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ABSTRACT
In this paper, we define some Einstein operations on cubic fuzzy set (CFS) and develop three arithmetic averaging operators, which are cubic fuzzy Einstein weighted averaging (CFEWA) operator, cubic fuzzy Einstein ordered weighted averaging (CFEOWA) operator and cubic fuzzy Einstein hybrid weighted averaging (CFEHWA) operator, for aggregating cubic fuzzy data. The CFEHWA operator generalises both the CFEWA and CFEOWA operators. Furthermore, we develop various properties of these operators and derive the relationship between the proposed operators and the exiting aggregation operators. We apply CFEHWA operator to multiple attribute decision-making with cubic fuzzy data. Finally, a numerical example is constructed to demonstrate the established approach.
Acknowledgements
The authors would like to express appreciation to the anonymous reviewers and Editors for their very helpful comments that improved the paper.
Disclosure statement
No potential conflict of interest was reported by the authors.
Additional information
Notes on contributors
Aliya Fahmi
Aliya Fahmi received the M.Phil. degree in mathematics from Riphah International University, Islamabad, Pakistan in 2014. Currently she is a Ph.D. scholar at Department of Mathematics, Hazara University, Mansehra, Pakistan. Her research interests include aggregation operators, soft set, cubic set, decision-making, fuzzy decision-making, and their applications. She has published more than 16 papers in international journals. Email:[email protected]
Fazli Amin
Dr Fazli Amin received his M. Philin Mathematics, from Quaid-i-Azam University, Islamabad, Pakistan (2006) and Ph.D. in Mathematics, from Institute of Computational Mathematics, Technische Universität Braunschweig, Germany (2016). He spent twelve years as an Assistant professor of Mathematics in department of Mathematics, Hazara University Mansehra Pakistan. He has been serving as Chair of the Department of Mathematics & statistics since May 2018. He was awarded merit scholarship in M.Phil and overseas scholarship in Ph.D. by Higher Education Commission(HEC) of Pakistan. His research interests include fuzzy algebra, computational algebra in particular group theory, subnormal structure and their fuzzification, fuzzy decision-making and their applications. He is the author of morethan30research papers in International journals. Email: [email protected]
Saleem Abdullah
Saleem Abdullah received the M.Phil. and Ph.D. degrees in mathematics from Quaid-i-Azim University, Islamabad, Pakistan. Currently he is working as Assistant Professor at Department of Mathematics Abdul Wali Khan University, Mardan, Pakistan. His research area is fuzzy logic, fuzzy set theory and decision-making. He has published more than 80 papers in international journals. Email:[email protected]
Asad Ali
Dr Asad Ali received his M. Philin Mathematics, from Hazara University, Mansehra, Pakistan (2012) and Ph.D. in Pure Mathematics, from Beijing Institute of Technology (2016). He spent twelve years as an Assistant professor of Mathematics in department of Mathematics, Hazara University Mansehra Pakistan. He was awarded merit scholarship in M.Phil and Chinese Government Scholarship for PhD. His research interests include Fuzzy Algebra, Group Theory, Soft Set Theory and Non Associative Algebraic Structures. Email: [email protected]