Power Aggregation Operators Based on Aczel-Alsina T-Norm and T-Conorm for Intuitionistic Hesitant Fuzzy Information and Their Application to Logistics Service Provider Selection

Information Science Artificial Intelligence Engineering Transportation Engineering Computer Science
Power Aggregation Operators Decision-Making Technique Intuitionistic Hesitant Fuzzy Sets Logistics Service Provider Selection Aczel-Alsina T-Norm

Academic Background

In modern supply chain management, the selection of logistics service providers is a complex and critical issue. Enterprises need to evaluate and choose third-party organizations capable of efficiently managing and executing logistics tasks. However, the decision-making process in reality often involves significant uncertainty and ambiguity, which traditional decision methods struggle to handle effectively. To address this issue, Fuzzy Set Theory (FST) and its extensions, such as Intuitionistic Fuzzy Sets (IFS) and Hesitant Fuzzy Sets (HFS), have been widely applied in Multi-Attribute Decision Making (MADM) problems.

In recent years, Intuitionistic Hesitant Fuzzy Sets (IHFS) have gradually gained attention in academia as a new tool for representing fuzzy information. IHFS combines the advantages of hesitant fuzzy sets and intuitionistic fuzzy sets, enabling better handling of uncertainty and ambiguity in decision-making processes. However, existing IHFS aggregation operators still face certain limitations when dealing with extreme values and complex decision problems. To address these limitations, Peng Wang and colleagues proposed a power aggregation operator based on Aczel-Alsina norms, aiming to solve these issues and apply it to the selection of logistics service providers.

Source of the Paper

The paper was co-authored by Peng Wang, Baoying Zhu, Keyan Yan, Ziyu Zhang, Zeeshan Ali, and Dragan Pamucar, from multiple universities and research institutions in China and Serbia. The paper was accepted on February 12, 2025, and published in the journal Artificial Intelligence Review, with the article number 58:204 and DOI 10.1007/s10462-025-11155-4.

Research Process

1. Research Background and Problem Analysis

The paper first analyzes the complexity of logistics service provider selection and the limitations of existing models. Traditional decision methods are insufficient in handling fuzzy information, especially when facing extreme values and complex decision environments. To address this, the authors proposed a power aggregation operator based on Aczel-Alsina norms, aiming to better handle intuitionistic hesitant fuzzy information and apply it to the selection of logistics service providers.

2. Aczel-Alsina Operational Laws for Intuitionistic Hesitant Fuzzy Sets

The authors first analyzed the Aczel-Alsina operational laws for intuitionistic hesitant fuzzy sets and proposed new operational rules. These rules are based on Aczel-Alsina t-norms and t-conorms, enabling more flexible handling of the aggregation of intuitionistic hesitant fuzzy information.

3. Derivation of Power Aggregation Operators

Based on the Aczel-Alsina operational laws, the authors derived four new power aggregation operators: the Intuitionistic Hesitant Fuzzy Aczel-Alsina Power Averaging Operator (IHFAAPO-A), the Intuitionistic Hesitant Fuzzy Aczel-Alsina Weighted Power Averaging Operator (IHFAAWPO-A), the Intuitionistic Hesitant Fuzzy Aczel-Alsina Power Geometric Operator (IHFAAPO-G), and the Intuitionistic Hesitant Fuzzy Aczel-Alsina Weighted Power Geometric Operator (IHFAAWPO-G). These operators possess power averaging and power geometric properties, effectively eliminating the impact of extreme values on decision results.

4. Proof of Operator Properties

The authors proved the fundamental properties of these operators, including idempotency, monotonicity, and boundedness. These properties provide theoretical support for the mathematical feasibility of the operators in solving decision problems.

5. Decision Model for Logistics Service Provider Selection

To validate the effectiveness of the proposed operators, the authors applied them to the problem of logistics service provider selection. Using multi-attribute decision-making methods, the authors evaluated the performance of multiple logistics service providers and compared the ranking results of the proposed operators with existing techniques. The results demonstrated that the proposed method exhibits higher effectiveness and stability in handling complex decision problems.

Main Results

1. Proposal and Validation of Operational Laws

The Aczel-Alsina operational laws proposed by the authors enable more flexible handling of the aggregation of intuitionistic hesitant fuzzy information. Through mathematical induction, the authors validated the correctness and effectiveness of these operational laws.

2. Derivation and Properties of Power Aggregation Operators

Based on the Aczel-Alsina operational laws, the authors successfully derived four new power aggregation operators and proved their idempotency, monotonicity, and boundedness. These properties provide theoretical support for the application of the operators in decision problems.

3. Decision Results for Logistics Service Provider Selection

By applying the proposed operators, the authors evaluated the performance of five logistics service providers and derived the corresponding ranking results. Compared to existing techniques, the proposed method demonstrated higher stability and effectiveness in handling extreme values and complex decision problems.

Conclusion and Significance

This study proposed a power aggregation operator for intuitionistic hesitant fuzzy information based on Aczel-Alsina norms and successfully applied it to the problem of logistics service provider selection. The proposed operational laws and operators enable more flexible handling of fuzzy information, effectively eliminating the impact of extreme values on decision results. This study not only provides new theoretical tools for fuzzy information processing but also offers effective solutions for practical decision problems such as logistics service provider selection.

Research Highlights

  1. Novel Operational Laws: Proposed Aczel-Alsina operational laws for intuitionistic hesitant fuzzy information, enabling more flexible handling of fuzzy information aggregation.
  2. New Power Aggregation Operators: Derived four new power aggregation operators with power averaging and power geometric properties, effectively eliminating the impact of extreme values on decision results.
  3. Practical Application Validation: Applied the proposed operators to the problem of logistics service provider selection, validating their effectiveness and stability in complex decision problems.

Other Valuable Information

The authors also pointed out that future research could attempt to extend the proposed multifunctional aggregation operators to other forms of information, such as Dual Hesitant Q-Rung Orthopair Fuzzy Sets and Spherical Fuzzy Sets. Additionally, the method could be applied to more practical problems, such as talent evaluation and ecological governance evaluation.

Through this paper, Peng Wang and colleagues have provided new theoretical tools for the field of fuzzy information processing and offered effective solutions for practical decision problems such as logistics service provider selection. This research holds significant academic value and has broad application prospects.