In this paper, we discuss two special classes of 2-uninorms which we call uni-nullnorms and null-uninorms. They are combinations of uninorms and nullnorms. We prove that uni-nullnorms (resp. null-uninorms) are dual to null-uninorms (resp. uni-nullnorms) under a strong negation. We study their classifications, structures and idempotence. Moreover, we investigate De Morgan triples for uni-nullnorms and null-uninorms.
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