The problem of distributivity was posed many years ago and investigated in families of certain operations, for example, t-norms, t-conorms, uninorms and nullnorms. In this paper, we continue to investigate the same topic as the above by focusing on semi-t-operators over semi-uninorms, which are generalizations of t-operators and uninorms by omitting commutativity, and associativity and commutativity, respectively. The obtained results are the full characterizations, and extend the previous ones about distributivity between nullnorms over uninorms, and also between semi-nullnorms over semi-uninorms.
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Thanks to the support by National Natural Science Foundation of China (Nos. 61165014 and 11161023), A Foundation for the Author of National Excellent Doctoral Dissertation of PR China (No. 2007B14), Jiangxi Natural Science Foundation (No. 20122BAB201009), and the Scientific Research Foundation of Jiangxi Provincial Education Department (No. GJJ12176).
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