Abstract
In this manuscript, we use the concepts of continuous t-norms and continuous t-conorms to introduce some definitions, in which intuitionistic fuzzy rectangular metric spaces, intuitionistic fuzzy rectangular metric-like spaces, intuitionistic fuzzy rectangular b-metric spaces, intuitionistic fuzzy rectangular b-metric-like spaces, neutrosophic rectangular metric spaces, neutrosophic rectangular metric-like spaces, neutrosophic rectangular b-metric spaces, and neutrosophic rectangular b-metric-like spaces are included. Continuous t-norms and continuous t-conorms are used to generalize the probability distribution of triangular inequalities in metric space axioms. Nontrivial examples, some fixed point results, and an application to the integral equation are imparted in this manuscript.