Optimal Interaction Priority Calculation From Hesitant Fuzzy Preference Relations Based on the Monte Carlo Simulation...

Area of Science:

• Decision Sciences
• Operations Research
• Fuzzy Mathematics

Background:

• Traditional consistency testing for preference relations often requires complete data and strict adherence to consistency rules.
• Hesitant fuzzy preference relations (HFPRs) offer a more flexible way to represent uncertain preferences but require specific consistency measures.
• Existing methods may not adequately handle incomplete data or situations where perfect consistency is not feasible or necessary.

Purpose of the Study:

• To introduce a stepwise optimization model-based method for testing Acceptable Additive Consistency (AAC) in HFPRs.
• To define AAC for HFPRs and develop models for handling incomplete HFPRs (iHFPRs).
• To provide methods for revising inconsistent HFPRs, minimizing adjustments, and achieving consensus in Group Decision Making (GDM).

Main Methods:

• Developed a stepwise optimization model for testing AAC of HFPRs.
• Constructed optimization models to complete iHFPRs and revise unacceptably consistent HFPRs, maximizing Ordinal Consistency (OC).
• Utilized distance measures for determining weights of HFPRs and decision makers (DMs), and employed Monte Carlo simulations to study consistency and consensus thresholds.

Main Results:

• A novel AAC concept for HFPRs was defined and tested.
• Optimization models were proposed for completing iHFPRs and revising inconsistent relations while preserving OC.
• A GDM algorithm integrating HFPRs, DM weighting, and consensus models was presented and validated through an example.

Conclusions:

• The proposed stepwise optimization method effectively addresses the need for acceptable consistency in HFPRs, even with incomplete data.
• The developed models enhance the revision process by minimizing changes and maximizing ordinal consistency, facilitating better GDM.
• The new procedure offers an efficient and practical approach for handling hesitant fuzzy preference relations in complex decision-making scenarios.