The least square B-nucleolus for fuzzy cooperative games is proposed based on the bi-excess of fuzzy coalitions. The proposed solutions consider not only the size of fuzzy coalitions, but also the blocking and constructive powers. The uniqueness of the least square B-prenucleolus for fuzzy cooperative games is proved detailedly. Some quadratic programming models for generating the least square B-nucleolus of complete and incomplete fuzzy cooperative games are presented, respectively. The least square B-prenucleolus is extended to the multiplicative setting, and the logarithmic least square B-prenucleolus for multiplicative fuzzy cooperative games is derived.
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