In this study, a new family of polynomial‐type fuzzy contractions defined on metric spaces is introduced. Under filtered assumptions, it is demonstrated that such non‐crisp set‐valued operators possess some fixed points. Because of the higher‐order terms polynomial nature of the contractions, a few important corollaries, some of which drop to existing results are highlighted and discussed. In contrast to many of the known Lispchitz‐type inequalities, the proposed class of fuzzy contractive inequalities herein do not impose continuity on the mapping under consideration. A comparative example is constructed to support the premises forming the obtained ideas and show that the overall concept of this research improves and unifies the corresponding ones in the literature. From application point of view, one of the examined results is utilized to study new conditions for the existence of solutions to a multi‐group SEIRV epidemic model formulated as a differential inclusion. The key finding of this research is that many invariant point results within the context of crisp set‐valued and point‐valued operators remain valid in the framework of polynomial fuzzy contractions. This discovery obviously widens the applications of fixed point results to the systems with either fuzzy or non‐statistical uncertainties.
Noorwali et al. (Thu,) studied this question.