On a conjecture on the symmetric means

Gao, Peng

doi:10.1016/j.jmaa.2007.04.011

Cited by 11 publications

(7 citation statements)

References 11 publications

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“…From the above analysis, we can see that most of the existing q ‐rung orthopair fuzzy aggregation operators are based on the algebraic product and algebraic sum of q‐ROFs to carry the aggregation process that does not consider the interrelationship among the multi‐input arguments. In recent years, many researchers studied the MSM operator and its applications that only consider the case that arguments take the form of crisp numbers …”

Section: Introductionmentioning

confidence: 99%

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

et al. 2018

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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 the multi‐input arguments. In this paper, we extend the MSM operator and dual MSM operator to q‐rung orthopair fuzzy sets to propose the q‐rung orthopair fuzzy MSM operator, q‐rung orthopair fuzzy dual MSM operator, q‐rung orthopair fuzzy weighted MSM operator, and q‐rung orthopair fuzzy weighted dual MSM operator. Then, some desirable properties and special cases of these operators are discussed in detail. Finally, a numerical example is provided to illustrate the feasibility of the proposed methods and deliver the sensitivity analysis and comparative analysis.

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Section: Introductionmentioning

confidence: 99%

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

et al. 2018

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“…From above analysis, we can see that most of the existing Pythagorean fuzzy aggregation operators are based on the algebraic product and algebraic sum of PFSs to carry out the aggregation process that do not consider the interrelationship among the multiinput arguments. In recent years, many researchers studied the MSM operator and their applications which only consider the case that arguments take the form of crisp numbers …”

Section: Introductionmentioning

confidence: 99%

“…In recent years, many researchers studied the MSM operator and their applications which only consider the case that arguments take the form of crisp numbers. [42][43][44] To date, we have not seen any research based on MSM for information fusion under Pythagorean fuzzy environment. Therefore, it is meaningful to pay attention to this issue.…”

Section: Introductionmentioning

confidence: 99%

Pythagorean Fuzzy Maclaurin Symmetric Mean Operators in Multiple Attribute Decision Making

Wei

2017

Int. J. Intell. Syst.

232

124

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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 the multiinput arguments. In this paper, we extend MSM to Pythagorean fuzzy environment to propose the Pythagorean fuzzy Maclaurin symmetric mean and Pythagorean fuzzy weighted Maclaurin symmetric mean operators. Then, some desirable properties and special cases of these operators are discussed in detail. Finally, a numerical example is provided to illustrate the feasibility of the proposed methods and deliver a comparative analysis.

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“…From the existing literatures [30][31][32], we can see that the MSM is only considering the case that arguments take the form of crisp numbers. However, due to the increasing complexity of the social-economic environment, there are limitations of various factors, such as time pressing, lack of information, uncertainty of the decision-making environment, difficulties in information extraction etc., therefore, it is usually difficult to determine the arguments with a crisp numbers.…”

Section: Introductionmentioning

confidence: 99%

An approach to intuitionistic fuzzy multiple attribute decision making based on Maclaurin symmetric mean operators

Qin

Liu

2014

Journal of Intelligent &Amp; Fuzzy Systems

132

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The Maclaurin symmetric mean (MSM) was originally introduced by Maclaurin and then generalized by Detemple and Robertson. The prominent characteristic of the MSM is that it can capture the interrelationship among the multi-input arguments. However, the researches on MSM are very rare, especially in fuzzy decision making. In this paper, we investigate the MSM operator and extend the MSM operator to intuitionistic fuzzy environment. Some new aggregation operators based on MSM for dealing with intuitionistic fuzzy information are developed, such as the intuitionistic fuzzy Maclaurin symmetric mean (IFMSM) and the weighted intuitionistic fuzzy Maclaurin symmetric mean (WIFMSM). Some desirable properties and special cases of these operators are discussed in detail. Based on WIFMSM operator, an approach to multiple attribute decision making (MADM) problems with intuitionistic fuzzy information is developed. Finally, a practical example is provided to illustrate the practicality and effectiveness of the proposed method.Keywords: Maclaurin symmetric mean (MSM), intuitionistic fuzzy set (IFS), intuitionistic fuzzy Maclaurin symmetric mean (IFMSM), weighted intuitionistic fuzzy Maclaurin symmetric mean (WIFMSM), multiple attribute decision making * Corresponding author. Xinwang Liu,

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On a conjecture on the symmetric means

Abstract: In this paper, we study some inequalities involving the symmetric means. The main result is a proof of a conjecture of Alzer et al.

Cited by 11 publications

References 11 publications

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

Pythagorean Fuzzy Maclaurin Symmetric Mean Operators in Multiple Attribute Decision Making

An approach to intuitionistic fuzzy multiple attribute decision making based on Maclaurin symmetric mean operators

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