In the present paper we introduce positive linear three-dimensional Bernstein-Chlodowsky polynomials on a non-tetrahedron domain and we get their q-analogue. We obtain aproximation properties for these positive linear operators and their generalizations in this work. The rate of convergence of these operators is calculated by means of the modulus of continuity.

The aim in our study is giving a generalization of the two-dimensional (𝑝, 𝑞)-Bernstein-Stancu operators in a particular domain. In addition, by creating some direct results of these operators, rate of convergence is studied by Lipschitz type functions and modulus of continuity.

In this study, Neutrophic normed spaces, which is one of the popular mathematics topics of recent times, is discussed. The Neutrosophic approach, which argues that it is insufficient to evaluate the problems in daily life as just right and wrong, is based on the principle that the degree of indecision should be taken into account. Now, rough statistical convergence of triple sequences is defined in Neutrosophic normed spaces. Moreover, the important topological properties about to the set of cluster points of roughly statistical convergent triple sequences are given.

Due to insufficient healthcare facilities for the fight against cancer, a large percentage of individuals die. Utilizing computational tools inside the health and medical system helps to minimize fatalities. Timely cancer detection enhances the likelihood of effective therapy. Cancer risk assessment is important for legal and regulatory reasons, for cancer prevention, and to avoid the risks. The approach for assessing cancer risk based on the q-rung orthopair fuzzy set (q-ROFS) is described. The technique is predicated on a multifactor evaluation of the likelihood of a cancerous. q-ROFS is a robust approach for modeling uncertainties in multicriteria decision making (MCDM). The combinative distance-based assessment (CODAS) technique integrates two separate approaches, namely the “simple additive weighting” (SAW) method and the “weighted product method (WPM)”. In this study, the CODAS approach is extended to the q-rung orthopair fuzzy framework with application to cancer risk assessment. Additionally, the symmetry of the optimal decision in cancer risk assessment is carried out by a comparison analysis of the suggested model with some existing models.

In this paper, λI-statistical convergence is defined to generalize statistical convergence on Neutrosophic normed spaces. As it is known, Neutrosophic theory, which brings a new breath to daily life and complex scientific studies which we encounter with many uncertainties, is a rapidly developing field with many new study subjects. Thus, researchers show great interest in this philosophical approach and try to transfer related topics to this field quickly. For this purpose, in this study, besides the definition of λI-statistical convergence, the important features of Hilbert sequence space and λI-statistical convergence in Neutrosophic spaces are examined with the help of these defined sequences. By giving the relationship between Hilbert λI-statistical convergence and Hilbert I-statistical convergence, it has been evaluated whether the definitions contain a coverage relationship as in fuzzy and intuitionistic fuzzy. As a result, it is thought that the selected convergence type is suitable for the Neutrosophic normed space structure and is a guide for new convergence types.