Comprehensive Ranking of Neutrosophic Data using Information Measures in AI-Based Multi Criteria Decision-Making Models

Abstract

In this research, a novel and inclusive framework involving existential set theory is pro posed with regard to uncertainty of the single-valued neutrosophic environment where the existential set refers to an approach that emphasizes the most possible or dominant membership values, while the effects of non-membership and indeterminacy are indirectly handled through their complemented forms. This idea is motivated by the observation that traditional neutrosophic measures, such as distance and cardinality, directly use non membership and indeterminacy degrees, which often introduces ambiguity in accurate measurement. By focusing on what is most likely to exist rather than what is uncertain or absent, the existential approach improves the interpretability and realism of neutro sophic modeling. Fuzzy and other traditional models show a lot of difficulties in capturing the complexity of the uncertain or conflicting data. In order to have a solution to these constraints, a parametric family of cardinality measure which is referred to as Paramet ric Class of Existential Weighted Average Cardinality is derived. It can be applied to single-valued neutrosophic sets and generalized neutrosophic trapezoidal numbers, allow ing comparing the entire neutrosophic data of different shapes and forms, including exist ing degrees of membership through adding the existential levels of membership to enhance interpretability and realism. Toenhancethemodelingofhumanjudgmentandbehavior, aparametricfamilyoffuzzy distance measures named the Multivariate Neutro-Existential Minkowski Distance is proposed. Building on this, a new confidence-based metric, Confidence Existential De gree, is designed to reflect cognitive attitudes such as optimism, pessimism, and neutrality.