<p>In this paper, we investigate several construction methods for uninorms on bounded lattices by employing t-subnorms, t-superconorms, closure and interior operators under suitable additional constraints. Some of these construction methods extend and generalize existing approaches to uninorms in the literature. Moreover, we analyze the relationships between the resulting uninorms and the classes <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\mathcal {U}_{\max }^{}$</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi mathvariant="script">U</mi> <mrow> <mo movablelimits="true">max</mo> </mrow> <mrow> <mrow /> <mo>∗</mo> </mrow> </msubsup> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\mathcal {U}_{\min }^{}$</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi mathvariant="script">U</mi> <mrow> <mo movablelimits="true">min</mo> </mrow> <mrow> <mrow /> <mo>∗</mo> </mrow> </msubsup> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\mathcal {U}_{\max }$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">U</mi> <mo movablelimits="true">max</mo> </msub> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\mathcal {U}_{\min }$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">U</mi> <mo movablelimits="true">min</mo> </msub> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$\mathcal {U}_{\max }^{0}$</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi mathvariant="script">U</mi> <mrow> <mo movablelimits="true">max</mo> </mrow> <mn>0</mn> </msubsup> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$\mathcal {U}_{\min }^{1}$</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi mathvariant="script">U</mi> <mrow> <mo movablelimits="true">min</mo> </mrow> <mn>1</mn> </msubsup> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$\mathcal {U}_{\max }^{r}$</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi mathvariant="script">U</mi> <mrow> <mo movablelimits="true">max</mo> </mrow> <mi>r</mi> </msubsup> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq8"> <EquationSource Format="TEX">$\mathcal {U}_{\min }^{r}$</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi mathvariant="script">U</mi> <mrow> <mo movablelimits="true">min</mo> </mrow> <mi>r</mi> </msubsup> </math></EquationSource> </InlineEquation>.</p>

Construction methods for uninorms on bounded lattices via t-subnorms and t-superconorms

期刊论文
发表日期：

2026年5月2日

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Yingying An,
Zhenyu Xiu

摘要

In this paper, we investigate several construction methods for uninorms on bounded lattices by employing t-subnorms, t-superconorms, closure and interior operators under suitable additional constraints. Some of these construction methods extend and generalize existing approaches to uninorms in the literature. Moreover, we analyze the relationships between the resulting uninorms and the classes $\mathcal {U}_{\max }^{*}$ $U_{max}^{*}$ , $\mathcal {U}_{\min }^{*}$ $U_{min}^{*}$ , $\mathcal {U}_{\max }$ $U_{max}$ , $\mathcal {U}_{\min }$ $U_{min}$ , $\mathcal {U}_{\max }^{0}$ $U_{max}^{0}$ , $\mathcal {U}_{\min }^{1}$ $U_{min}^{1}$ , $\mathcal {U}_{\max }^{r}$ $U_{max}^{r}$ and $\mathcal {U}_{\min }^{r}$ $U_{min}^{r}$ .