Abstract
Complex fuzzy (CF) sets (CFSs) have a significant role in modelling the problems involving two-dimensional information. Recently, the extensions of CFSs have gained the attention of researchers studying decision-making methods. The complex T-spherical fuzzy set (CTSFS) is an extension of the CFSs introduced in the last times. In this paper, we introduce the Dombi operations on CTSFSs. Based on Dombi operators, we define some aggregation operators, including complex T-spherical Dombi fuzzy weighted arithmetic averaging (CTSDFWAA) operator, complex T-spherical Dombi fuzzy weighted geometric averaging (CTSDFWGA) operator, complex T-spherical Dombi fuzzy ordered weighted arithmetic averaging (CTSDFOWAA) operator, complex T-spherical Dombi fuzzy ordered weighted geometric averaging (CTSDFOWGA) operator, and we obtain some of their properties. In addition, we develop a multi-criteria decision-making (MCDM) method under the CTSF environment and present an algorithm for the proposed method. To show the process of the proposed method, we present an example related to diagnosing the COVID-19. Besides this, we present a sensitivity analysis to reveal the advantages and restrictions of our method.
Highlights
The fuzzy set (FS) theory was inaugurated by Zadeh [1] in 1965 to handle modelling of some problems containing uncertain data in real life
Weakness of score and accuracy function defined by Ali et al [57] was pointed out and new score and accuracy functions were defined for complex T-spherical fuzzy number (CTSFN)
Set theoretical operations was introduced and some aggregation operators based on Dombi t-norms and t-conorms were defined under complex T-spherical fuzzy (CTSF) environment with their examples
Summary
The fuzzy set (FS) theory was inaugurated by Zadeh [1] in 1965 to handle modelling of some problems containing uncertain data in real life. Since FS theory is a very useful tool for modelling uncertainty, it has many applications in the modelling and solving of the problems in many fields such as medical science, data mining and clustering. In an FS, if the membership degree (MD) of an element x is μ(x), its non-membership degree (NMD) is 1 − μ(x), that is, in the FS, hesitation degree of an element is “0”. This is one of the limited aspects of FS in modelling real-life problems. The intuitionistic FS (IFS) was suggested by Atanassov [2] as Complex & Intelligent Systems (2021) 7:2711–2734
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