The fixed-point theorem gives the conditions under which maps (single or multi-valued) have solutions. Fixed point theory itself is a mixture of analysis that is pure and applied, topology, and geometry. In the past 50 years, the theory of fixed points has come to show something that had been hidden as a very powerful and important tool in the study of non-linear phenomena. In fixed points in particular, the techniques have been applied to fields as diverse as chemistry, economics, biology, engineering, game theory, and physics. Fixed point theory plays an important role in solving real-life problems. This study aims to use tangential and generalized coincidence properties to create some coupled common results (CCFP) in a fuzzy metric space for two pairs of single-valued mappings that meet the contractive constraints of integral type. Our results generalize and extend other similar discoveries without relying on their completeness or continuity. We apply a variety of special generalized contractions to fuzzy metric spaces that incorporate integral-type mappings. Examples are also given in view of the established results.
