An extended TDM method under probabilistic interval-valued hesitant fuzzy environment for stock selection

Area of Science:

• Decision Sciences
• Fuzzy Set Theory
• Financial Risk Management

Background:

• Real-world decision-making often requires evaluating alternatives based on limited information, focusing on potential risks or gains.
• Traditional methods may use all data, but decision-makers sometimes prefer insights from

Purpose of the Study:

• To introduce and evaluate Deemed Value at Risk (DVaR) and Reckoned Value at Risk (RVaR) for measuring tail information within the probabilistic interval-valued hesitant fuzzy set (PIVHFS) environment.
• To develop a novel group decision-making model utilizing PIVHFS and tail information for selecting optimal alternatives.
• To demonstrate the practicality and effectiveness of the proposed methods through a real-world stock selection case study.

Main Methods:

• Introduction of Value at Risk (VaR) from finance and probabilistic interval-valued hesitant fuzzy set (PIVHFS) as a generalization of probabilistic hesitant fuzzy set (PHFS).
• Proposal and theoretical validation of Deemed Value at Risk (DVaR) and Reckoned Value at Risk (RVaR) for PIVHF environments.
• Development of a complete group decision-making model based on PIVHFS and tail information analysis.
• Application and validation using a stock selection example with comparative analysis against existing methods.

Main Results:

• Reckoned Value at Risk (RVaR) is demonstrated to be more effective than Deemed Value at Risk (DVaR) in differentiating probabilistic interval-valued hesitant fuzzy elements.
• The proposed group decision-making model successfully identified optimal stock alternatives based on different certainty degrees using both DVaR and RVaR.
• The RVaR method showed distinct results compared to DVaR, with E4 consistently selected as the best alternative and E2 as the worst across various certainty levels.

Conclusions:

• The proposed DVaR and RVaR metrics provide valuable tools for decision-making under uncertainty using tail information within PIVHFS.
• The novel group decision-making model offers an effective framework for selecting optimal alternatives when focusing on limited, critical information.
• The study highlights the practical applicability and superiority of RVaR over DVaR for specific decision-making scenarios in financial contexts.