Some intuitionistic uncertain linguistic Heronian mean operators and their application to group decision making

Лю, Пэйдэ; Liu, Zhengmin; Zhang, Xin

doi:10.1016/j.amc.2013.12.133

Cited by 151 publications

(110 citation statements)

References 18 publications

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“…The information aggregation operators have attracted more and more attentions, and they have become a hot research topic [23][24][25][26][27]32]. Yager [13] firstly proposed a power averaging (PA) operator, the power weighted averaging (PWA) operator and the power ordered weighted averaging (POWA) operator.…”

Section: Introductionmentioning

confidence: 99%

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Multiple attribute decision making method based on normal neutrosophic generalized weighted power averaging operator

Лю¹,

Teng²

2015

Int. J. Mach. Learn. & Cyber.

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Normal neutrosophic numbers (NNNs) are an important tool to describe the decision making problems, and they are more appropriate to express the incompleteness, indeterminacy and inconsistency of the evaluation information. In this paper, we firstly introduce the definition, the properties, the score function, the accuracy function, and the operational laws of the NNNs. Then, some operators are proposed, such as the normal neutrosophic power averaging operator, the normal neutrosophic weighted power averaging operator, the normal neutrosophic power geometric operator, the normal neutrosophic weighted power geometric operator, the normal neutrosophic generalized power averaging operator, the normal neutrosophic generalized weighted power averaging (NNGWPA) operator. Furthermore, some properties of them are discussed. Thirdly, we propose a multiple attribute decision making method based on the NNGWPA operator. Finally, we use an illustrative example to demonstrate the practicality and effectiveness of the proposed method.

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Section: Introductionmentioning

confidence: 99%

“…Multiple attribute decision making (MADM) as the important research branch of decision theory has a wide application in many fields [10,12,14,[21][22][23][24][25][26][27][28][29][30][31][32]. Churchman et al [1] firstly proposed the multiple attribute decision making method and applied it to select the enterprise investment policy.…”

Section: Introductionmentioning

confidence: 99%

Multiple attribute decision making method based on normal neutrosophic generalized weighted power averaging operator

Лю¹,

Teng²

2015

Int. J. Mach. Learn. & Cyber.

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“…Now, more and more researchers pay attention to the information aggregation operators, which have become an important research topic [18][19][20][21][22][23][24][25][26]. Some new extended aggregation operators for NS and INS were proposed [27][28][29][30][31], and new intuitionistic normal fuzzy aggregation operators were developed [18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Multiple attribute decision-making method based on some normal neutrosophic Bonferroni mean operators

Лю

2015

Neural Comput & Applic

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Normal neutrosophic numbers (NNNs) are a significant tool of describing the incompleteness, indeterminacy, and inconsistency of the decision-making information. In this paper, we firstly propose the definition and the properties of the NNNs, and the accuracy function, the score function, and the operational laws of the NNNs are developed. Then, some operators are presented, including the normal neutrosophic Bonferroni mean operator, the normal neutrosophic weighted Bonferroni mean (NNWBM) operator, the normal neutrosophic geometric Bonferroni mean operator, and the normal neutrosophic weighted geometric Bonferroni mean (NNWGBM) operator. We also study their properties and special cases. Further, we put forward a multiple attribute decision-making method which is based on the NNWBM and NNWGBM operators. Finally, an illustrative example is given to verify the practicality and validity of the proposed method.

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“…Furthermore, Liu and Jin [4] proposed the concept of an intuitionistic uncertain linguistic variable (IULV), which is an extension of the ILV concept, and developed an intuitionistic uncertain linguistic weighted geometric averaging (IULWGA) operator, an intuitionistic uncertain linguistic ordered weighted geometric (IULOWG) operator, and an intuitionistic uncertain linguistic hybrid geometric (IULHG) operator, which generalizes both the IULWGA operator and the IULOWG operator, and then they applied these operators to multiple attribute group decision-making problems with IULVs. Liu et al [5] further developed some intuitionistic uncertain linguistic Heronian mean operators, including an intuitionistic uncertain linguistic arithmetic Heronian (IULAH) operator, an intuitionistic uncertain linguistic weighted arithmetic Heronian (IUL-WAH) operator, an intuitionistic uncertain linguistic geometric Heronian (IULGH) operator, and an intuitionistic uncertain linguistic weighted geometric Heronian (IULWGH) operator, and then applied them to group decision making.…”

Section: Introductionmentioning

confidence: 99%

Multiple attribute group decision making based on interval neutrosophic uncertain linguistic variables

2015

Int. J. Mach. Learn. & Cyber.

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To deal with decision-making problems with interval neutrosophic uncertain linguistic information, the paper proposes a multiple attribute group decision-making method under an interval neutrosophic uncertain linguistic environment. Firstly, the concept of an interval neutrosophic uncertain linguistic set and an interval neutrosophic uncertain linguistic variable (INULV) is presented by combining an uncertain linguistic variable with an interval neutrosophic set. Secondly, we introduce the operation rules of INULVs and the score function, accuracy function and certainty function of an INULV. Thirdly, we develop an interval neutrosophic uncertain linguistic weighted arithmetic averaging (INULWAA) operator and an interval neutrosophic uncertain linguistic weighted geometric averaging (INULWGA) operator and investigate their properties. Fourthly, a group decision-making method is established based on the INULWAA and INULWGA operators to solve multiple attribute group decision-making problems with interval neutrosophic uncertain linguistic information. Finally, an illustrative example is provided to demonstrate the application of the developed approach.

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Some intuitionistic uncertain linguistic Heronian mean operators and their application to group decision making

Cited by 151 publications

References 18 publications

Multiple attribute decision making method based on normal neutrosophic generalized weighted power averaging operator

Multiple attribute decision making method based on normal neutrosophic generalized weighted power averaging operator

Multiple attribute decision-making method based on some normal neutrosophic Bonferroni mean operators

Multiple attribute group decision making based on interval neutrosophic uncertain linguistic variables

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