Simplified Interval-Valued Intuitionistic Fuzzy Line Integrals and Their Application

In the past few years, the intuitionistic fuzzy calculus (IFC) has been proposed, which is based on some basic operational laws of intuitionistic fuzzy numbers (IFNs). The interval-valued intuitionistic fuzzy sets have received great attention of scholars since they can describe the characters of things comprehensively. However, so far, the interval-valued IFC is in the original stage. In this paper, we focus on investigating the simplified interval-valued intuitionistic fuzzy line integrals (SIVIFLIs). First, we construct the SIVIFLIs step by step, and then provide their concrete values. In order to further describe the characteristic of the SIVIFLIs, we discuss their basic properties, and particularly, we investigate a kind of the order in intuitionistic fuzzy circumstance in detail. Finally, we offer an application and address it by the proposed SIVIFLIs to demonstrate their effectiveness and practicability.