In this article, we present new methods for constructing uninorms on bounded lattices under the additional constraints and prove that some of these constraints are sufficient and necessary for the uninorms. Moreover, some illustrative examples for the construction of uninorms are provided. At last, we show that the additional constraints on t-norms (t-conorms) and t-subnorms (t-subconorms) of some uninorms in the literature are exactly sufficient and necessary.
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