Belief and Possibility Belief Interval-Valued N-Soft Set and Their Applications in Multi-Attribute Decision-Making...

Area of Science:

• Mathematical analysis
• Decision theory
• Uncertainty quantification

Background:

• Soft set theory offers a framework for handling uncertainty.
• N-soft set theory enhances precision and uncertainty management compared to soft sets.
• Existing theories lack robust methods for integrating possibility and belief intervals in decision-making.

Purpose of the Study:

• Introduce and define possibility belief interval-valued N-soft sets.
• Extend the belief interval-valued soft set concept.
• Develop and validate algorithms for decision-making under uncertainty.

Main Methods:

• Defined theoretical notions for possibility belief interval-valued N-soft sets.
• Established algebraic operations and fundamental properties.
• Developed two decision-making algorithms using max-AND and min-OR operations.

Main Results:

• Successfully defined possibility belief interval-valued N-soft sets and their operations.
• Demonstrated the theoretical underpinnings of the new concept.
• Validated the practical applicability of the developed algorithms through numerical examples.

Conclusions:

• Possibility belief interval-valued N-soft sets provide a powerful tool for decision-making in uncertain environments.
• The proposed algorithms effectively address complex decision problems.
• This research advances the application of N-soft set theory in handling nuanced uncertainties.