New exponential operational laws and their aggregation operators for interval-valued Pythagorean fuzzy multicriteria decision-making

In this article, we define two new exponential operational laws about the interval-valued Pythagorean fuzzy set (IVPFS) and their corresponding aggregation operators. However, the exponential parameters (weights) of all the existing operational laws of IVPFSs are crisp values in IVPFS decision-making problems. As a supplement, this paper first introduces new exponential operational laws of IVPFS, where bases are crisp values or interval numbers and exponents are interval-valued Pythagorean fuzzy numbers. The prominent characteristic of these proposed operations is studied. Based on these laws, we develop some new weighted aggregation operators, namely the interval-valued Pythagorean fuzzy weighted exponential averaging operator and the dual interval-valued Pythagorean fuzzy weighted exponential averaging. Finally, a decision-making approach is presented based on these operators and illustrated with some numerical examples to validate the developed approach.