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<p>Dual hesitant fuzzy sets (DHFSs) powerfully characterize uncertainty information by combining intuitionistic and hesitant mechanisms, and their aggregation operators (AOs) facilitate multi-attribute decision making (MADM). AOs mainly rely on underlying operations (such as addition and multiplication) determined by triangular norm/conorm (t-norm/t-conorm); in particular, Heronian mean operators systematically reveal interrelationships among aggregation arguments, while the Aczel-Alsina t-norm/t-conorm effectively acquires the parametric flexibility. Aiming at DHFSs, this paper constructs extended Heronian mean operators based on Aczel-Alsina t-norm/t-conorm, so new AOs are developed to motivate MADM. At first, Aczel-Alsina operations of addition, multiplication, scalar multiplication and power action are defined for DHFSs, and their operational laws are acquired. Then by Aczel-Alsina operations, basic and geometric Heronian mean operators on DHFSs are determined from direct and weighted perspectives, and thus <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(2\times 2=4\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>2</mn> <mo>×</mo> <mn>2</mn> <mo>=</mo> <mn>4</mn> </mrow> </math></EquationSource> </InlineEquation> AOs systematically emerge, including dual hesitant fuzzy Aczel-Alsina basic and geometric Heronian mean operators (i.e., DHFAAHM and DHFAAGHM) and their weighted forms (i.e., DHFAAWHM, DHFAAWGHM). These four new AOs achieve essential analytic expressions and in-depth mathematical properties (including idempotence, boundedness, monotonicity). Finally, the two weighted aggregation operators – DHFAAWHM and DHFAAWGHM – are utilized to construct a novel method of MADM for dual hesitant fuzzy information processing, and its applicability, robustness, effectiveness are verified via a practical example and corresponding approach comparisons.</p>

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Dual hesitant fuzzy Aczel-Alsina Heronian mean operators and their applications in multi-attribute decision making

  • 期刊论文

  • 发表日期：

    2026年2月13日

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  • Huarong Feng,
  • Xianyong Zhang,
  • Mengdi Liu,
  • Zhiwen Mo

摘要

Dual hesitant fuzzy sets (DHFSs) powerfully characterize uncertainty information by combining intuitionistic and hesitant mechanisms, and their aggregation operators (AOs) facilitate multi-attribute decision making (MADM). AOs mainly rely on underlying operations (such as addition and multiplication) determined by triangular norm/conorm (t-norm/t-conorm); in particular, Heronian mean operators systematically reveal interrelationships among aggregation arguments, while the Aczel-Alsina t-norm/t-conorm effectively acquires the parametric flexibility. Aiming at DHFSs, this paper constructs extended Heronian mean operators based on Aczel-Alsina t-norm/t-conorm, so new AOs are developed to motivate MADM. At first, Aczel-Alsina operations of addition, multiplication, scalar multiplication and power action are defined for DHFSs, and their operational laws are acquired. Then by Aczel-Alsina operations, basic and geometric Heronian mean operators on DHFSs are determined from direct and weighted perspectives, and thus \(2\times 2=4\) 2 × 2 = 4 AOs systematically emerge, including dual hesitant fuzzy Aczel-Alsina basic and geometric Heronian mean operators (i.e., DHFAAHM and DHFAAGHM) and their weighted forms (i.e., DHFAAWHM, DHFAAWGHM). These four new AOs achieve essential analytic expressions and in-depth mathematical properties (including idempotence, boundedness, monotonicity). Finally, the two weighted aggregation operators – DHFAAWHM and DHFAAWGHM – are utilized to construct a novel method of MADM for dual hesitant fuzzy information processing, and its applicability, robustness, effectiveness are verified via a practical example and corresponding approach comparisons.