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

Abstract

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. [ ,
 L U
 T T =
 ] [0.7,0.9]
 complex membership functions incorporating phase angles (e.g., [
 i
 
 L
 ,
 i
 e e 
 U
 ]
 "high yield stability"). Interval 
) 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.

DOI: 10.5281/zenodo.15733567