Abstract This paper investigates the left and right distributivity between semi-uninorms and semi-S-uninorms without the commutativity and associativity. Firstly, we study the left and right distributivity for special disjunctive (resp. conjunctive) semi-uninorms in N e max (resp. N e min ) over S-uninorms with the underlying uninorms in N e ′ min . Secondly, semi-S-uninorms are proposed by omitting the commutativity and associativity of S-uninorms. Thirdly, the left and right distributivity for semi-S-uninorms over semi-uninorms in N e min (resp. N e max ) are studied, where the underlying semi-uninorms of semi-S-uninorms are semi-uninorms in N e ′ min . Especially, the distributivity between semi-uninorms and semi-S-uninorms has the distributivity between uninorms and S-uninorms as a special case.

中文翻译：

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半单模与半S单模之间的左右分布

摘要 本文研究了没有交换性和结合性的半单范数和半S-单范数之间的左右分配性。首先，我们研究了 N e max (resp. N e min ) 上的特殊析取 (resp. conjunctive) 半单范数在 S-uninorms 上的左右分配性，其中潜在的单范数在 N e ' min 。其次，通过省略S-uninorms的交换性和结合性，提出了半S-uninorms。第三，研究了半S-uninorms在N e min (resp. N e max )上的半单范数的左右分布，其中半S-uninorms的潜在半单范数是N e 的半单范数'分钟。尤其是，半单范数和半S单范数之间的分布性具有单范数和S-单范数之间的分布性作为特例。