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The uninorms with continuous underlying t-norm and t-conorm are characterizedvia an extended ordinal sum construction. Using the results of [18], where eachuninorm with continuous underlying operations was characterized by propertiesof its set of discontinuity points, it is shown that each such a uninorm can bedecomposed into an extended ordinal sum of representable uninorms, continuousArchimedean t-norms, continuous Archimedean t-conorms and internal uninorms.

Characterization of uninorms with continuous underlying t-norm and t-conorm by means of an extended ordinal sum