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00925njm 22002777a 4500 dc Fernandez-Peralta, Raquel author Massanet, Sebastia author Mesiarová-Zemánková, Andrea author Mir, Arnau author 2023 The continuous completions of conditionally cancellative pre-t-norms defined in the regions linked to the characterization of (S, N)-implications when Sis a continuous t-conorm and Nis a fuzzy negation with one point of discontinuity are determined. The results have been divided in two parts. In this first part we provide three main results: we determine the existence and expression of the additive generator of a cancellative pre-t-norm known above a level curve and, using this result as a basis, we provide the continuous completions of pre-t-norms determined in regions of the type [0, 1]2\(0, a)2or [0, 1]2\(a, 1)2 with a∈(0, 1). It is highlighted that, differently from the cancellative case where all the results provide unique continuous completions, in the analogous situations in the conditionally cancellative case the corresponding continuous completions might not be unique. This fact causes more complex results for the remaining regions, which are discussed in the second paper of this study. Fernandez-Peralta R, Massanet S, Mesiarová-Zemánková A, Mir A. Determination of the continuous completions of conditionally cancellative pre-t-norms associated with the characterization of (S,N)-implications: Part I. Fuzzy Sets Syst. 2023 Sep;468:108614. 10.1016/j.fss.2023.108614 0165-0114 Fuzzy Sets and Systems https://hdl.handle.net/20.500.13003/19297 2-s2.0-85162021815 https://hdl.handle.net/20.500.12105/23629 1028270300001 Determination of the continuous completions of conditionally cancellative pre-t-norms associated with the characterization of (S,N)-implications: Part I