Dombi Weighted Geometric Aggregation Operators on the Class of Trapezoidal-Valued Intuitionistic Fuzzy Numbers and Their Applications to Multi-Attribute Group Decision-Making
Academic Background
In modern engineering and management fields, decision-making problems are often accompanied by uncertainty and ambiguity. Traditional fuzzy set theory has certain limitations when dealing with these issues, especially in complex Multi-Attribute Group Decision-Making (MAGDM) problems. Intuitionistic Fuzzy Set (IFS), as an extended fuzzy set theory, can better capture the uncertainty and ambiguity in the decision-making process. However, existing Intuitionistic Fuzzy Numbers (IFNs) still have shortcomings when dealing with certain complex problems, particularly when it comes to Trapezoidal-Valued Intuitionistic Fuzzy Numbers (TrVIFNs).
To address this issue, this paper proposes a weighted geometric aggregation operator based on Dombi t-norm and t-conorm, and applies it to multi-attribute group decision-making problems involving trapezoidal intuitionistic fuzzy numbers. Due to the flexible parameter settings of Dombi operations, they can better adapt to different decision-making environments, thereby improving the reliability and flexibility of the decision-making process.
Source of the Paper
This paper is co-authored by Bibhuti Bhusana Meher, Jeevaraj S, and Melfi Alrasheedi, from research institutions in India and academic institutions in Saudi Arabia. The paper was accepted by the journal Artificial Intelligence Review on March 13, 2025, and published in Volume 58, Issue 205 of Artificial Intelligence Review in the same year, with the DOI 10.1007/s10462-025-11200-2.
Research Process and Results
1. Research Process
a) Definition and Operational Rules of Trapezoidal Intuitionistic Fuzzy Numbers
This paper first defines Trapezoidal Intuitionistic Fuzzy Numbers (TrVIFNs) and proposes new operational rules based on Dombi t-norm and t-conorm. These operational rules include addition, multiplication, scalar multiplication, and power operations, which can effectively handle operations between trapezoidal intuitionistic fuzzy numbers.
b) Construction of Dombi Weighted Geometric Aggregation Operators
After defining the operational rules, this paper proposes three Dombi-based geometric aggregation operators: Trapezoidal Intuitionistic Fuzzy Dombi Weighted Geometric Operator (TrVIFDWG), Trapezoidal Intuitionistic Fuzzy Dombi Ordered Weighted Geometric Operator (TrVIFDOWG), and Trapezoidal Intuitionistic Fuzzy Dombi Hybrid Geometric Operator (TrVIFDHG). These operators can effectively aggregate multiple trapezoidal intuitionistic fuzzy numbers, providing new tools for multi-attribute group decision-making.
c) Construction of Multi-Attribute Group Decision-Making Algorithm
Based on the above aggregation operators, this paper constructs a Trapezoidal Intuitionistic Fuzzy Multi-Attribute Group Decision-Making Algorithm (TrVIFMAGDM). By aggregating expert opinions and attribute weights, this algorithm can effectively solve complex decision-making problems.
d) Application to Photovoltaic Site Selection Problem
To validate the effectiveness of the proposed algorithm, this paper applies it to a photovoltaic site selection problem. Through the analysis of a real-world case, the superiority of the algorithm in solving practical problems is demonstrated.
e) Sensitivity Analysis and Comparative Analysis
Finally, this paper conducts a sensitivity analysis of the proposed algorithm, verifying its stability and reliability by changing parameter weights. Additionally, a comparative analysis with other existing group decision-making methods further proves the superiority of the proposed method.
2. Main Results
a) Validation of Operational Rules
Through specific numerical examples, this paper validates the effectiveness of the proposed operational rules. The results show that the Dombi-based operational rules can accurately handle operations between trapezoidal intuitionistic fuzzy numbers.
b) Effectiveness of Aggregation Operators
Through theoretical proofs and numerical examples, this paper validates the effectiveness of the three proposed aggregation operators. The results show that these operators can effectively aggregate multiple trapezoidal intuitionistic fuzzy numbers, providing new tools for multi-attribute group decision-making.
c) Application of Multi-Attribute Group Decision-Making Algorithm
In the application to the photovoltaic site selection problem, this paper demonstrates the superiority of the proposed algorithm. The analysis of the real-world case shows that the algorithm can effectively solve complex decision-making problems.
d) Sensitivity Analysis and Comparative Analysis
The sensitivity analysis results show that the proposed algorithm exhibits good stability and reliability under different parameter weights. Compared with other existing group decision-making methods, the proposed method has higher accuracy and flexibility in handling complex decision-making problems.
Conclusions and Significance
This paper proposes a Dombi weighted geometric aggregation operator for trapezoidal intuitionistic fuzzy numbers and its application in multi-attribute group decision-making. By defining new operational rules and aggregation operators, this paper provides new tools for handling complex multi-attribute group decision-making problems. The application to real-world cases and sensitivity analysis further validate the effectiveness and superiority of the proposed method.
The research in this paper has significant scientific and practical value. In terms of scientific value, the proposed Dombi operational rules and aggregation operators provide new ideas and methods for the study of trapezoidal intuitionistic fuzzy numbers. In terms of practical value, the proposed multi-attribute group decision-making algorithm can effectively solve complex decision-making problems in practical engineering and management, with broad application prospects.
Research Highlights
- Novel Operational Rules: This paper proposes new operational rules based on Dombi t-norm and t-conorm, which can better handle operations between trapezoidal intuitionistic fuzzy numbers.
- Innovative Aggregation Operators: This paper proposes three Dombi-based geometric aggregation operators, providing new tools for multi-attribute group decision-making.
- Validation Through Practical Application: Through the application to the photovoltaic site selection problem, this paper demonstrates the superiority of the proposed algorithm in solving practical problems.
- Sensitivity Analysis and Comparative Analysis: This paper conducts a sensitivity analysis of the proposed algorithm and compares it with other existing group decision-making methods, further proving the superiority of the proposed method.
Other Valuable Information
This paper also discusses in detail the total ordering principle of trapezoidal intuitionistic fuzzy numbers, which can avoid ranking different fuzzy numbers equally in the decision-making process, thereby improving the accuracy of decisions. Additionally, the research in this paper provides new ideas and methods for future related studies, offering significant reference value.