Ordinal sums of representable uninorms

We investigate properties of an ordinal sum of uninorms introduced in [8] in the case that the summands are proper representable uninorms. We show sufficient and necessary conditions for a uninorm to be an ordinal sum of representable uninorms.Comment: Submitted to Fuzzy Sets and Systems on October 8, 201

Characterization of uninorms with continuous underlying t-norm and t-conorm by their set of discontinuity points

Uninorms with continuous underlying t-norm and t-conorm are discussed and properties of the set of discontinuity points of such a uninorm are shown. This set is proved to be a subset of the graph of a special symmetric, surjective, non-increasing multi-function. A sufficient condition for a uninorm to have continuous underlying operations is also given. Several examples are included.Comment: Submitted to IEEE TFS (on October 27, 2014) as a part of the longer paper. This part remained in IEEE (resubmission on April 27, 2015). arXiv admin note: text overlap with arXiv:1506.07820, arXiv:1506.0695

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

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.Comment: Originally 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:1506.0695

Ordinal Sums of Fuzzy Negations: Main Classes and Natural Negations

In the context of fuzzy logic, ordinal sums provide a method for constructing new functions from existing functions, which can be triangular norms, triangular conorms, fuzzy negations, copulas, overlaps, uninorms, fuzzy implications, among others. As our main contribution, we establish conditions for the ordinal sum of a family of fuzzy negations to be a fuzzy negation of a specific class, such as strong, strict, continuous, invertible and frontier. Also, we relate the natural negation of the ordinal sum on families of t-norms, t-conorms and fuzzy implications with the ordinal sum of the natural negations of the respective families of t-norms, t- conorms and fuzzy implications. This motivated us to introduces a new kind of ordinal sum for families of fuzzy implications