The induced generalized interval-valued intuitionistic fuzzy hybrid Shapley averaging operator and its application in decision making

Meng, Fanyong; Tan, Chunqiao; Zhang, Qiang

doi:10.1016/j.knosys.2012.12.006

Cited by 71 publications

(39 citation statements)

References 44 publications

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“…Meng et al (2013b) proposed the induced generalized interval-valued intuitionistic fuzzy hybrid Shapley averaging (IG-IVIFHSA) operator:…”

Section: Induced Generalized Interval-valued Intuitionistic Fuzzy Aggmentioning

confidence: 99%

“…Definition 3.22 (Meng et al 2013b) An IG-IVIFHSA operator of dimension n is a mapping IG-IVIFHSA: X n ! X defined on the set of second arguments of two tuples u 1 ;ã 1 h i; u 2 ;ã 2 h i; .…”

Section: Induced Generalized Interval-valued Intuitionistic Fuzzy Aggmentioning

confidence: 99%

“…Moreover, Meng et al (2013b) introduced the induced generalized interval-valued intuitionistic fuzzy hybrid Shapley averaging (IG-IVIFHSA) operator and the induced generalized quasi interval-valued intuitionistic fuzzy hybrid Shapley averaging (IGQ-IVIFHSA) operator, respectively: Definition 3.23 (Meng et al 2013b) An IG-IVIFHSA operator of dimension n is a mapping IG-IVIFHSA: X n ! X defined on the set of second arguments of two tuples u 1 ;ã 1 h i; u 2 ;ã 2 h i; .…”

Section: Induced Generalized Interval-valued Intuitionistic Fuzzy Aggmentioning

confidence: 99%

“…Moreover, Meng et al (2013b) used the Shapley function to propose an IG-IVIFHSA operator, and developed an approach to MADM under interval-valued intuitionistic fuzzy environment. Based on the Choquet integral and the generalized Shapley function, Meng et al (2014) introduced the IGS-IVIFHCAA and IGS-IVIFHCGM operators, and developed an approach to MADM under interval-valued intuitionistic fuzzy environment.…”

Section: Decision-makingmentioning

confidence: 99%

See 3 more Smart Citations

An overview of interval-valued intuitionistic fuzzy information aggregations and applications

Zhang

Gou

2016

Granul. Comput.

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Interval-valued intuitionistic fuzzy set, generalized by Atanassov and Gargov, can be used to characterize the uncertain information more sufficiently and accurately when we face the fact that the values of the membership function and the non-membership function in an intuitionistic fuzzy set are difficult to be expressed as exact real numbers in many real-world decision-making problems. In this paper, we provide an overview of interval-valued intuitionistic fuzzy information aggregation techniques, and their applications in various fields such as decisionmaking, entropy measure, supplier selection and some practical decision-making problems. Meanwhile, we also review some important methods for decision-making with interval-valued intuitionistic fuzzy information, including the QUALIFLEX-based method, the TOPSIS method, the extended VIKOR method, the module partition schemes evaluation (MPSE) approach, the outranking choice method, the inclusion-based LINMAP method and the risk attitudinal ranking method, the evidential reasoning methodology, etc. Finally, we point out some possible directions for future research.

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“…Meng et al (2013b) proposed the induced generalized interval-valued intuitionistic fuzzy hybrid Shapley averaging (IG-IVIFHSA) operator:…”

Section: Induced Generalized Interval-valued Intuitionistic Fuzzy Aggmentioning

confidence: 99%

Section: Induced Generalized Interval-valued Intuitionistic Fuzzy Aggmentioning

confidence: 99%

Section: Induced Generalized Interval-valued Intuitionistic Fuzzy Aggmentioning

confidence: 99%

Section: Decision-makingmentioning

confidence: 99%

See 2 more Smart Citations

An overview of interval-valued intuitionistic fuzzy information aggregations and applications

Zhang

Gou

2016

Granul. Comput.

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“…(5), it drives the following programming for the optimal weight vector on the ordered set N = {1, 2, 3}. Step 5: According to the IVIHWA operator, the comprehensive Atanassov's interval-valued intuitionistic fuzzy prospect gain value of the alternative a 1 is obtained as follows: The IIWAA operator [13] The IIOWA operator [13] The IIHA operator [13] The IIFWGA operator [12] The IIFOWGA operator [12] The IIFWHGA operator [12] The IVIFCA operator [14] The IVIFCG operator [14] The IVIFHSA operator [42] The GSAIVIFCA operator [48] …”

Section: Co-published By Atlantis Press and Taylor And Francismentioning

confidence: 99%

An approach to Atanassov's interval-valued intuitionistic fuzzy multi-attribute decision making based on prospect theory

Meng¹,

Tan²,

Chen³

2015

IJCIS

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Prospect theory is a very effective method to express behavioral decision making under uncertainty. This paper attempts to develop a method to multi-attribute decision making with Atanassov's interval-valued intuitionistic fuzzy information using prospect theory. This method first transforms Atanassov's interval-valued intuitionistic fuzzy variables into the prospect values using the value function in prospect theory. Based on the aspiration levels, Atanassov's intuitionistic fuzzy prospect gain and loss matrices are obtained. Then, using the Atanassov's interval-valued intuitionistic hybrid weight averaging (IVIHWA) operator or the Atanassov's interval-valued intuitionistic hybrid Shapley weight averaging (IVIHSWA) operator, the comprehensive Atanassov's interval-valued intuitionistic fuzzy prospect value of each alternative is calculated. According to the comprehensive Atanassov's interval-valued intuitionistic fuzzy prospect values, a ranking method of alternatives is presented. Finally, two illustrative examples are selected to show the feasibility and availability of the proposed method.

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Pythagorean fuzzy multiple criteria decision analysis based on Shapley fuzzy measures and partitioned normalized weighted Bonferroni mean operator

et al. 2018

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Pythagorean fuzzy sets are powerful techniques for modeling vagueness in practice. The aim of this article is to investigate an effective means to aggregate uncertain information and then employ it into settling multiple criteria decision making (MCDM) problems within the Pythagorean fuzzy circumstances. To capture the nature of the reality, some special cases should be comprehensively considered. First, though correlation commonly exist among criteria, a deep insight should also be provided into some realistic situations, in which not all the criteria are interrelated to others. Besides, it is more reasonable to take the importance of the input arguments into consideration. Effected by aforementioned point, this article explores a Pythagorean fuzzy partitioned normalized weighted Bonferroni mean (PFPNWBM) operator with the combination of partitioned Bonferroni mean (BM) and normalized weighted BM operators considering Shapley fuzzy measure. Subsequently, in the context of partially known weight information, models are established to identify the optimal Shapley fuzzy measure. Moreover, integrated the PFPNWBM operator with the optimal Shapley fuzzy measure identification model, a Pythagorean fuzzy MCDM approach is designed. Finally, an illustrative example and detailed analyses are performed to demonstrate its feasibility and reliability.

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The induced generalized interval-valued intuitionistic fuzzy hybrid Shapley averaging operator and its application in decision making

Cited by 71 publications

References 44 publications

An overview of interval-valued intuitionistic fuzzy information aggregations and applications

An overview of interval-valued intuitionistic fuzzy information aggregations and applications

An approach to Atanassov's interval-valued intuitionistic fuzzy multi-attribute decision making based on prospect theory

Pythagorean fuzzy multiple criteria decision analysis based on Shapley fuzzy measures and partitioned normalized weighted Bonferroni mean operator

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