<p>This paper characterizes the cross-migrativity of disjunctive uninorms over <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$g$</EquationSource> <EquationSource Format="MATHML"><math> <mi>g</mi> </math></EquationSource> </InlineEquation>-implications (resp. <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$f$</EquationSource> <EquationSource Format="MATHML"><math> <mi>f</mi> </math></EquationSource> </InlineEquation>-implications). Firstly, on the basis of the generator <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$g$</EquationSource> <EquationSource Format="MATHML"><math> <mi>g</mi> </math></EquationSource> </InlineEquation>, we study the cross-migrativity of disjunctive uninorms over <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$g$</EquationSource> <EquationSource Format="MATHML"><math> <mi>g</mi> </math></EquationSource> </InlineEquation>-implications in the cases <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$g(1)=\infty $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>g</mi> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>=</mo> <mi>∞</mi> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$g(1)<\infty $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>g</mi> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo><</mo> <mi>∞</mi> </mrow> </math></EquationSource> </InlineEquation>, respectively. Secondly, we discuss the <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$\alpha $</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>-cross-migrativity of a disjunctive uninorm <InlineEquation ID="IEq8"> <EquationSource Format="TEX">$U$</EquationSource> <EquationSource Format="MATHML"><math> <mi>U</mi> </math></EquationSource> </InlineEquation> with the neutral element <InlineEquation ID="IEq9"> <EquationSource Format="TEX">$e$</EquationSource> <EquationSource Format="MATHML"><math> <mi>e</mi> </math></EquationSource> </InlineEquation> over an <InlineEquation ID="IEq10"> <EquationSource Format="TEX">$f$</EquationSource> <EquationSource Format="MATHML"><math> <mi>f</mi> </math></EquationSource> </InlineEquation>-implication <InlineEquation ID="IEq11"> <EquationSource Format="TEX">$I_{f}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>I</mi> <mi>f</mi> </msub> </math></EquationSource> </InlineEquation> similarly to the case <InlineEquation ID="IEq12"> <EquationSource Format="TEX">$g(1)=\infty $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>g</mi> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>=</mo> <mi>∞</mi> </mrow> </math></EquationSource> </InlineEquation> except the special situation <InlineEquation ID="IEq13"> <EquationSource Format="TEX">$\alpha \in [0,e[$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>α</mi> <mo>∈</mo> <mo stretchy="false">[</mo> <mn>0</mn> <mo>,</mo> <mi>e</mi> <mo stretchy="false">[</mo> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq14"> <EquationSource Format="TEX">$f(0)<\infty $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>f</mi> <mo stretchy="false">(</mo> <mn>0</mn> <mo stretchy="false">)</mo> <mo><</mo> <mi>∞</mi> </mrow> </math></EquationSource> </InlineEquation>, where <InlineEquation ID="IEq15"> <EquationSource Format="TEX">$U$</EquationSource> <EquationSource Format="MATHML"><math> <mi>U</mi> </math></EquationSource> </InlineEquation> is not <InlineEquation ID="IEq16"> <EquationSource Format="TEX">$(\alpha ,I_{f})$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>α</mi> <mo>,</mo> <msub> <mi>I</mi> <mi>f</mi> </msub> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-cross-migrative. We also present some numerical examples to show our conclusions.</p>

Cross-migrativity of disjunctive uninorms over g- and f-implications

期刊论文
发表日期：

2026年1月16日

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Chun Yong Wang,
Xue Han Ma,
Xin Ru Shi,
Bo Zhang

摘要

This paper characterizes the cross-migrativity of disjunctive uninorms over $g$ $g$ -implications (resp. $f$ $f$ -implications). Firstly, on the basis of the generator $g$ $g$ , we study the cross-migrativity of disjunctive uninorms over $g$ $g$ -implications in the cases $g(1)=\infty $ $g (1) = \infty$ and $g(1)<\infty $ $g (1) < \infty$ , respectively. Secondly, we discuss the $\alpha $ $α$ -cross-migrativity of a disjunctive uninorm $U$ $U$ with the neutral element $e$ $e$ over an $f$ $f$ -implication $I_{f}$ $I_{f}$ similarly to the case $g(1)=\infty $ $g (1) = \infty$ except the special situation $\alpha \in [0,e[$ $α \in [0, e [$ and $f(0)<\infty $ $f (0) < \infty$ , where $U$ $U$ is not $(\alpha ,I_{f})$ $(α, I_{f})$ -cross-migrative. We also present some numerical examples to show our conclusions.