Implementation of the extended degree theory in the neutrosophic multicriteria method using three forms of aggregation: weighted sum, geometric mean and fuzzy techniques.

Abstract

The implementation of extended degree theory in the neutrosophic multicriteria approach, using three aggregation methods—weighted sum, geometric mean, and fuzzy techniques—offers a robust framework for addressing complexity and uncertainty in the decision-making process. This approach leverages neutrosophic theory's ability to handle truth, falsity, and indeterminacy through extended degree analysis, providing a more nuanced and accurate assessment of available alternatives. The weighted sum allows for the direct integration of the different degrees of importance of each criterion, facilitating the assignment of clear priorities and combining the assessments of the different criteria into a single quantitative result. The geometric mean, meanwhile, offers a balanced approach that minimizes the influence of extreme values ​​and ensures a more equitable representation of alternatives, capturing the complex interaction between criteria in neutrosophic contexts. Fuzzy techniques, by incorporating fuzzy logic, allow for the modeling of the uncertainty and vagueness inherent in qualitative assessments, providing an additional layer of flexibility in data interpretation. This integration of aggregation methods with extended degree theory not only improves the analysis's ability to adapt to dynamic and multifaceted decision environments but also facilitates the evaluation of varied scenarios with greater accuracy. By combining weighted sum, geometric mean, and fuzzy techniques within the neutrosophic framework, the multicriteria method provides a powerful and adaptable tool that effectively responds to the complexity and ambiguity of decision-making, offering a comprehensive and detailed view of the available alternatives.