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The Equation \(\mathcal{I}(\mathcal{S}(x,y),z) = \mathcal{T}(\mathcal{I}(x,z),\mathcal{I}(y,z))\) for t-representable t-conorms and t-norms Generated from Continuous, Archimedean Operations

  • Michał Baczyński
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8256)

Abstract

In this article we continue investigations presented at previous WILF 2011 conference which are connected with distributivity of implication operations over t-representable t-norms and t-conorms. Our main goal is to show the general method of solving the following distributivity equation \(\mathcal{I}(\mathcal{S}(x,y),z) = \mathcal{T}(\mathcal{I}(x,z),\mathcal{I}(y,z))\), when \(\mathcal{S}\) is a t-representable t-conorm on \(\mathcal{L}^I\) generated from two continuous, Archimedean t-conorms, \(\mathcal{T}\) is a t-representable t-norm on \(\mathcal{L}^I\) generated from two continuous, Archimedean t-norms and \(\mathcal{I}\) is an unknown function.

Keywords

Interval-valued fuzzy sets Triangular norm Triangular conorm Distributivity equations Functional equations 

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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Michał Baczyński
    • 1
  1. 1.Institute of MathematicsUniversity of SilesiaKatowicePoland

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