Consensus-based Deck of Cards Method for Constructing Fuzzy Linguistic Scales

Bibliographic Data

ID21585253
AuthorsDiego García-Zamora (Universidad de Jaén, corresponding author), Bapi Dutta (0000-0002-2796-8914, Universidad de Jaén), José Rui Figueira (0000-0001-9822-1167, University of Lisbon)
Year2026
Volume35
Issue3
Publication date2026-09-01
Open AccessYes
TypeARTICLE
VenueGroup Decision and Negotiation (JOURNAL)
Journal identifiersISSN: 0926-2644 • E-ISSN: 1572-9907
PublisherSpringer Science and Business Media LLC (PUBLISHER)
DOI10.1007/s10726-026-10008-x
OpenAlexW7167833919
LanguageEN
References cited25

The construction of the semantics of fuzzy linguistic scales is a crucial task in decision analysis, as it requires translating decision-makers’ qualitative perceptions into quantitative representations. While recent approaches such as the Deck of Cards Method for Membership Function construction (DoC-MF) have enhanced interpretability and cognitive transparency, they remain limited to individual elicitation. In many real-world settings, however, fuzzy linguistic models must reflect the shared semantic understanding among decision-makers, calling for mechanisms that reconcile heterogeneous judgments without compromising semantic meaning. This paper proposes a consensus-based extension of the Deck of Cards Method for group decision-making. The approach introduces an optimization-based consensus protocol, denoted (C–DoC), that guides experts toward agreement by making minimal adjustments to their individual assessments. The protocol is applied across four stages: (i) building an agreed value scale, (ii) defining the cores of fuzzy levels, (iii) determining their supports, and (iv) shaping the left and right-hand sides of the membership functions using a ratio-based version of the DoC. Each stage combines human interpretability with mathematical rigor, ensuring that the resulting fuzzy scales are both semantically coherent and collectively validated. The resulting framework bridges the gap between fuzzy linguistic modeling and agreed scales by embedding interpretability and fairness within an optimization-driven process

Fuzzy logic · Fuzzy set · Hierarchy · Interpretability · Membership function · Cognitive Science and Mapping · Multi-Criteria Decision Making · Qualitative Comparative Analysis Research

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