Some aggregation operators for IVI-octahedron sets and their application to MCDGM

Document Type : Research Paper

Authors

1 School of Big Data $\&$Financiall Statistics,and Institute of Basic Natural Science,Wonkwang University, IkSan, South Korea

2 Dept. of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar university of Kerman, Kerman, Iran

3 Department of Applied Mathematics, Wonkwang University, IkSan, South Korea

Abstract

In this paper, in order to apply the concept of IVI-octahedron sets to MCDGM problems, we define some aggregation operators via IVI-octahedron sets and obtain some their properties. We  define some aggregation operators via IVI-octahedron sets and obtain some their properties.  We present a MCGDM method with linguistic variables in IVI-octahedron set environment. Finally, we give a numerical examples  for MCGDM problems.

Keywords

References

[1] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 87-96.
2] K. T. Atanassov, G. Gargov, Interval-valued intuitionistic fuzzy sets, Fuzzy Sets and Systems, 31 (1989), 343-349.
[3] S. Broumi, F. Smarandache, Several similarity measures of neutrosophic sets, Neutrosophic Theory and its Applications, 1 (2013), 307-316.
[4] N. Chen, Z. Xu, M. Xia, Correlation coefficients of hesitant fuzzy sets and their applications to clustering analysis,
Applied Mathematical Modelling, 37(4) (2013), 2197-2211.
[5] M. Cheong, K. Hur, Intuitionistic interval-valued fuzzy sets, Journal of Korean Institute of Intelligent Systems,
20(6) (2010), 864-874.
[6] H. Dyckhoff, W. Pedrycz, Generalized means as model of compensative connectives, Fuzzy Sets and Systems, 14
(1984), 417-154.
[7] H. Garg, R. Arora, Bonferroni mean aggregation operators under intuitionistic fuzzy soft set environment and their
applications to decision-making, Journal of the Operational Research Society, 69 (2018), 1711-1724.
[8] T. Gerstenkorn, J. Ma´nko, Correlation of intuitionistic fuzzy sets, Fuzzy Sets and Systems, 44 (1991), 39-43.
[9] M. B. Gorzalczany, A method of inference in approximate reasoning based on interval-valued fuzzy sets, Fuzzy Sets
and Systems, 21 (1987), 1-17.
[10] G. Kaur, H. Garg, Multi-attribute decision-making based on Bonferroni mean operators under cubic intuitionistic
fuzzy environment, Entropy, 20(1) (2018), 1-26.
[11] J. Kim, A. Borumand Saeid, J. G. Lee, M. Cheong, K. Hur, IVI-octahedron sets and their application to groupoids,
Annals of Fuzzy Mathematics and Informatics, 20(2) (2020), 157-195.
[12] J. G. Lee, G. S¸enel, P. K. Lim, J. Kim, K. Hur, Octahedron sets, Annals of Fuzzy Mathematics and Informatics, 19(3) (2020), 211-238.
[13] P. Liu, S. M. Chen, J. Liu, Multiple attribute group decision making based on intuitionistic fuzzy interaction
partitioned Bonferroni mean operators, Information Sciences, 411 (2017), 98-121.
[14] D. Molodtsov, Soft set theory–first results, Computers and Mathematics with Applications, 37 (1999), 19-31.
[15] T. K. Mondal, S. K. Samanta, Topology of interval-valued fuzzy sets, Indian Journal of Pure and Applied Mathematics, 30(1) (1999), 133-189.
[16] D. G. Park, Y. C. Kwun, J. H. Park, Correlation coefficient of interval-valued intuitionistic fuzzy sets and its
application to multiple attribute group decision making problems, Mathematical and Computer Modelling, 50(9-10) (2009), 1279-1293.
[17] Z. Pawlak, Rough sets, International Journal of Information and Computer Sciences, 11 (1982), 341-356.
[18] H. Ren, G. Wang, An interval-valued intuitionistic fuzzy MADM method based on a new similarity measure,
Information, 6 (2015), 880-894.
[19] G. S¸enel, J. G. Lee, K. Hur, Distance and similarity measures for octahedron sets and their application to MCGDM
problems, Mathematics, 8(10) (2020), 1-16. DOI:10.3390/math8101690.
[20] V. Torra, Y. Narukawa, Modeling decision: Information fusion and aggregation operators, Springer, 2007.
[21] Z. S. Xu, On consistency of the weighted geometric mean complex judgement matrix in AHP, European Journal
of Operational Research, 126(3) (2000), 683-687.
[22] Z. S. Xu, Q. Chen, A multi-criteria decision making procedure based on interval-valued intuitionistic fuzzy Bonferroni means, Journal of Systems Science and Systems Engineering, 20 (2011), 217-228.
[23] J. Ye, Cosine similarity measures for intuitionistic fuzzy sets and their applications, Mathematical and Computer
Modelling, 53(1-2) (2011), 91-97.
[24] J. Ye, Multicriteria decision-making method using the correlation coefficient under single valued neutrosophic environment, International Journal of General Systems, 42(4) (2013), 386-394.
[25] J. Ye, Similarity measures between interval neutrosophic sets and their multicriteria decision-making method, Journal of Intelligent and Fuzzy Systems, 26 (2014), 167-172.
[26] J. Ye, Single valued neutrosophic similarity measures based on cotangent function and their application in the fault
diagnosis of steam turbine, Soft Computing, 21 (2017), 817-825.
[27] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353.
[28] L. A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning-I, Information Sciences, 8 (1975), 199-249.
[29] Z. M. Zhang, Hesitant fuzzy power aggregation operators and their application to multiple attribute group decision
making, Information Sciences, 234 (2013), 150-181.
[30] Z. M. Zhang, Interval-valued intuitionistic hesitant fuzzy aggregation operators and their application in group decision-making, Journal of Applied Mathematics, (2013), 1-33. DOI:10.1155/2013/670285.
Iranian Journal of Fuzzy Systems
Volume 20, Issue 2
March and April 2023
Pages 135-149

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