Multi-criteria decision-making method based on single-valued neutrosophic linguistic Maclaurin symmetric mean operators

A generalized interval-valued p,q Rung orthopair fuzzy Maclaurin symmetric mean and modified regret theory based sustainable supplier selection method

A novel interval valued p,q Rung orthopair fuzzy (IVPQ-ROF) multiple attribute group decision making (MAGDM) method for sustainable supplier selection (SSS) is proposed in this paper. This study mainly contains two research points: (1) tackling the interrelation between attributes; and (2) describing the psychological state and risk attitude of decision makers (DMs). For the first research point, we introduce the Archimedean operation rules for interval valued p,q Rung orthopair fuzzy sets (IVPQ-ROFSs), then the generalized interval valued p, q Rung orthopair fuzzy Maclaurin symmetric mean (GIVPQ-ROFMSM) operator and the generalized interval valued p, q Rung orthopair fuzzy weighted Maclaurin symmetric mean (GIVPQ-ROFWMSM) operator are defined to reflect the correlation between attributes. For the second research point, we introduce the positive ideal degree (PID) and negative ideal degree (NID) based on projection of IVPQ-ROFSs, and modified regret theory. Both of them consider the best alternative and worst alternative, so as to reflect the psychological state and risk attitude of DMs. Finally, a SSS problem is presented to manifest the effectiveness of the designed method. We also provide sensitivity analysis and comparative analysis to further demonstrate the rationality and validity of the proposed method.

Multivalued neutrosophic power partitioned Hamy mean operators and their application in MAGDM

The novel multivalued neutrosophic aggregation operators are proposed in this paper to handle the complicated decision-making situations with correlation between specific information and partitioned parameters at the same time, which are based on weighted power partitioned Hamy mean (WMNPPHAM) operators for multivalued neutrosophic sets (MNS) proposed by combining the Power Average and Hamy operators. Firstly, the power partitioned Hamy mean (PPHAM) is capable of capture the correlation between aggregation parameters and the relationship among attributes dividing several parts, where the attributes are dependent definitely within the interchangeable fragment, other attributes in divergent sections are irrelevant. Secondly, because MNS can effectively represent imprecise, insufficient, and uncertain information, we proposed the multivalued neutrosophic PMHAM (WMNPHAM) operator for MNS and its partitioned variant (WMNPPHAM) with the characteristics and examples. Finally, this multiple attribute group decision making (MAGDM) technique is proven to be feasible by comparing with the existing methods to confirm this method's usefulness and validity.

Decision Support System Based on Complex Fractional Orthotriple Fuzzy 2-Tuple Linguistic Aggregation Operator

In this research, we provide tools to overcome the information loss limitation resulting from the requirement to estimate the results in the discrete initial expression domain. Through the use of 2-tuples, which are made up of a linguistic term and a numerical value calculated between [0.5,0.5), the linguistic information will be expressed. This model supports continuous representation of the linguistic data within its scope, permitting it to express any information counting received through an aggregation procedure. This study provides a novel approach to develop a linguistic multi-attribute group decision-making (MAGDM) approach with complex fractional orthotriple fuzzy 2-tuple linguistic (CFOF2TL) assessment details. Initially, the concept of a complex fractional orthotriple fuzzy 2-tuple linguistic set (CFO2TLS) is proposed to convey uncertain and fuzzy information. In the meantime, simple aggregation operators, such as CFOF2TL weighted average and geometric operators, are defined. In addition, the CFOF2TL Maclaurin’s symmetric mean (CFOF2TLMSM) operators and their weighted shapes are presented, and their attractive characteristics are also discussed. A new MAGDM approach is built using the developed aggregation operators to address managing economic crises under COVID-19 with the CFOF2TL information. As a result, the effectiveness and robustness of the developed method are accompanied by an empirical example, and a comparative study is carried out by contrasting it with previous approaches.

Complex Pythagorean uncertain linguistic group decision-making model based on Heronian mean aggregation operator considering uncertainty, interaction and interrelationship

To effectively solve the mixed problem of considering the uncertainty of individuals and groups, the interaction between membership degree (MD) and non-membership (ND), and the interrelationship between attribute variables in complicated multiple attribute group decision-making (MAGDM) problems, in this paper, a concept of complex Pythagorean uncertain linguistic (CPUL) set (CPULS) is introduced, the interaction operational laws (IOLs) of CPUL variables (CPULVs) are defined. The CPUL interaction weighted averaging and geometric operators are presented. A new concept of CPUL rough number (CPULRN) is further constructed. The CPUL rough interaction weighted averaging and geometric aggregation operators (AOs) are extended. The ordering rules of any two CPULRNs are defined. The CPUL rough interaction Heronian mean (HM) (CPULRIHM) operator and its weighted form are advanced, related properties and special cases are explored. An MAGDM model based on CPUL rough interaction weighted HM (CPULRIWHM) operator is built. Lastly, we conduct a case study of location selection problem for logistics town project to show the applicability of the proposed methodology. The sensitivity and methods comparison are analyzed to verify the effectively and superiority.

Some Single-Valued Neutrosophic Uncertain Linguistic Maclaurin Symmetric Mean Operators and Their Application to Multiple-Attribute Decision Making

The Maclaurin symmetric mean (MSM) operator has a good aggregation effect. It can capture the relationships between multiple input parameters, and the neutrosophic uncertain linguistic numbers can well represent some indeterminate and incomplete information. In this paper, we combine the MSM operator with the singled-valued neutrosophic uncertain linguistic set and propose some MSM operators based on single-valued neutrosophic uncertain linguistic environment, such as single-valued neutrosophic uncertain linguistic Maclaurin symmetric mean(SVNULMSM) operator and single-valued neutrosophic uncertain linguistic generalized Maclaurin symmetric mean(SVNULGMSM) operator. First of all, according to the neutrosophic set and uncertain linguistic numbers, we propose the single-valued neutrosophic uncertain linguistic numbers and give some operating rules. Furthermore, considering the influence of attribute weight on the results, we introduce the weighted SVNULMSM operator and weighted SVNULGMSM operator. Then, we propose a method to deal with MSDM problems and give the specific steps to solve the problem. Finally, an investment example is used to verify the effectiveness of our method, and the superiority of the method is proved by comparing with other methods.

Multiple-attribute decision making method based on power generalized maclaurin symmetric mean operators under normal wiggly hesitant fuzzy environment

A normal wiggly hesitant fuzzy set is a very useful tool to mine the potential uncertain information given by decision makers, which is considered as an extension of hesitant fuzzy set and can improve the effectiveness of decision making. Power average operator can relieve the impact on decision result of unreasonable data, and the generalized Maclaurin symmetric mean operator (GMSM) is an extension of Maclaurin symmetric mean operator with wider range of applications, which can consider the relationship among decision attributes. By integrating the advantages of them, in this paper, we develop the normal wiggly hesitant fuzzy power GMSM (NWHFPGMSM) operator and its weighted form based on the distance measure of two normal wiggly hesitant fuzzy elements, then we further discuss their properties and some special cases. Thus, a new multi-attribute decision making method based on the NWHFPGMSM operator under normal wiggly hesitant fuzzy environment is proposed. Finally, we select some examples to illustrate the effectiveness and superiority of the proposed method in this paper through comparison and analysis with other methods.

Multi-Attribute Group Decision-Making Based on Interval-Valued q-Rung Orthopair Fuzzy Power Generalized Maclaurin Symmetric Mean Operator and Its Application in Online Education Platform Performance Evaluation

This paper aims to propose a novel multi-attribute group decision-making (MAGDM) method based on interval-valued q-rung orthopair fuzzy sets (IVq-ROFSs). The IVq-ROFSs have been proved to be effective in handling MAGDM problems, and several novel decision-making methods have been proposed. Nevertheless, it is worth pointing out that these approaches still have some limitations, and there still exist some realistic situations that cannot be solved by existing MAGDM methods. Hence, the objective of this paper is to introduce a novel MAGDM method, which can overcome some of the drawbacks of existing approaches. To effectively and appropriately aggregate interval-valued q-rung orthopair fuzzy numbers (IVq-ROFNs), we combine the power average with generalized Maclaurin symmetric mean (GMSM), propose the power GMSM operator and extend it into IVq-ROFSs. Afterwards, a collection of new aggregation operators for IVq-ROFNs are developed. In this paper, we study definitions of these operators and investigate their characteristics as well as special cases. Then, based on the new aggregation operators, we present a new MAGDM method. Finally, we apply the proposed MAGDM method in online education platform performance evaluation to illustrate its effectiveness and validity. In addition, we also provide comparative analysis to explain why decision-makers should use our method instead of the others.

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.

A Decision Support Model for Hotel Recommendation Based on the Online Consumer Reviews Using Logarithmic Spherical Hesitant Fuzzy Information

Spherical hesitant fuzzy sets have recently become more popular in various fields. It was proposed as a generalization of picture hesitant fuzzy sets and Pythagorean hesitant fuzzy sets in order to deal with uncertainty and fuzziness information. Technique of Aggregation is one of the beneficial tools to aggregate the information. It has many crucial application areas such as decision-making, data mining, medical diagnosis, and pattern recognition. Keeping in view the importance of logarithmic function and aggregation operators, we proposed a novel algorithm to tackle the multi-attribute decision-making (MADM) problems. First, novel logarithmic operational laws are developed based on the logarithmic, t-norm, and t-conorm functions. Using these operational laws, we developed a list of logarithmic spherical hesitant fuzzy weighted averaging/geometric aggregation operators to aggregate the spherical hesitant fuzzy information. Furthermore, we developed the spherical hesitant fuzzy entropy to determine the unknown attribute weight information. Finally, the design principles for the spherical hesitant fuzzy decision-making have been developed, and a practical case study of hotel recommendation based on the online consumer reviews has been taken to illustrate the validity and superiority of presented approach. Besides this, a validity test is conducted to reveal the advantages and effectiveness of developed approach. Results indicate that the proposed method is suitable and effective for the decision process to evaluate their best alternative.

Linguistic interval-valued intuitionistic fuzzy copula power aggregation operators for multiattribute group decision making

For the sake of better handle the imprecise and uncertain information in decision making problems(DMPs), linguistic interval-valued intuitionistic fuzzy numbers(LIVIFNs) based aggregation operators (AOS) are proposed by combining extended Copulas (ECs), extended Co-copulas (ECCs), power average operator and linguistic interval-valued intuitionistic fuzzy information (LIVIFI). First of all, ECs and ECCs, some specifics of ECs and ECCs, score and accuracy functions of LIVIFNs are gained. Then, based on ECs and ECCs, several aggregation operators are proposed to aggregate LIVIFI, which can offer decision makers (DMs) desirable generality and flexibility. In addition, the desired properties of proposed AOS are discussed. Last but not least, a MAGDM approach is constructed based on proposed AOs; Consequently, the effectiveness of the proposed approach is verified by a numerical example, and then the advantages are showed by comparing with other approaches.

Single-Valued Neutrosophic Linguistic Logarithmic Weighted Distance Measures and Their Application to Supplier Selection of Fresh Aquatic Products

A single-valued neutrosophic linguistic set (SVNLS) is a popular fuzzy tool for describing deviation information in uncertain complex situations. The aim of this paper is to study some logarithmic distance measures and study their usefulness in multiple attribute group decision making (MAGDM) problems within single-valued neutrosophic linguistic (SVNL) environments. For achieving the purpose, SVNL weighted logarithmic averaging distance (SVNLWLAD) and SVNL ordered weighted logarithmic averaging distance (SVNLOWLAD) measures are firstly developed based on the logarithmic aggregation method. Then, the SVNL combined weighted logarithmic averaging distance (SVNLCWLAD) measure is presented by unifying the advantages of the previous SVNLWLAD and SVNLOWLAD measures. Moreover, a new MAGDM model by utilizing the SVNLCWLAD measure is presented under SVNL environments. Finally, a supplier selection for fresh aquatic products is taken as a case to illustrate the performance of the proposed framework.

Novel Multiple Attribute Group Decision-Making Methods Based on Linguistic Intuitionistic Fuzzy Information

As an effective technique to qualitatively depict assessment information, a linguistic intuitionistic fuzzy number (LIFN) is more appropriate to portray vagueness and indeterminacy in actual situations than intuitionistic fuzzy number (IFN). The prominent feature of a Muirhead mean (MM) operator is that it has the powerful ability to capture the correlations between any input-data and MM operator covers other common operators by assigning the different parameter vectors. In the article, we first analyze the limitations of the existing ranking approaches of LIFN and propose a novel ranking approach to surmount these limitations. Secondly, we propound several novel MM operators to fuse linguistic intuitionistic fuzzy (LIF) information, such as the LIF Muirhead mean (LIFMM) operator, the weighted LIF Muirhead mean (WLIFMM) operator and their dual operators, the LIFDMM operator and the WLIFDMM operator. Subsequently, we discuss several desirable properties along with exceptional cases of them. Moreover, two novel multiple attribute group decision-making approaches are developed based upon these operators. Ultimately, the effectuality and practicability of the propounded methods are validated through dealing with a global supplier selection issue, and the comparative analysis and the merits of the presented approaches are demonstrated by comparing them with existing approaches.

Single-Valued Neutrosophic Linguistic-Induced Aggregation Distance Measures and Their Application in Investment Multiple Attribute Group Decision Making

This paper studied the single-valued neutrosophic linguistic distance measures based on the induced aggregation method. Firstly, we proposed a single-valued neutrosophic linguistic-induced ordered weighted averaging distance (SVNLIOWAD) measure, which is a new extension of the existing distance measures based on the induced aggregation view. Then, based on the proposed SVNLIOWAD, a novel induced distance for single-valued neutrosophic linguistic sets, namely the single-valued neutrosophic linguistic weighted induced ordered weighted averaging distance (SVNLWIOWAD), was developed to eliminate the defects of the existing methods. The relationship between the two proposed distance measures was also explored. A multiple attribute group decision making (MAGDM) model was further presented based on the proposed SVNLWIOWAD measure. Finally, a numerical example concerning an investment selection problem was provided to demonstrate the usefulness of the proposed method under a single-valued neutrosophic linguistic environment and, then, a comparison analysis was carried out to verify the flexibility and effectiveness of the proposed work.

Some Novel Picture 2-Tuple Linguistic Maclaurin Symmetric Mean Operators and Their Application to Multiple Attribute Decision Making

When solving multiple attribute decision making (MADM) problems, the 2-tuple linguistic variable is an effective tool that can not only express complex cognitive information but also prevent loss of information in calculation. The picture fuzzy set (PFS) has three degrees and has more freedom to express cognitive information. In addition, Archimedean t-conorm and t-norm (ATT) can generalize most existing t-conorms and t-norms and Maclaurin symmetric mean (MSM) operators can catch the relationships among the multi-input parameters. Therefore, we investigate several novel aggregation operators, such as the picture 2-tuple linguistic MSM (2TLMSM) operator based on the ATT (ATT-P2TLMSM) and the picture 2-tuple linguistic generalized MSM (2TLGMSM) operator based on ATT (ATT-P2TLGMSM). Considering that the input parameters have different importance, we proposed picture 2-tuple linguistic weighted MSM (2TLWMSM) operators based on ATT (ATT-P2TLWMSM) and picture 2-tuple linguistic weighted generalized MSM (2TLWGMSM) operators based on ATT (ATT-P2TLWGMSM). Finally, a MADM method is introduced, and an expositive example is presented to explain the availability and applicability of the developed operators and methods.

Generalized Hamacher Aggregation Operators for Intuitionistic Uncertain Linguistic Sets: Multiple Attribute Group Decision Making Methods

In this paper, we consider multiple attribute group decision making (MAGDM) problems in which the attribute values take the form of intuitionistic uncertain linguistic variables. Based on Hamacher operations, we developed several Hamacher aggregation operators, which generalize the arithmetic aggregation operators and geometric aggregation operators, and extend the algebraic aggregation operators and Einstein aggregation operators. A number of special cases for the two operators with respect to the parameters are discussed in detail. Also, we developed an intuitionistic uncertain linguistic generalized Hamacher hybrid weighted average operator to reflect the importance degrees of both the given intuitionistic uncertain linguistic variables and their ordered positions. Based on the generalized Hamacher aggregation operator, we propose a method for MAGDM for intuitionistic uncertain linguistic sets. Finally, a numerical example and comparative analysis with related decision making methods are provided to illustrate the practicality and feasibility of the proposed method.

A Single-Valued Neutrosophic Linguistic Combined Weighted Distance Measure and Its Application in Multiple-Attribute Group Decision-Making

The aim of this paper is to present a multiple-attribute group decision-making (MAGDM) framework based on a new single-valued neutrosophic linguistic (SVNL) distance measure. By unifying the idea of the weighted average and ordered weighted averaging into a single-valued neutrosophic linguistic distance, we first developed a new SVNL weighted distance measure, namely a SVNL combined and weighted distance (SVNLCWD) measure. The focal characteristics of the devised SVNLCWD are its ability to combine both the decision-makers’ attitudes toward the importance, as well as the weights, of the arguments. Various desirable properties and families of the developed SVNLCWD were contemplated. Moreover, a MAGDM approach based on the SVNLCWD was formulated. Lastly, a real numerical example concerning a low-carbon supplier selection problem was used to describe the superiority and feasibility of the developed approach.

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.

A novel financial risk assessment model for companies based on heterogeneous information and aggregated historical data

The financial risk not only affects the development of the company itself, but also affects the economic development of the whole society; therefore, the financial risk assessment of company is an important part. At present, numerous methods of financial risk assessment have been researched by scholars. However, most of the extant methods neither integrated fuzzy sets with quantitative analysis, nor took into account the historical data of the past few years. To settle these defects, this paper proposes a novel financial risk assessment model for companies based on heterogeneous multiple-criteria decision-making (MCDM) and historical data. Subjective and objective indexes are comprehensively taken into consideration in the financial risk assessment index system of the model, which combines fuzzy theory with quantitative data analysis. Moreover, the assessment information obtained from historical financial information of company, credit rating agency and decision makers, including crisp numbers, triangular fuzzy numbers and neutrosophic numbers. Furthermore, the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method is used to determine the ranking order of companies according to their financial risk. Finally, an empirical study of financial risk assessment for companies is conducted, and the results of comparative analysis and sensitivity analysis suggest that the proposed model can effectively and reliably obtain the company with the lowest financial risk.

On Homomorphism Theorem for Perfect Neutrosophic Extended Triplet Groups

Some homomorphism theorems of neutrosophic extended triplet group (NETG) are proved in the paper [Fundamental homomorphism theorems for neutrosophic extended triplet groups, Symmetry 2018, 10(8), 321; doi:10.3390/sym10080321]. These results are revised in this paper. First, several counterexamples are given to show that some results in the above paper are not true. Second, two new notions of normal NT-subgroup and complete normal NT-subgroup in neutrosophic extended triplet groups are introduced, and their properties are investigated. Third, a new concept of perfect neutrosophic extended triplet group is proposed, and the basic homomorphism theorem of perfect neutrosophic extended triplet groups is established.

Multi-Criteria Decision-Making Method Based on Prioritized Muirhead Mean Aggregation Operator under Neutrosophic Set Environment

The aim of this paper is to introduce some new operators for aggregating single-valued neutrosophic (SVN) information and to apply them to solve the multi-criteria decision-making (MCDM) problems. Single-valued neutrosophic set, as an extension and generalization of an intuitionistic fuzzy set, is a powerful tool to describe the fuzziness and uncertainty, and Muirhead mean (MM) is a well-known aggregation operator which can consider interrelationships among any number of arguments assigned by a variable vector. In order to make full use of the advantages of both, we introduce two new prioritized MM aggregation operators, such as the SVN prioritized MM (SVNPMM) and SVN prioritized dual MM (SVNPDMM) under SVN set environment. In addition, some properties of these new aggregation operators are investigated and some special cases are discussed. Furthermore, we propose a new method based on these operators for solving the MCDM problems. Finally, an illustrative example is presented to testify the efficiency and superiority of the proposed method by comparing it with the existing method.

An OWA Distance-Based, Single-Valued Neutrosophic Linguistic TOPSIS Approach for Green Supplier Evaluation and Selection in Low-Carbon Supply Chains

This paper presents a technique based on the ordered weighted averaging (OWA) distance for the single-valued neutrosophic linguistic (SVNL) technique for order preference by similarity to an ideal solution (TOPSIS). First, the inadequacies of the existing SVNL TOPSIS are analyzed in detail. Second, a SVNL OWA distance (SVNLOWAD) measure is presented, and based on this, a modified TOPSIS, termed the SVNLOWAD-TOPSIS, is developed for multiple attribute decision-making problems with SVNL information. Third, a revised relative coefficient is proposed to rank potential alternatives. Finally, a numerical example concerning green supplier selection in low-carbon supply chains is introduced to demonstrate the effectiveness of the model.