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

Abstract

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

arXiv commentOriginally submitted to IEEE TFS (on October 27, 2014) as a part of the longer paper which was after recommendation divided into two papers. This part was submitted to International Journal of Approximate Reasoning on February 04, 2015. arXiv admin note: text overlap with arXiv:1506.06952