Since its inception, fuzzy set theory has been widely used to model uncertainty and imprecision in decision-making. However, conventional fuzzy sets, often referred to as type-1 fuzzy sets (T1FSs), have limitations in capturing higher levels of uncertainty, particularly when decision-makers (DMs) express hesitation or ambiguity in membership degrees. To address this, interval type-2 fuzzy sets (IT2FSs) have been introduced by incorporating uncertainty in membership degree allocation, enhancing flexibility in modeling subjective judgments. Despite their advantages, existing IT2FS construction methods often lack active involvement from DMs, which limits the interpretability and effectiveness of decision models. This study proposes a novel socio-technical co-constructive approach for developing IT2FS models of linguistic terms by facilitating the active involvement of DMs in preference elicitation and applies it to multicriteria decision-making (MCDM) problems. Our method is structured in two phases. The first phase involves an interactive process between the DM and the analyst, in which a modified version of the deck of cards (DoC) method is proposed to construct T1FS membership functions on a ratio scale. We then extend this method to incorporate ambiguity in subjective judgments, resulting in an IT2FS model that better captures uncertainty in DMs’ linguistic assessments. The second phase formalizes the constructed IT2FS model for application in MCDM by defining a mathematical formalization of the fuzzy information, including aggregation rules and an admissible ordering principle. The proposed framework enhances both the reliability and effectiveness of fuzzy decision-making by capturing the personalized semantics of linguistic information. A numerical example and a practical case illustrate its real-world applicability. • Introduces a novel co-constructive approach for building IT2FSs with active involvement of decision-makers. • Proposes a two-phase framework combining a modified Deck-of-Cards method and formalization for MCDM. • Enhances interpretability and effectiveness of fuzzy decision-making with real-world applicability.
Dutta et al. (Sun,) studied this question.