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

2020 ◽  
Author(s):  
Aliya Fahmi ◽  
Naveed Yaqoob ◽  
Wathek Chammam
Keyword(s):  
Fuzzy Number ◽  
Aggregation Operators ◽  
Maclaurin Symmetric Mean

Pythagorean probabilistic hesitant fuzzy aggregation operators and their application in decision-making

Kybernetes ◽  
2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Bushra Batool ◽  
Saleem Abdullah ◽  
Shahzaib Ashraf ◽  
Mumtaz Ahmad
Keyword(s):  
Decision Making ◽  
Fuzzy Number ◽  
Weighted Average ◽  
Aggregation Operators ◽  
Content Type ◽  
Operational Laws ◽  
Fuzzy Aggregation ◽  
Emergency Decision Making ◽  
Emergency Decision ◽  
Established Technique

PurposeThis is mainly because the restrictive condition of intuitionistic hesitant fuzzy number (IHFN) is relaxed by the membership functions of Pythagorean probabilistic hesitant fuzzy number (PyPHFN), so the range of domain value of PyPHFN is greatly expanded. The paper aims to develop a novel decision-making technique based on aggregation operators under PyPHFNs. For this, the authors propose Algebraic operational laws using algebraic norm for PyPHFNs. Furthermore, a list of aggregation operators, namely Pythagorean probabilistic hesitant fuzzy weighted average (PyPHFWA) operator, Pythagorean probabilistic hesitant fuzzy weighted geometric (PyPHFWG) operator, Pythagorean probabilistic hesitant fuzzy ordered weighted average (PyPHFOWA) operator, Pythagorean probabilistic hesitant fuzzy ordered weighted geometric (PyPHFOWG) operator, Pythagorean probabilistic hesitant fuzzy hybrid weighted average (PyPHFHWA) operator and Pythagorean probabilistic hesitant fuzzy hybrid weighted geometric (PyPHFHWG) operator, are proposed based on the defined algebraic operational laws. Also, interesting properties of these aggregation operators are discussed in detail.Design/methodology/approachPyPHFN is not only a generalization of the traditional IHFN, but also a more effective tool to deal with uncertain multi-attribute decision-making problems.FindingsIn addition, the authors design the algorithm to handle the uncertainty in emergency decision-making issues. At last, a numerical case study of coronavirus disease 2019 (COVID-19) as an emergency decision-making is introduced to show the implementation and validity of the established technique. Besides, the comparison of the existing and the proposed technique is established to show the effectiveness and validity of the established technique.Originality/valuePaper is original and not submitted elsewhere.

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

2019 ◽  
Vol 18 (01) ◽  
pp. 105-146 ◽  
Author(s):  
Fei Teng ◽  
Peide Liu ◽  
Li Zhang ◽  
Juan Zhao
Keyword(s):  
Decision Making ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
Linguistic Variables ◽  
Numerical Example ◽  
Maclaurin Symmetric Mean ◽  
Multiple Attribute ◽  
Linguistic Term

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.

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

Symmetry ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 943
Author(s):  
Min Feng ◽  
Yushui Geng
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
Linguistic Variable ◽  
Maclaurin Symmetric Mean ◽  
Multiple Attribute ◽  
Picture Fuzzy Set ◽  
Input Parameters ◽  
Cognitive Information

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.

scholarly journals 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

Information ◽  
2021 ◽  
Vol 12 (9) ◽  
pp. 372
Author(s):  
Jun Wang ◽  
Yang Zhou
Keyword(s):  
Decision Making ◽  
Performance Evaluation ◽  
Online Education ◽  
Group Decision Making ◽  
Group Decision ◽  
Aggregation Operators ◽  
Maclaurin Symmetric Mean ◽  
Special Cases ◽  
Education Platform ◽  
Interval Valued

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.

scholarly journals Archimedean Muirhead Aggregation Operators of q-Rung Orthopair Fuzzy Numbers for Multicriteria Group Decision Making

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-33 ◽  
Author(s):  
Yuchu Qin ◽  
Xiaolan Cui ◽  
Meifa Huang ◽  
Yanru Zhong ◽  
Zhemin Tang ◽  
...  
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Fuzzy Number ◽  
Group Decision ◽  
Aggregation Operators ◽  
Decision Makers ◽  
Intuitionistic Fuzzy Number ◽  
Fuzzy Information ◽  
Qualitative And Quantitative ◽  
Multicriteria Group Decision Making

q-Rung orthopair fuzzy number (qROFN) is a flexible and superior fuzzy information description tool which can provide stronger expressiveness than intuitionistic fuzzy number and Pythagorean fuzzy number. Muirhead mean (MM) operator and its dual form geometric MM (GMM) operator are two all-in-one aggregation operators for capturing the interrelationships of the aggregated arguments because they are applicable in the cases in which all arguments are independent of each other, there are interrelationships between any two arguments, and there are interrelationships among any three or more arguments. Archimedean T-norm and T-conorm (ATT) are superior operations that can generate general and versatile operational rules to aggregate arguments. To take advantage of qROFN, MM operator, GMM operator, and ATT in multicriteria group decision making (MCGDM), an Archimedean MM operator, a weighted Archimedean MM operator, an Archimedean GMM operator, and a weighted Archimedean GMM operator for aggregating qROFNs are presented to solve the MCGDM problems based on qROFNs in this paper. The properties of these operators are explored and their specific cases are discussed. On the basis of the presented operators, a method for solving the MCGDM problems based on qROFNs is proposed. The effectiveness of the proposed method is demonstrated via a numerical example, a set of experiments, and qualitative and quantitative comparisons. The demonstration results suggest that the proposed method has satisfying generality and flexibility at aggregating q-rung orthopair fuzzy information and capturing the interrelationships of criteria and the attitudes of decision makers and is feasible and effective for solving the MCGDM problems based on qROFNs.

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