Decision-making method under the interval-valued complex fuzzy soft environment

In this paper, we introduce some set-theoretic operations and laws of the IV-CFSSs, such as interval-valued complex fuzzy soft complement, union, intersection, t-norm, s-norm, simple product, Cartesian product, probabilistic sum, simple difference, and the convex linear sum of min and max operators. We define the distance measure of two IV-CFSSs. This distance measure is then used to define the \(\delta \) $\delta$ -equality of IV-CFSSs. We establish some particular examples and basic results of these operations and laws. Moreover, we use IV-CFSSs in decision-making problems. We develop a new decision-making method using the interval-valued complex fuzzy distance measures under the environments of IV-CFSSs. We discuss the real-life case based on the proposed decision-making method. A real-life example demonstrates that the decision-making method developed in the paper can be utilized to deal with problems of uncertainty. Further, the comparative study of IV-CFSSs with complex fuzzy soft sets, interval-valued fuzzy soft sets, and fuzzy soft sets is established.