A Decision-Making Model with Cloud Model, Z-Numbers, and Interval-Valued Linguistic Neutrosophic Sets

Area of Science:

• Decision Sciences
• Information Science
• Artificial Intelligence

Background:

• Interval-valued linguistic neutrosophic sets (IVLNSs), Z-numbers, and trapezium clouds are key for modeling uncertainty.
• Existing methods face challenges in accurately quantifying and processing complex uncertain information.

Purpose of the Study:

• To develop a novel Z-interval-valued linguistic neutrosophic set-trapezium-trapezium cloud (Z-IVLNS-TTC) model.
• To integrate IVLNSs and Z-numbers for enhanced expression of uncertainty.
• To minimize information loss and distortion in quantification.

Main Methods:

• A novel combination of IVLNSs and Z-numbers is introduced.
• The Z-IVLNS-TTC model is proposed for improved information representation.
• Objective weights are calculated using multi-objective programming (MOP).
• A p-norm based distance measure for Z-IVLNS-TTCs is developed, inspired by TOPSIS.

Main Results:

• The proposed Z-IVLNS-TTC model effectively reduces information loss and distortion.
• A new objective weight calculation method using MOP is presented.
• A novel distance measure enhances comparison of uncertain information.
• The method demonstrates practical applicability in group decision-making.

Conclusions:

• The Z-IVLNS-TTC model offers a robust framework for handling complex uncertainty.
• The developed methods provide effective tools for decision-making under uncertainty.
• Sensitivity analysis and comparisons confirm the method's effectiveness and feasibility.