In　this　paper,　we　shall　introduce　the　concept　of　a　fuzzy　set-valued　square　integrable　martingale,　define　a　metric　between　two　fuzzy　set-valued　square　integrable　martingales.　Then　we　prove　that　the　family　of　all　right-continuous　fuzzy　set-valued　square　integrable　martingales　with　respect　to　the　metric　is　a　complete　space　and　the　family　of　all　continuous　fuzzy　set-valued　square　integrable　martingales　is　its　closed　subset.　This　discussion　will　be　useful　in　the　study　of　fuzzy　set-valued　stochastic　integrals,　stochastic　differential　equations　with　applications　in　finance.