On averaging operators for Atanassov’s intuitionistic fuzzy sets

Beliakov, Gleb; Bustince, Humberto; Goswami, Damodar Prasad; Mukherjee, Utsab; Pal, Nikhil R.

doi:10.1016/j.ins.2010.11.024

Cited by 267 publications

(124 citation statements)

References 37 publications

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“…As Beliakov et al [16] pointed for IFNs, there exist some undesirable properties of the operational laws on IVIFSs [17] as well as the ranking method for the score and accuracy functions [18], such as the operations (3) and (4) …”

Section: Atanassov's Interval-valued Intuitionistic Fuzzy Setsmentioning

confidence: 99%

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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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Section: Atanassov's Interval-valued Intuitionistic Fuzzy Setsmentioning

confidence: 99%

“…, 2, …, n. Furthermore, if w j =1/n for all j=1, 2, …, n, then the IHWA operator reduces to be the IWAA operator [16], and if i =1/n for all i=1, 2, …, n, then the IHWA operator degenerates to be the Atanassov's intuitionistic ordered weight averaging (IOWA) operator …”

Section: Atanassov's Interval-valued Intuitionistic Fuzzy Prospect Gamentioning

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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“…MADM problems and granular computing have got more attentions from the literatures (Beliakov et al 2011;Beliakov et al 2010;Wei and Zhao 2012;Chen 2014;Bedregal et al 2014;Livi and Sadeghian 2015;Pedrycz and Chen 2015;Chen and Chang 2015;Rodríguez et al 2012Rodríguez et al , 2013Rodríguez et al , 2014He et al 2015;Chen et al 2016;Apolloni et al 2016;Antonelli et al 2016;Ciucci 2016;Lingras et al 2016;Loia et al 2016;Maciel et al 2016;Min and Xu 2016;Peters and Weber 2016;Skowron et al 2016;Wilke and Portmann 2016;Xu and Wang 2016;Yao 2016). Considering the different backgrounds of experts, Xu and Wang (2016) gave an overview on managing multigranularity linguistic term sets for MADM problems.…”

Section: Introductionmentioning

confidence: 99%

Multi-attribute decision-making based on the SPIFGIA operators

Wang

Meng

et al. 2017

Granul. Comput.

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The work considers the prioritized relationships between different criteria with priority labels, and develops the scaled prioritized intuitionistic fuzzy geometric interaction averaging (SPIFGIA) operator, the scaled prioritized intuitionistic fuzzy weighted geometric interaction averaging (SPIFWGIA) operator, the scaled prioritized intuitionistic fuzzy hybrid geometric interaction averaging (SPIFHGIA) operator, and the scaled prioritized intuitionistic fuzzy hybrid weighted geometric interaction averaging (SPIFHWGIA) operator. We investigate the properties of the new SPIFGIA and SPIFWGIA operators, and the prioritized relationships between criteria in different situations for decision-making problems, and we also discuss the constructions of intuitionistic fuzzy sets with granularity. Then, we develop new approaches to intuitionistic fuzzy decision-making problems based on the presented SPIFGIA, SPIFWGIA, SPIFHGIA, and SPIFHWGIA operators. Finally, the paper shows the effectiveness and feasibility of the new methods by an example, and gives some comparisons.Keywords Multi-attribute decision-making problems Á Granularity Á Scaled prioritized intuitionistic fuzzy geometric interaction operators

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“…As in decision making problems we must also aggregate the information furnished by the experts by means of aggregation functions [5,6,7], we have decided to use these functions to generate the orders.…”

Section: Introductionmentioning

confidence: 99%