Abstract
Multi-attribute decision-making problems can be solved using a Fermatean vague set. Fermatean vague sets are extension of vague sets. We initiated generalized Fermatean vague weighted averaging, generalized Fermatean vague weighted geometric, power generalized Fermatean vague weighted averaging and power generalized Fermatean vague weighted geometric. The algebraic structures such as associative, distributive, idempotent, bounded, commutativity and monotonicity properties are satisfied by generalized Fermatean vague numbers. We discussed some mathematical properties of these sets, as well as the Hamming distance and Euclidean distance. An algorithm that uses aggregation operators to solves multi-attribute decision-making problems. The fields of computer science and medicine are essential for medical diagnosis research. Choosing cancer treatment is a complex process. Patients and health care professionals must communicate effectively to make the right decision about their cancer treatment. There are a number of factors that influence patients treatment decisions. As far as cancer patients are concerned, there are five types of cancer patients. Many different treatments are currently available and they are often combined as part of an overall treatment plan involving various treatment options. Patients with which cancer can be treated in various ways, such as cystoscopy, biopsy, blood tests and CT scan of the urogram. We intended to choose the best treatment based on our comparisons and options. Thus, it is evident that natural number q has a significant influence on the models. Additionally, flowchart based multi-criteria decision-making is offered and applied to a numerical example to show the efficiency of the recommended approach. The results are evaluated for different values of the parameter. Moreover, a comparative analysis has been performed to illustrate the superior outcomes of the suggested approach in comparison with existing methodologies.