Definite integrals of multiplicative intuitionistic fuzzy information in decision making

In this paper, we investigate the definite integrals of multiplicative intuitionistic fuzzy information in decision making. Firstly, we propose a new order of multiplicative intuitionistic fuzzy numbers (MIFNs) and study its properties. Secondly, we consider the limiting process from which the definite integrals of multiplicative intuitionistic fuzzy functions (MIFFs) over a closed interval are derived. Furthermore, we study the forms of indefinite integrals, deduce the fundamental theorem of calculus, derive the concrete formulas for ease of calculating definite integrals from different angles, and discuss some useful properties of the proposed definite integrals. Finally, we give applications of the subtraction definite integral of MIFFs in decision making.