Abstract
Since its original formulation, the theory of fuzzy sets has spawned a number of extensions where the role of membershipvalues in the real unit interval [0; 1] is handed over to more complex mathematical entities. Amongst the many existingextensions, two similar ones, the fuzzy multisets and the hesitant fuzzy sets, rely on collections of several distinct valuesto represent fuzzy membership, the key difference being that the fuzzy multisets allow for repeated membership valueswhereas the hesitant fuzzy sets do not. But in neither case are these collections of values ordered, as they are simplyrepresented through multisets or sets. In this paper, we study ordered fuzzy multisets, where the membership valuecan be an ordered n-tuple of values, thus accounting for both order and repetition. We present some basic de finitionsand results and explore the relation between these ordered fuzzy multisets and the fuzzy multisets and hesitant fuzzysets.
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