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<p>Despite the fact that the Fermatean Fuzzy Soft Sets (FFSSs) take into account both parameters and specific material choices, certain general patterns associated with parameters are often significant in complex Multi-Criteria Decision Making (MCDM) problems. The purpose of this research is to present generalized FFSSs (GFFSSs) by incorporating crucial information along with the attributes of FFSSs at the same time. In GFFSSs the Fermatean Fuzzy Numbers (FFNs) represent a higher space where membership and non-membership are obtained; however, having a suitable knowledge representation framework alongside trustworthy tools, such as aggregation operators, is crucial for effectively addressing uncertainty. This study introduces Generalized Fermatean Fuzzy Soft Hamacher Weighted Averaging (GFFSHWA) and Generalized Fermatean Fuzzy Soft Hamacher Ordered Weighted Averaging (GFFSHOWA) operators along with their properties. On the other hand, MCDM techniques have made substantial use of VIekriterijumsko KOmpromisno Rangiranje (VIKOR) and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) in recent decades. VIKOR and TOPSIS approaches for FFSSs use criterion and option information, however, implicit information is usually addressed using integrated techniques in real and complex material choice situations. This study presents an integrated application of the VIKOR and TOPSIS methods in the context of GFFSSs. In supply chain management (SCM), selecting an appropriate supply chain analyst (SCA) is a essential decision making problem for enhancing the efficiency, cost-effectiveness, and trustworthiness of an organization’s supply chain through the collection, analysis, and interpretation of data pertaining to purchase, inventory, production, and distribution. On the basis of the information obtained through GFFSSs, a case study is presented that discusses the selection of an SCA for the purpose of SCM robustness. The discussion on three distinct proposed MCDM approaches is conducted through the conclusive outcomes of the case study. This study demonstrated the robustness and sensitivity of the proposed MCDM methods through a comparative analysis with established techniques.</p>

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Enhanced TOPSIS, VIKOR and Hamacher Averaging Aggregation Operators on Generalized Fermatean Fuzzy Soft Sets and Their Application in Supply Chain Management

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月10日

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  • Nadeem Ajaib,
  • Xiao-Peng Yang,
  • Khizar Hayat,
  • Kamran Kausar

摘要

Despite the fact that the Fermatean Fuzzy Soft Sets (FFSSs) take into account both parameters and specific material choices, certain general patterns associated with parameters are often significant in complex Multi-Criteria Decision Making (MCDM) problems. The purpose of this research is to present generalized FFSSs (GFFSSs) by incorporating crucial information along with the attributes of FFSSs at the same time. In GFFSSs the Fermatean Fuzzy Numbers (FFNs) represent a higher space where membership and non-membership are obtained; however, having a suitable knowledge representation framework alongside trustworthy tools, such as aggregation operators, is crucial for effectively addressing uncertainty. This study introduces Generalized Fermatean Fuzzy Soft Hamacher Weighted Averaging (GFFSHWA) and Generalized Fermatean Fuzzy Soft Hamacher Ordered Weighted Averaging (GFFSHOWA) operators along with their properties. On the other hand, MCDM techniques have made substantial use of VIekriterijumsko KOmpromisno Rangiranje (VIKOR) and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) in recent decades. VIKOR and TOPSIS approaches for FFSSs use criterion and option information, however, implicit information is usually addressed using integrated techniques in real and complex material choice situations. This study presents an integrated application of the VIKOR and TOPSIS methods in the context of GFFSSs. In supply chain management (SCM), selecting an appropriate supply chain analyst (SCA) is a essential decision making problem for enhancing the efficiency, cost-effectiveness, and trustworthiness of an organization’s supply chain through the collection, analysis, and interpretation of data pertaining to purchase, inventory, production, and distribution. On the basis of the information obtained through GFFSSs, a case study is presented that discusses the selection of an SCA for the purpose of SCM robustness. The discussion on three distinct proposed MCDM approaches is conducted through the conclusive outcomes of the case study. This study demonstrated the robustness and sensitivity of the proposed MCDM methods through a comparative analysis with established techniques.