On intuitionistic fuzzy numbers and compact intervals

In this paper, we investigate the relationship between intuitionistic fuzzy numbers and compact intervals. We give necessary and sufficient conditions for a family of intervals to define an intuitionistic fuzzy number. We also give a method for constructing non-linear intuitionistic fuzzy numbers. Our approach provides a new standpoint for understanding the structure of intuitionistic fuzzy numbers and offers a tool that may simplify further analysis in intuitionistic fuzzy calculus, particularly non-linear intuitionistic fuzzy integral and differential equations. Clarifying examples are also presented to illustrate the key findings.