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K. Rahman, Muhammad Khan, S. Abdullah, Fawad Husain, M. Ibrar (2017)
Some Properties of Pythagorean Fuzzy Hybrid Averaging Aggregation Operator
Z. Xu (2000)
On consistency of the weighted geometric mean complex judgement matrix in AHPEur. J. Oper. Res., 126
Zhi-xin Su, Guoping Xia, Ming-yuan Chen (2011)
Some induced intuitionistic fuzzy aggregation operators applied to multi-attribute group decision makingInternational Journal of General Systems, 40
K Rahman, S Abdullah, MS Ali Khan, M Shakeel (2016)
Pythagorean fuzzy hybrid geometric aggregation operator and their applications to multiple attribute decision makingInt. J. Comput. Sci. Inf. Secur., 14
Xiaolu Zhang (2016)
Multicriteria Pythagorean fuzzy decision analysis: A hierarchical QUALIFLEX approach with the closeness index-based ranking methodsInf. Sci., 330
Harish Garg (2016)
A new generalized improved score function of interval-valued intuitionistic fuzzy sets and applications in expert systemsAppl. Soft Comput., 38
Harish Garg (2017)
A Novel Improved Accuracy Function for Interval Valued Pythagorean Fuzzy Sets and Its Applications in the Decision‐Making ProcessInternational Journal of Intelligent Systems, 32
K. Rahman, S. Abdullah, R. Ahmed, M. Ullah (2017)
Pythagorean fuzzy Einstein weighted geometric aggregation operator and their application to multiple attribute group decision makingJ. Intell. Fuzzy Syst., 33
Xindong Peng, Huiyong Yuan, Yong Yang (2017)
Pythagorean Fuzzy Information Measures and Their ApplicationsInternational Journal of Intelligent Systems, 32
Xiaolu Zhang, Zeshui Xu (2014)
Extension of TOPSIS to Multiple Criteria Decision Making with Pythagorean Fuzzy SetsInternational Journal of Intelligent Systems, 29
Harish Garg (2016)
A novel accuracy function under interval-valued Pythagorean fuzzy environment for solving multicriteria decision making problemJ. Intell. Fuzzy Syst., 31
K. Rahman, S. Abdullah, M. Shakeel, M. Khan, M. Ullah (2017)
Interval-valued Pythagorean fuzzy geometric aggregation operators and their application to group decision making problemCogent Mathematics, 4
Harish Garg (2017)
Generalized Pythagorean Fuzzy Geometric Aggregation Operators Using Einstein t‐Norm and t‐Conorm for Multicriteria Decision‐Making ProcessInternational Journal of Intelligent Systems, 32
K. Rahman, S. Abdullah, Muhammad Khan (2018)
Some Interval-Valued Pythagorean Fuzzy Einstein Weighted Averaging Aggregation Operators and Their Application to Group Decision MakingJournal of Intelligent Systems, 29
K. Rahman (2018)
Some Interval-Valued Pythagorean Fuzzy Weighted Averaging Aggregation Operators and Their Application to Multiple Attribute Decision Making
K. Rahman, Ackas Ali, M. Shakeel, Muhammad Khan, M. Ullah (2017)
Pythagorean Fuzzy Weighted Averaging Aggregation Operator and its Application to Decision Making TheoryNucleus, 54
K. Atanassov (1986)
Intuitionistic fuzzy setsFuzzy Sets and Systems, 20
Xindong Peng, Ganeshsree Selvachandran (2017)
Pythagorean fuzzy set: state of the art and future directionsArtificial Intelligence Review, 52
Xindong Peng, Yong Yang (2016)
Fundamental Properties of Interval‐Valued Pythagorean Fuzzy Aggregation OperatorsInternational Journal of Intelligent Systems, 31
Xindong Peng (2018)
New operations for interval-valued Pythagorean fuzzy setScientia Iranica, 26
Zhou-Jing Wang, Kevin Li, Weize Wang (2009)
An approach to multiattribute decision making with interval-valued intuitionistic fuzzy assessments and incomplete weightsInf. Sci., 179
K. Rahman, S. Abdullah, Muhammad Jamil, Muhammad Khan (2018)
Some Generalized Intuitionistic Fuzzy Einstein Hybrid Aggregation Operators and Their Application to Multiple Attribute Group Decision MakingInternational Journal of Fuzzy Systems, 20
R. Yager (2014)
Pythagorean Membership Grades in Multicriteria Decision MakingIEEE Transactions on Fuzzy Systems, 22
Junding Sun, Xiaosheng Wu (2007)
An Effective Approach towards Contour-Shape Retrieval2007 International Conference on Computational Intelligence and Security (CIS 2007)
Z. Xu, Jing Chen (2007)
Approach to Group Decision Making Based on Interval-Valued Intuitionistic Judgment MatricesSystems Engineering - Theory & Practice, 27
K. Rahman, Muhammad Khan, M. Ullah, A. Fahmi (2017)
Multiple Attribute Group Decision Making for Plant Location Selection with Pythagorean Fuzzy Weighted Geometric Aggregation OperatorNucleus, 54
LA Zadeh (1965)
Fuzzy setsInf. Control, 8
Harish Garg (2016)
A Novel Correlation Coefficients between Pythagorean Fuzzy Sets and Its Applications to Decision‐Making ProcessesInternational Journal of Intelligent Systems, 31
G. Wei, Xiaorong Wang (2007)
Some Geometric Aggregation Operators Based on Interval-Valued Intuitionistic Fuzzy Sets and their Application to Group Decision Making2007 International Conference on Computational Intelligence and Security (CIS 2007)
K. Rahman, S. Abdullah, Fawad Husain, Muhammad Khan, M. Shakeel (2017)
Pythagorean Fuzzy Ordered Weighted Geometric Aggregation Operator and Their Application to Multiple Attribute Group Decision Making
K. Atanassov (2019)
On Interval Valued Intuitionistic Fuzzy SetsInterval-Valued Intuitionistic Fuzzy Sets
Harish Garg (2016)
A New Generalized Pythagorean Fuzzy Information Aggregation Using Einstein Operations and Its Application to Decision MakingInternational Journal of Intelligent Systems, 31
R. Yager, A. Abbasov (2013)
Pythagorean Membership Grades, Complex Numbers, and Decision MakingInternational Journal of Intelligent Systems, 28
K. Rahman, S. Abdullah, Asad Ali, F. Amin (2017)
Some Induced Averaging Aggregation Operators Based on Pythagorean Fuzzy NumbersMachine Learning, 3
Xindong Peng, Jingguo Dai (2017)
Approaches to Pythagorean Fuzzy Stochastic Multi‐criteria Decision Making Based on Prospect Theory and Regret Theory with New Distance Measure and Score FunctionInternational Journal of Intelligent Systems, 32
K. Rahman, Asad Ali, S. Abdullah, F. Amin (2018)
Approaches to Multi-Attribute Group Decision Making Based on Induced Interval-Valued Pythagorean Fuzzy Einstein Aggregation OperatorNew Math. Nat. Comput., 14
K Rahman, S Abdullah, A Ali, F Amin (2017)
Some induced averaging aggregation operators based on Pythagorean fuzzy numbersMath. Lett., 3
Xindong Peng, Yong Yang (2015)
Some Results for Pythagorean Fuzzy SetsInternational Journal of Intelligent Systems, 30
R. Yager (2013)
Pythagorean fuzzy subsets2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS)
Zeshui Xu (2010)
Choquet integrals of weighted intuitionistic fuzzy informationInf. Sci., 180
K. Rahman, S. Abdullah, Asad Ali (2019)
Some induced aggregation operators based on interval-valued Pythagorean fuzzy numbersGranular Computing, 4
For the multi-attribute group decision-making problems where attribute values are the interval-valued Pythagorean fuzzy numbers, the group decision-making method based on induced Einstein averaging aggregation operators are developed. Firstly, induced interval-valued Pythagorean fuzzy Einstein ordered weighted averaging (I-IVPFEOWA) aggregation operator and induced interval-valued Pythagorean fuzzy Einstein hybrid weighted averaging (I-IVPFEHWA) aggregation operator, were proposed. Some general properties of these operators, such as idempotency, commutativity, monotonicity and boundedness, were discussed, and some special cases in these operators were analyzed. Furthermore, the method for multi-attribute group decision-making problems based on these operators was developed, and the operational progressions were explained in detail. These methods provide more general, more accurate and precise results as compared to the existing methods. Therefore these methods play a vital role in daily life problems. At the end of the paper the proposed operators have been applied to decision making problems to show the weight, practicality and effectiveness of the new approach.
Bulletin of the Brazilian Mathematical Society, New Series – Springer Journals
Published: May 16, 2018
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