Multi-criteria decision-making method based on normal intuitionistic fuzzy-induced generalized aggregation operator

Wang, Jian Qiang; Zhou, P.; Li, Kang jian; Zhang, Hong Yu; Chen, Xiao Hong

doi:10.1007/s11750-014-0314-3

Cited by 53 publications

(54 citation statements)

References 28 publications

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“…Comparing with the method proposed by Wang et al [23], there are the same ranking results e 4 and e 2 . However, we also give another ranking result, i.e., the best may be e 1 when λ ≤ 0.5.…”

Section:  supporting

confidence: 54%

“…Let us take the method based on N IFGWPI A operator to solve the following example (cited from Reference [23]). …”

Section: Illustrative Examplementioning

confidence: 99%

“…However, we also give another ranking result, i.e., the best may be e 1 when λ ≤ 0.5. The advantages of the developed method in this paper are that it considers the relationships of different attribute values by PA operator and the interaction between the MD and NMD, and the advantages of the developed method by Wang et al [23] are that it considers the OWA and the induced variables.…”

Section:  mentioning

confidence: 99%

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Multiple Attribute Decision-Making Methods Based on Normal Intuitionistic Fuzzy Interaction Aggregation Operators

Лю¹

2017

Symmetry

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Normal intuitionistic fuzzy numbers (NIFNs), which combine the normal fuzzy number (NFN) with intuitionistic number, can easily express the stochastic fuzzy information existing in real decision making, and power-average (PA) operator can consider the relationships of different attributes by assigned weighting vectors which depend upon the input arguments. In this paper, we extended PA operator to process the NIFNs. Firstly, we defined some basic operational rules of NIFNs by considering the interaction operations of intuitionistic fuzzy sets (IFSs), established the distance between two NIFNs, and introduced the comparison method of NIFNs. Then, we proposed some new aggregation operators, including normal intuitionistic fuzzy weighted interaction averaging (NIFWIA) operator, normal intuitionistic fuzzy power interaction averaging (NIFPIA) operator, normal intuitionistic fuzzy weighted power interaction averaging (NIFWPIA) operator, normal intuitionistic fuzzy generalized power interaction averaging (NIFGPIA) operator, and normal intuitionistic fuzzy generalized weighted power interaction averaging (NIFGWPIA) operator, and studied some properties and some special cases of them. Based on these operators, we developed a decision approach for multiple attribute decision-making (MADM) problems with NIFNs. The significant characteristics of the proposed method are that: (1) it is easier to describe the uncertain information than the existing fuzzy sets and stochastic variables; (2) it used the interaction operations in part of IFSs which could overcome the existing weaknesses in operational rules of NIFNs; (3) it adopted PA operator which could relieve the influence of unreasonable data given by biased decision makers; and (4) it made the decision-making results more flexible and reliable because it was with generalized parameter which could be regard as the risk attitude value of decision makers. Finally, an illustrative example is given to verify its feasibility, and to compare with the existing methods.Keywords: power average (PA); normal intuitionistic fuzzy number (NIFN); normal intuitionistic fuzzy power interaction averaging (NIFPIA) operator; interaction operations; multiple attribute decision-making (MADM)

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Section:  supporting

confidence: 54%

“…Let us take the method based on N IFGWPI A operator to solve the following example (cited from Reference [23]). …”

Section: Illustrative Examplementioning

confidence: 99%

Section:  mentioning

confidence: 99%

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Multiple Attribute Decision-Making Methods Based on Normal Intuitionistic Fuzzy Interaction Aggregation Operators

Лю¹

2017

Symmetry

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“…Based on the score function and accuracy function of IFSs [10][11][12][13][14][15][16][17][18][19][20][21] , the score function and accuracy function of a MVNN can be provided below. …”

Section: Comparison Methodsmentioning

confidence: 99%

“…Moreover, in some actual cases, the membership degree, non-membership degree and hesitation degree of an element in IFSs may not be a specific number; hence, they were extended to the interval-valued intuitionistic fuzzy sets (IVIFSs) 9 . To date, IFSs and IVIFSs have been widely applied in solving MCDM and MCGDM problems [10][11][12][13][14][15][16][17][18][19][20][21] . In order to handle situations where people are hesitant in expressing their preference regarding objects in a decision-making process, hesitant fuzzy sets (HFSs) were introduced by Torra and Narukawa [22][23] .…”

Section: Introductionmentioning

confidence: 99%

Multi-valued Neutrosophic Sets and Power Aggregation Operators with Their Applications in Multi-criteria Group Decision-making Problems

Peng¹,

Wang

Wu³

et al. 2015

IJCIS

Self Cite

159

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In recent years, hesitant fuzzy sets (HFSs) and neutrosophic sets (NSs) have become a subject of great interest for researchers and have been widely applied to multi-criteria group decision-making (MCGDM) problems. In this paper, multi-valued neutrosophic sets (MVNSs) are introduced, which allow the truth-membership, indeterminacymembership and falsity-membership degree have a set of crisp values between zero and one, respectively. Then the operations of multi-valued neutrosophic numbers (MVNNs) based on Einstein operations are defined, and a comparison method for MVNNs is developed depending on the related research of HFSs and Atanassov's intuitionistic fuzzy sets (IFSs). Furthermore, the multi-valued neutrosophic power weighted average (MVNPWA) operator and the multi-valued neutrosophic power weighted geometric (MVNPWG) operator are proposed and the desirable properties of two operators are also discussed. Finally, an approach for solving MCGDM problems is explored by applying the power aggregation operators, and an example is provided to illustrate the application of the proposed method, together with a comparison analysis.

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Multiple criteria decision making method based on normal interval‐valued intuitionistic fuzzy generalized aggregation operator

Лю

Teng

2015

Complexity

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On the basis of the normal intuitionistic fuzzy numbers (NIFNs), we proposed the normal interval-valued intuitionistic fuzzy numbers (NIVIFNs) in which the values of the membership and nonmembership were extended to interval numbers. First, the definition, the properties, the score function and accuracy function of the NIVIFNs are briefly introduced, and the operational laws are defined. Second, some aggregation operators based on the NIVIFNs are proposed, such as normal interval-valued intuitionistic fuzzy weighted arithmetic averaging operator, normal interval-valued intuitionistic fuzzy ordered weighted arithmetic averaging operator, normal interval-valued intuitionistic fuzzy hybrid weighted arithmetic averaging operator, normal interval-valued intuitionistic fuzzy weighted geometric averaging operator, normal interval-valued intuitionistic fuzzy ordered weighted geometric averaging operator, normal interval-valued intuitionistic fuzzy hybrid weighted geometric averaging operator, and normal interval-valued intuitionistic fuzzy generalized weighted averaging operator, normal interval-valued intuitionistic fuzzy generalized ordered weighted averaging operator, normal interval-valued intuitionistic fuzzy generalized hybrid weighted averaging operator, and some properties of these operators, such as idempotency, monotonicity, boundedness, commutativity, are studied. Further, an approach to the decision making problems with the NIVIFNs is established. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness. V C 2015 Wiley Periodicals, Inc. Complexity 21: 277-290, 2016 Key Words: multicriteria decision making; normal interval-valued intuitionistic fuzzy numbers; normal interval-valued intuitionistic fuzzy aggregation operator C O M P L E X I T Y 277 Q

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Multi-criteria decision-making method based on normal intuitionistic fuzzy-induced generalized aggregation operator

Cited by 53 publications

References 28 publications

Multiple Attribute Decision-Making Methods Based on Normal Intuitionistic Fuzzy Interaction Aggregation Operators

Multiple Attribute Decision-Making Methods Based on Normal Intuitionistic Fuzzy Interaction Aggregation Operators

Multi-valued Neutrosophic Sets and Power Aggregation Operators with Their Applications in Multi-criteria Group Decision-making Problems

Multiple criteria decision making method based on normal interval‐valued intuitionistic fuzzy generalized aggregation operator

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