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<p>In this paper, we explore the additive generators of <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(\Theta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Θ</mi> </math></EquationSource> </InlineEquation>-<InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(\Xi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Ξ</mi> </math></EquationSource> </InlineEquation> functions, which generalize overlap and grouping functions in aggregation operator theory. Specifically, we firstly introduce additive generator pairs for <InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(\Theta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Θ</mi> </math></EquationSource> </InlineEquation>-<InlineEquation ID="IEq10"> <EquationSource Format="TEX">\(\Xi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Ξ</mi> </math></EquationSource> </InlineEquation> functions, defined through the boundary values <InlineEquation ID="IEq11"> <EquationSource Format="TEX">\(\iota \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ι</mi> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq12"> <EquationSource Format="TEX">\(\varrho .\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ϱ</mi> <mo>.</mo> </mrow> </math></EquationSource> </InlineEquation> Subsequently, we establish the necessary and sufficient conditions for <InlineEquation ID="IEq13"> <EquationSource Format="TEX">\(\Theta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Θ</mi> </math></EquationSource> </InlineEquation>-<InlineEquation ID="IEq14"> <EquationSource Format="TEX">\(\Xi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Ξ</mi> </math></EquationSource> </InlineEquation> functions generated by the additive generator pairs.</p>

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Constructing \(\Theta \)-\(\Xi \) functions by means of additive generators

  • 期刊论文

  • 发表日期：

    2026年3月13日

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  • Tiantian Chen,
  • Yifan Wang,
  • Jing Lu

摘要

In this paper, we explore the additive generators of \(\Theta \) Θ - \(\Xi \) Ξ functions, which generalize overlap and grouping functions in aggregation operator theory. Specifically, we firstly introduce additive generator pairs for \(\Theta \) Θ - \(\Xi \) Ξ functions, defined through the boundary values \(\iota \) ι and \(\varrho .\) ϱ . Subsequently, we establish the necessary and sufficient conditions for \(\Theta \) Θ - \(\Xi \) Ξ functions generated by the additive generator pairs.