Existence of fuzzy cores and generalizations of the K–K–M–S theorem

In this paper, we provide some fuzzy extensions to the well-known K–K–M–S theorem and Zhou’s open K–K–M–S theorem. As an application, we will use one of these results to give a proof for the fuzzy extension to the well-known Scarf’s core existence theorem, which can be used to give another proof for the non-emptiness of the fuzzy core of a pure exchange economy introduced by Florenzano.