Building Interval Type-2 Fuzzy Membership Function: A Deck of Cards based Co-constructive Approach

2025-03-03

AI Summary

Existing interval type-2 fuzzy set (IT2FS) construction methods lack deep involvement of decision-makers, resulting in insufficient interpretability and semantic fidelity. This paper proposes a socio-technical co-construction paradigm, extending the enhanced Deck-of-Cards method to the interval type-2 domain to enable active decision-maker participation in constructing type-1 membership functions, thereby generating IT2FS structures that explicitly represent judgmental ambiguity. Key contributions include: (i) the first IT2FS co-construction methodology featuring deep decision-maker engagement; and (ii) a complete, mathematically rigorous IT2FS-based multi-criteria decision-making (MCDM) framework integrating ratio-scale membership function elicitation, aggregation rules, and a well-defined ranking relation. Experimental evaluation demonstrates that the approach significantly improves representation of expert subjective uncertainty and simultaneously enhances both semantic fidelity and decision robustness across multiple MCDM case studies.

Technology Category

• Reasoning under Uncertainty: Uncertainty Representations
• Knowledge Representation and Reasoning: Preferences
• Multiagent Systems: Multiagent Systems under Uncertainty

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

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.

Problem

• Addresses limitations of type-1 fuzzy sets in capturing uncertainty.
• Proposes a co-constructive approach for Interval Type-2 Fuzzy Sets.
• Enhances decision-making by involving decision-makers in model construction.

Innovation

• Deck-of-Cards method for T1FS construction
• Extension to IT2FS for capturing uncertainty
• Socio-technical co-constructive approach for MCDM