Approximation of Interval Type-2 Neutrosophic Bézier Surface Model for Uncertainty Data

Abstract

Some data will be wasted during the data collection process due to uncertain criteria or noise information. In the context of the interval type-2 neutrosophic set (IT2NS) theory's ability to handle uncertain data, this study will use geometric models to illustrate how all data will be processed. IT2NS is a generalization of the type-1 neutrosophic set, interval type-2 fuzzy set, and intuitionistic fuzzy set. This study will show how to use the approximation approach to visualize the interval type-2 neutrosophic Bézier surface (IT2NBS) model. However, the existence of truth, indeterminacy, and falsity membership functions in neutrosophic features makes the model challenging to visualize. Apart from that, the attributes of IT2NS have an upper and lower bound, which makes it difficult. Using the IT2NS theory, this study will first introduce an interval type-2 neutrosophic control net (IT2NCN) to build the model. The IT2NBS models will be represented by blending the IT2NCN and the Bernstein basis function. Afterward, the truth, indeterminacy, and falsity memberships of the IT2NBSs are approximated for the mean, upper and lower bounds of the IT2NCN. A review of the algorithm used to create the IT2NBS approximation models will wrap up the study. Fortunately, the results of this study will yield a predictive model that is used in some medical applications or bathymetry data collection that involves the uncertainty data problem in the data collection.