Building Interval Type-2 Fuzzy Membership Function: A Deck of Cards based Co-constructive Approach
This work addresses the need for more interpretable and effective fuzzy decision models in multicriteria decision-making by actively involving decision-makers, though it appears incremental as it builds on existing IT2FS methods with a novel elicitation technique.
The study tackled the problem of limited decision-maker involvement in constructing Interval Type-2 Fuzzy Sets (IT2FSs) for handling uncertainty in decision-making by proposing a socio-technical co-constructive approach using a modified Deck-of-Cards method, resulting in enhanced reliability and effectiveness in modeling linguistic assessments for multicriteria decision-making.
Since its inception, Fuzzy Set has been widely used to handle 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 degree. To address this, Interval Type-2 Fuzzy Sets (IT2FSs) have been introduced by incorporating uncertainty in membership degree allocation, which enhanced flexibility in modelling subjective judgments. Despite their advantages, existing IT2FS construction methods often lack active involvement from DMs and that limits the interpretability and effectiveness of decision models. This study proposes a socio-technical co-constructive approach for developing IT2FS models of linguistic terms by facilitating the active involvement of DMs in preference elicitation and its application in multicriteria decision-making (MCDM) problems. Our methodology is structured in two phases. The first phase involves an interactive process between the DM and the decision analyst, in which a modified version of 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 judgment and that resulted in an IT2FS model that better captures uncertainty in DM's linguistic assessments. The second phase formalizes the constructed IT2FS model for application in MCDM by defining an appropriate mathematical representation of such information, aggregation rules, and an admissible ordering principle. The proposed framework enhances the reliability and effectiveness of fuzzy decision-making not only by accurately representing DM's personalized semantics of linguistic information.