This study proposes the multi attribute group decision making in the presence of incomplete multi attribute and incomplete multi decision while making a decision with preferences in an incomplete information system. We then consider resolving the problem in an incomplete information system by using two different approximation strategies, that is seeking the common reserving difference and common rejecting difference, four kinds of soft dominance based multi-granulation rough sets namely soft dominance based optimestic multi-granulation rough sets and soft dominance based pessimistic multi-granulation rough sets are presented. Another worth mentioning contibution of this paper is to disclose the ideas of two kinds of approximate precision, rough degree, approximate quality, maximal and minimal rough member ships and their mutual relationships. Finally the validity of these concepts are proved by constructing two algorithms and applying them in solving incomplete multi-agent conflict analysis problem.
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