operator, generalized MSM (GMSM), and dual MSM (DMSM) operator with interval-valued 2-tuple linguistic Pythagorean fuzzy numbers (IV2TLPFNs) to propose the interval-valued 2-tuple linguistic Pythagorean fuzzy MSM (IV2TLPFMSM) operator, interval-valued 2-tuple linguistic Pythagorean fuzzy weighted MSM (IV2TLPFWMSM) operator, interval-valued 2-tuple linguistic Pythagorean fuzzy GMSM (IN2TLPFGMSM) operator, interval-valued 2-tuple linguistic Pythagorean fuzzy weighted GMSM (IV2TLPFWGMSM) operator, interval-valued 2-tuple linguistic Pythagorean fuzzy DMSM (IN2TLPFDMSM) operator, Interval-valued 2-tuple linguistic Pythagorean fuzzy weighted DMSM (IV2TLPFWDMSM) operator. Then the multiple attribute decision making (MADM) methods are developed with these three operators. Finally, an example of green supplier selection is used to show the proposed methods.

Some Partitioned Maclaurin Symmetric Mean Based on q-Rung Orthopair Fuzzy Information for Dealing with Multi-Attribute Group Decision Making

In respect to the multi-attribute group decision making (MAGDM) problems in which the evaluated value of each attribute is in the form of q-rung orthopair fuzzy numbers (q-ROFNs), a new approach of MAGDM is developed. Firstly, a new aggregation operator, called the partitioned Maclaurin symmetric mean (PMSM) operator, is proposed to deal with the situations where the attributes are partitioned into different parts and there are interrelationships among multiple attributes in same part whereas the attributes in different parts are not related. Some desirable properties of PMSM are investigated. Then, in order to aggregate the q-rung orthopair fuzzy information, the PMSM is extended to q-rung orthopair fuzzy sets (q-ROFSs) and two q-rung orthopair fuzzy partitioned Maclaurin symmetric mean (q-ROFPMSM) operators are developed. To eliminate the negative influence of unreasonable evaluation values of attributes on aggregated result, we further propose two q-rung orthopair fuzzy power partitioned Maclaurin symmetric mean (q-ROFPPMSM) operators, which combine the PMSM with the power average (PA) operator within q-ROFSs. Finally, a numerical instance is provided to illustrate the proposed approach and a comparative analysis is conducted to demonstrate the advantage of the proposed approach.

INTUITIONISTIC FUZZY INTERACTION MACLAURIN SYMMETRIC MEANS AND THEIR APPLICATION TO MULTIPLE-ATTRIBUTE DECISION-MAKING

The Maclaurin symmetric mean (MSM) can capture the interrelationship among the multi-input arguments and it also can generalize most of the existing operators. Now MSM has been extended to intuitionistic fuzzy sets (IFSs) which can easily express the vague information. However, the operational rules of IFSs used in the extended MSM operator didn’t consider the interaction between the membership function and non-membership function, so there are some weaknesses. In this paper, in order to combine the advantages of the MSM and interaction operational rules of IFSs, we propose the intuitionistic fuzzy interaction Maclaurin symmetric mean (IFIMSM) operator, the intuitionistic fuzzy weighted interaction Maclaurin symmetric mean (IFWIMSM) operator, respectively. Furthermore, we research some desirable properties and some special cases of them. Further, we develop a new method to deal with some multi-attribute group decision-making (MAGDM) problems under intuitionistic fuzzy environment based on these operators. Finally, an illustrative example is given to testify the availability of the developed method by comparing with the other existing methods.

Multi-Criteria Decision-Making Method Based on Simplified Neutrosophic Linguistic Information with Cloud Model

This study introduces simplified neutrosophic linguistic numbers (SNLNs) to describe online consumer reviews in an appropriate manner. Considering the defects of studies on SNLNs in handling linguistic information, the cloud model is used to convert linguistic terms in SNLNs to three numerical characteristics. Then, a novel simplified neutrosophic cloud (SNC) concept is presented, and its operations and distance are defined. Next, a series of simplified neutrosophic cloud aggregation operators are investigated, including the simplified neutrosophic clouds Maclaurin symmetric mean (SNCMSM) operator, weighted SNCMSM operator, and generalized weighted SNCMSM operator. Subsequently, a multi-criteria decision-making (MCDM) model is constructed based on the proposed aggregation operators. Finally, a hotel selection problem is presented to verify the effectiveness and validity of our developed approach.

Some power Maclaurin symmetric mean aggregation operators based on Pythagorean fuzzy linguistic numbers and their application to group decision making

The power average (PA) operator and Maclaurin symmetric mean (MSM) operator are two important tools to handle the multiple attribute group decision-making (MAGDM) problems, and the combination of two operators can eliminate the influence of unreasonable information from biased decision makers (DMs) and can capture the interrelationship among any number of arguments. The Pythagorean fuzzy linguistic set (PFLS) is parallel to the intuitionistic linguistic set (ILS), which is more powerful to convey the uncertainty and ambiguity of the DMs than ILS. In this paper, we propose some power MSM aggregation operators for Pythagorean fuzzy linguistic information, such as Pythagorean fuzzy linguistic power MSM operator and Pythagorean fuzzy linguistic power weighted MSM (PFLPWMSM) operator. At the same time, we further discuss the properties and special cases of these operators. Then, we propose a new method to solve the MAGDM problems with Pythagorean fuzzy linguistic information based on the PFLPWMSM operator. Finally, some illustrative examples are utilized to show the effectiveness of the proposed method.

Some Interval Neutrosophic Linguistic Maclaurin Symmetric Mean Operators and Their Application in Multiple Attribute Decision Making

There are many practical decision-making problems in people’s lives, but the information given by decision makers (DMs) is often unclear and how to describe this information is of critical importance. Therefore, we introduce interval neutrosophic linguistic numbers (INLNs) to represent the less clear and uncertain information and give their operational rules and comparison methods. In addition, since the Maclaurin symmetric mean (MSM) operator has the special characteristic of capturing the interrelationships among multi-input arguments, we further propose an MSM operator for INLNs (INLMSM). Furthermore, considering the weights of attributes are the important parameters and they can influence the decision results, we also propose a weighted INLMSM (WINLMSM) operator. Based on the WINLMSM operator, we develop a multiple attribute decision making (MADM) method with INLNs and some examples are used to show the procedure and effectiveness of the proposed method. Compared with the existing methods, the proposed method is more convenient to express the complex and unclear information. At the same time, it is more scientific and flexible in solving the MADM problems by considering the interrelationships among multi-attributes.

Multiple attribute group decision making based on Maclaurin symmetric mean operator under single-valued neutrosophic interval 2-tuple linguistic environment

Multiple attribute group decision making based on Maclaurin symmetric mean operator under single-valued neutrosophic interval 2-tuple linguistic environment