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<p>In this paper, we introduce two approaches for obtaining new classes of uninorms using the uninorm defined on a sublattice [0,&#xa0;<i>k</i>] (or [<i>t</i>,&#xa0;1] ) of a bounded lattice <i>L</i> with a neutral element <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="233_2025_10541_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="59" /> </InlineMediaObject> <EquationSource Format="TEX">\(e\in ] 0,k[ \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>e</mi> <mo>∈</mo> <mo stretchy="false">]</mo> <mn>0</mn> <mo>,</mo> <mi>k</mi> <mo stretchy="false">[</mo> </mrow> </math></EquationSource> </InlineEquation> (or <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="233_2025_10541_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="56" /> </InlineMediaObject> <EquationSource Format="TEX">\(e\in ] t,1[ \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>e</mi> <mo>∈</mo> <mo stretchy="false">]</mo> <mi>t</mi> <mo>,</mo> <mn>1</mn> <mo stretchy="false">[</mo> </mrow> </math></EquationSource> </InlineEquation>) . As a by-product, these tools encompass some of the existing construction methods for uninorms on <i>L</i>. Moreover, we provide some examples to assess the differences between our methods and the existing approaches.</p>

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On a new class of uninorms constructed by a uninorm on a sublattice of a bounded lattice

  • 期刊论文

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  • 发表日期：

    2025年5月28日

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  • Gül Deniz Çaylı,
  • Emrah Kurtuluş

摘要

In this paper, we introduce two approaches for obtaining new classes of uninorms using the uninorm defined on a sublattice [0, k] (or [t, 1] ) of a bounded lattice L with a neutral element \(e\in ] 0,k[ \) e ∈ ] 0 , k [ (or \(e\in ] t,1[ \) e ∈ ] t , 1 [ ) . As a by-product, these tools encompass some of the existing construction methods for uninorms on L. Moreover, we provide some examples to assess the differences between our methods and the existing approaches.