Interval-valued distributed preference relation and its application to group decision making.

Area of Science:

• Decision Sciences
• Operations Research
• Artificial Intelligence

Background:

• Distributed preference relation (DPR) models preferences but is limited when precise data is unavailable.
• Decision makers often face uncertainty due to lack of knowledge, experience, or data.
• Existing methods struggle to represent uncertain preference degrees simultaneously.

Purpose of the Study:

• To propose interval-valued distributed preference relations (IDPR) to address data uncertainty in preference modeling.
• To develop methods for transforming IDPR into comparable score matrices for decision analysis.
• To apply IDPR to solve complex multiple criteria group decision making (MCGDM) problems.

Main Methods:

• Introduced interval-valued distributed preference relations (IDPR) and defined its properties (validity, normalization).
• Developed two optimization models to convert IDPR matrices into score matrices.
• Analyzed score matrix properties and introduced additive consistency for rational comparisons.
• Applied the IDPR framework to MCGDM, analyzing individual and group consistency parameters.

Main Results:

• IDPR effectively represents uncertain preference degrees between alternatives.
• The proposed optimization models successfully transform IDPR into a usable score matrix.
• Additive consistency ensures the rationality of comparisons derived from the score matrix.
• The IDPR approach was successfully applied to a manager selection MCGDM problem.

Conclusions:

• IDPR provides a robust framework for decision-making under uncertainty where precise preferences are unknown.
• The developed methods enable quantitative comparison of alternatives using interval preference data.
• IDPR offers a valuable tool for addressing MCGDM problems with incomplete or uncertain information.