Towards granular calculus of single-valued neutrosophic functions under granular computing

Neutrosophic theory studies objects whose values vary in the sets of elements and are not true or false, but in between, that can be called by neutral, indeterminate, unclear, vague, ambiguous, incomplete or contradictory quantities. In this paper, we firstly introduce preliminaries on granular calculus and analysis related to single-valued neutrosophic functions. Based on horizontal membership functions approach, we establish some basic arithmetic operations of single-valued neutrosophic numbers, that red allow us to directly introduce the terms of neutrosophic function in usual mathematical formulas. Additionally, we build metrics on the space of single-valued neutrosophic numbers induced from Hamming distance. Then, we define some backgrounds on the limit, derivative and integral of single-valued neutrosophic functions. Finally, in order to demonstrate the usable of our theoretical results, we present some applications to well-known problems arising in engineering such as logistic model, the inverted pendulum system, Mass - Spring - Damper model.