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Distributivity of Implication Functions over Decomposable Uninorms Generated from Representable Uninorms in Interval-Valued Fuzzy Sets Theory

  • Michał BaczyńskiEmail author
  • Wanda Niemyska
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 610)

Abstract

In this work we investigate two distributivity equations \(\mathcal {I}(x,\mathcal {U}_1(y,z)) = \mathcal {U}_2(\mathcal {I}(x,y),\mathcal {I}(x,z))\), \(\mathcal {I}(\mathcal {U}_1(x,y),z) = \mathcal {U}_2(\mathcal {I}(x,z),\mathcal {I}(y,z))\) for implication operations and uninorms in interval-valued fuzzy sets theory. We consider decomposable (t-representable) uninorms generated from two conjunctive or disjunctive representable uninorms. Our method reduces to solve the following functional equation \(f(u_1+v_1,u_2+v_2) = f(u_1,u_2) + f(v_1,v_2)\), thus we present new solutions for this equation.

Keywords

Aggregation operators Uninorms Interval-valued fuzzy sets Distributivity equations Functional equations 

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of SilesiaKatowicePoland

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