Intuitionistic Fuzzy Normalized Weighted Bonferroni Mean and Its Application in Multicriteria Decision Making

Zhou, Wei; He, Jie

doi:10.1155/2012/136254

Cited by 56 publications

(57 citation statements)

References 26 publications

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“…Liu and Shi presented some neutrosophic uncertain linguistic number Heronian mean operators and their application to MAGDM [14]. Since the Bonferroni mean (BM) is a useful operator in decision-making [15], it was extended to hesitant fuzzy sets, IFSs, and interval-valued IFSs to propose their some Bonferroni mean operators for decision making [16][17][18][19][20]. Then, Fang and Ye proposed the linguistic neutrosophic numbers (LNN) and their basic operational laws [21].…”

Section: Introductionmentioning

confidence: 99%

Bonferroni Mean Operators of Linguistic Neutrosophic Numbers and Their Multiple Attribute Group Decision-Making Methods

Fan

et al. 2017

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Linguistic neutrosophic numbers (LNN) is presented by Fang and Ye in 2017, which can describe the truth, falsity, and indeterminacy linguistic information independently. In this paper, the LNN and the Bonferroni mean operator are merged together to propose a LNN normalized weighted Bonferroni mean (LNNNWBM) operator and a LNN normalized weighted geometric Bonferroni mean (LNNNWGBM) operator and the properties of these two operators are proved. Further, multi-attribute group decision methods are introduced based on the proposed LNNNWBM and LNNNWGBM operators, and then an example is provided to demonstrate the application and validity of the proposed methods. In addition, in order to consider the effect of the parameters p and q on the decision results, different pairs of parameter values are employed to verify the decision results.

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Section: Introductionmentioning

confidence: 99%

Bonferroni Mean Operators of Linguistic Neutrosophic Numbers and Their Multiple Attribute Group Decision-Making Methods

Fan

et al. 2017

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“…Further, Zhou and He [48] noted that the BM could not be obtained from the WBM when the weights of the aggregated parameters were equal; that is to say, the WBM did not have reducibility. It seemed to be counterintuitive.…”

Section: Preliminaries 21 Uncertain Linguistic Variablesmentioning

confidence: 99%

“…Zhou and He [48] proposed the Normalized WBM (NWBM) and the Generalized NWBM (GNWBM), and the Intuitionistic Fuzzy NWBM (IFNWBM) and the Generalized Intuitionistic Fuzzy NWBM (GIFNWBM), which had reducibility and re ected the interrelationship between two attributes. Tian et al [49] proposed some simpli ed neutrosophic linguistic normalized weighted BM operators and applied them to the multi-criteria decision making problems.…”

Section: Introductionmentioning

confidence: 99%

“…Motivated by the ideas of NWBM, GNWBM, IFNWBM, and GIFNWBM operators proposed by Zhou and He [48], this paper is to propose the Normalized Weighted GBM (NWGBM) and the Generalized NWGBM (GNWGBM), the 2-Dimensional Uncertain Linguistic NWGBM (2DULNWGBM) and the 2-Dimensional Uncertain Linguistic Generalized NWGBM (2DULGNWGBM). Based on these operators, the MADM approach with 2DULVs is developed.…”

Section: Introductionmentioning

confidence: 99%

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2-Dimension Uncertain Linguistic Generalized Normalized Weighted Geometric Bonferroni Mean and Its Application in Multiple Attribute Decision Making

Лю

2017

Scientia Iranica

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KEYWORDS Aggregation operators;Multiple-attribute decision making; Bonferroni mean; 2-dimensional uncertain linguistic variables.Abstract. 2-Dimensional Uncertain Linguistic Variables (2DULVs) are powerful tools to express the fuzzy or uncertain information, and the weighted Bonferroni mean can not only take the attribute importance into account, but also capture the interrelationship between the attributes. However, the traditional Bonferroni mean can only deal with the crisp numbers. In this paper, Bonferroni mean was extended to process the 2DULVs. Firstly, we proposed the Normalized Weighted Geometric Bonferroni Mean (NWGBM) operator and the Generalized Normalized Weighted Geometric Bonferroni Mean (GNWGBM) operator, which had the characteristic of reducibility and considered the interrelationships between two attributes. Then, we introduced the computation rules, characteristics, the expected value, and comparison method of the 2DULVs. Further, we developed the 2-Dimensional Uncertain Linguistic Normalized Weighted Geometric Bonferroni Mean (2DULNWGBM) and the 2-Dimensional Uncertain Linguistic Generalized Normalized Weighted Geometric Bonferroni Mean (2DULGNWGBM), and explored some properties and discussed some special cases of them. Finally, we developed a new decision making method based on these operators. An example is given to compare the method with the existing methods.

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“…BM operator was originally defined by Bonferroni [43] and has attracted widespread attention because of its characteristics of capturing interrelationship among arguments. Some achievements have been made on it [11,[44][45][46][47][48][49]. In order to aggregate neutrosophic linguistic information, some researches on aggregation operators under neutrosophic linguistic and neutrosophic uncertain linguistic environments have also been applied [28][29][30][31][32][33][34]50].…”

Section: Introductionmentioning

confidence: 99%

Multiple Criteria Decision Making Approach with Multivalued Neutrosophic Linguistic Normalized Weighted Bonferroni Mean Hamacher Operator

Wang

Yang

et al. 2018

Mathematical Problems in Engineering

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The neutrosophic set and linguistic term set are widely applied in recent years. Motivated by the advantages of them, we combine the multivalued neutrosophic set and linguistic set and define the concept of the multivalued neutrosophic linguistic set (MVNLS). Furthermore, Hamacher operation is an extension of the algebraic and Einstein operation. Additionally, the normalized weighted Bonferroni mean (NWBM) operator can consider the weight of each argument and capture the interrelationship of different arguments. Therefore, the combination of NWBM operator and Hamacher operation is more valuable and agile. Firstly, MVNLS and multivalued neutrosophic linguistic number (MVNLN) are defined, then some new operational rules of MVNLNs on account of Hamacher operations are developed, and the comparison functions for MVNLNs are given. Secondly, multivalued neutrosophic linguistic normalized weighted Bonferroni mean Hamacher operator (MVNLNWBMH) is proposed, and a number of expected characteristics of new operator are investigated. Meanwhile, some special cases of different parameters , , and are analyzed. Thirdly, the approach utilizing the MVNLNWBMH operator is introduced to manage multiple criteria decision making (MCDM) issue in multivalued neutrosophic linguistic environment. Ultimately, a practical example is presented and a comparative analysis is carried out, which validate the effectiveness and generalization of the novel approach.

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Intuitionistic Fuzzy Normalized Weighted Bonferroni Mean and Its Application in Multicriteria Decision Making

Cited by 56 publications

References 26 publications

Bonferroni Mean Operators of Linguistic Neutrosophic Numbers and Their Multiple Attribute Group Decision-Making Methods

Bonferroni Mean Operators of Linguistic Neutrosophic Numbers and Their Multiple Attribute Group Decision-Making Methods

2-Dimension Uncertain Linguistic Generalized Normalized Weighted Geometric Bonferroni Mean and Its Application in Multiple Attribute Decision Making

Multiple Criteria Decision Making Approach with Multivalued Neutrosophic Linguistic Normalized Weighted Bonferroni Mean Hamacher Operator

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