Abstract Recently, with the trisecting and acting models of human cognitive behaviors, three-way decisions are introduced to deal with uncertain decisions in many applications. To define and conduct the three-way decisions on the possible or necessary loser or co-loser and/or winner or co-winner, we first define the score-based common voting rules, where a score-based function is introduced to evaluate certain utility, including positional scoring rules, maximin, Bucklin, and so on. Then on one hand, it has been proved that under certain conditions three-way decisions on the possible loser or co-loser and/or winner or co-winner are NP-complete with positional scoring rules, maximin, and Bucklin, respectively. On the other hand, we have presented algorithms whose time complexity is polynomial to conduct three-way decisions on the necessary winner or co-winner and/or necessary loser or co-loser with positional scoring rules, maximin, and Bucklin in time O ( n m 2 ) , O ( n m 3 ) , and O ( n m 2 ) , respectively, which has been validated experimentally.

中文翻译：

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基于分数的公共投票规则下的加权偏序导向三向决策

摘要 近年来，随着人类认知行为的三分模型和行为模型的出现，许多应用中引入了三向决策来处理不确定决策。为了定义和进行关于可能或必要的失败者或共同失败者和/或获胜者或共同获胜者的三向决策，我们首先定义基于分数的共同投票规则，其中引入基于分数的函数来评估某些效用，包括位置评分规则、maximin、Bucklin 等。然后一方面，已经证明在某些条件下，关于可能的输家或共同输家和/或赢家或共同赢家的三向决策是 NP 完全的，分别具有位置评分规则、最大值和巴克林。另一方面，