A novel approach for arithmetic operations and ranking of generalized fuzzy numbers with application

Abstract

This study presents a novel approach to arithmetic operations and ranking of Generalized Fuzzy Numbers (GFNs) for decision-making under uncertainty. Traditional methods often yield irrational outputs when dealing with GFNs, especially in complex situations where precision and clarity are paramount. Our approach is based on the algebraic product and sum, allowing more accurate handling of GFNs with different heights. This height variation in GFNs is crucial as it represents the confidence or buoyancy of decision-makers judgments. Recognizing the inadequacies in existing ranking methods for GFNs, which often have significant shortcomings despite minor advantages, our model introduces a new ranking method. This method utilizes the algebraic sum of self-paired components of the GFNs, ensuring a more effective and precise ranking under uncertainty. The paper demonstrates the superiority of this new approach through a comparative analysis. This analysis reveals that our arithmetic model for GFNs effectively overcomes the issue of producing similar outputs for different inputs, a common problem in previous methods. Moreover, our ranking method shows clear advantages over existing approaches, particularly in dealing with the nonspecificity-based uncertainty measure, which adds a layer of precision previously unattainable. The practical applicability of our methods is further highlighted through various multicriteria decision-making problems. Examples include selecting a suitable car for an individual, choosing an efficient robot for an automobile company, and finding the most appropriate antivirus face mask as a preventive measure against the COVID-19 pandemic. These examples validate the usefulness and effectiveness of our proposed arithmetic operations and ranking techniques in real-world scenarios. The new models for arithmetic and ranking of GFNs presented in this paper promise significant improvements in rational decision-making across diverse fields. By addressing the limitations of previous methods and offering more precise and reliable tools, this research is poised to benefit the broader research community and practitioners in decision-making under uncertainty.