Decision-Making Modeling in Agro-Food Systems Using Type-2 Interval-Valued Linguistic Complex Neutrosophic Sets

Neutrosophic sets are a strong mathematical framework for representing decision-making uncertainty, ambiguity, and indeterminacy. They have three separate membership functions: truth (T), falsity (F), and indeterminacy. Neutrosophic sets and their extensions, such as complex neutrosophic sets, interval neutrosophic sets, and interval-valued complex neutrosophic sets, provide a versatile foundation for addressing multidimensional uncertainties in real-world applications [1]. However, numerical numbers for membership degrees sometimes fail to reflect decision-makers' subjective language preferences. Linguistic variables have been incorporated into the neutrosophic framework to convert qualitative assessments (e.g., "high risk," "moderate yield") into more structured, quantitative representations, often utilizing interval-valued or complex-number formats. This study presents the Type-2 Interval-Valued Linguistic Complex Neutrosophic Set, a new model. This enhanced extension enhances the flexibility and precision of agro-food choice analysis. It utilizes interval-valued linguistic terms to model truth, indeterminacy, and falsity (e.g. [ , ] [0.7,0.9] L U T T = "high yield stability"). Interval complex membership functions incorporating phase angles (e.g., [ , ] L U i i e e   ) are employed to represent spatiotemporal or contextual variations (e.g., seasonal droughts), while type-2 fuzzy logic is used to capture hierarchical uncertainties in linguistic evaluations. These elements provide a comprehensive and adaptable solution to the inherent ambiguity and complexity of real-world agriculture and food system decision-making.