Multicriteria Decision Making With Incomplete Weights Based on 2-D Uncertain Linguistic Choquet Integral Operators.

Area of Science:

• Decision Sciences
• Artificial Intelligence
• Operations Research

Background:

• Multicriteria decision making (MCDM) often involves complex data and uncertain criteria.
• Existing methods struggle with interactive criteria and incompletely known weights, especially with 2-D uncertain linguistic variables (2DULVs).

Purpose of the Study:

• To propose novel MCDM methods for problems with 2DULVs, interactive criteria, and unknown weights.
• To develop new operational laws for 2DULVs that respect linguistic term set boundaries.
• To introduce operators that effectively capture inter-criteria interactions and determine criteria weights.

Main Methods:

• Development of novel operational laws for 2DULVs.
• Introduction of four new operators: 2-D uncertain linguistic Choquet averaging (2DULCA), 2-D uncertain linguistic Choquet geometric (2DULCG), Shapley 2DULCA (S2DULCA), and Shapley 2DULCG (S2DULCG).
• Establishment of models using the maximization deviation approach and Shapley function for criteria weight determination.

Main Results:

• Proposed two novel MCDM methods tailored for 2-D uncertain linguistic environments.
• Demonstrated the applicability and effectiveness of the proposed methods through four illustrative examples.
• Comparative analysis highlighted the superior performance of the developed approaches.

Conclusions:

• The novel operational laws and operators provide robust tools for MCDM with 2DULVs.
• The proposed MCDM methods effectively address challenges of interactive criteria and unknown weights.
• The developed approaches offer significant advantages over existing methods in complex decision-making scenarios.