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On the basis of the theory of a falling shadow and fuzzy sets, the notion of a falling fuzzy BCI-commutative ideal of a BCI-algebra is introduced. Relations between falling fuzzy BCI-commutative ideals and falling fuzzy ideals are given. Relations between fuzzy BCI-commutative ideals and falling fuzzy BCIcommutative ideals are provided. Characterizations of a falling fuzzy BCI-commutative ideal are established, and conditions for a falling fuzzy (closed) ideal to be a falling fuzzydoi:10.5831/hmj.2014.36.3.555 fatcat:lrqwbdhsxnewxnlliizodxn74m