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The focus of this paper is to establish a new concept of <i>b</i>-hybrid fuzzy contraction regarding the study of fuzzy fixed-point theorems in the setting of <i>b</i>-metric spaces. This idea harmonizes and refines several well-known results in the direction of point-valued, multivalued, and fuzzy-set-valued maps in the comparable literature. To attract new researchers to this field, some important results are shown to be corollaries. Moreover, a result is presented to establish sufficient conditions for the existence of solutions of integral inclusion of Fredholm type. Lastly, illustrations are presented to validate the suppositions of the given theorems.