Table 2 Merits of the proposed FST vs. IVHFE–ELECTRE along key comparison parameters.

Modeling of uncertainty

Interval-valued hesitant fuzzy evaluations capture multiple possible membership degrees per entry and their uncertainty ranges; expert weights by extended PSI; criteria weights by maximizing deviation; outranking uses indifference/preference/veto thresholds.³⁴

Tensorized fuzzy-soft representation; native support for multiple experts and criteria with plug-in weights (entropy/AHP/risk-aware). In the revised version, FST also accepts interval/hesitant inputs and can invoke an optional outranking stage.

Handling incomplete information

Can operate with partial or imprecise evaluations via IVHF structures, but typically encourages completion before outranking³⁴

Supports bounded/interval fuzzification for missing entries or low-rank tensor completion; reports completeness diagnostics before aggregation.

Group aggregation and conflict

Late aggregation + outranking preserves individuality; thresholds control strictness and veto power³⁴

Aggregation is explicit and modular; consensus indices and late-fusion scoring are available. Optional outranking (ELECTRE-like) can be plugged in to handle conflicting judgments with veto behavior.

Dynamics/time-varying contexts

Primarily static (single-shot evaluation).

Extendable to time-aware tensors \(\mathcal {X}\in [0,1]^{m\times n\times k\times T}\) with dynamic entropy for criteria and similarity-based expert weights.

Interpretability

High, but requires tuning thresholds (indifference, preference, veto) and explaining IVHF semantics.³⁴

High; operations (weighting, aggregation, scoring) are auditable per mode. When outranking is used, threshold choices are localized to the final stage.

Computational complexity (big-O; m alts, n crit., k experts, h avg. hesitant terms)

Construction of concordance/discordance and pairwise outranking yields \(\mathcal {O}(k\,h\,m^{2}n)\) time and \(\mathcal {O}(m^{2})\) space for matrices, before thresholding and ranking index.³⁵

Core tensor weighting + aggregation is \(\mathcal {O}(k\,m\,n)\) time and \(\mathcal {O}(k\,m\,n)\) space. Optional outranking on top of FST adds \(\mathcal {O}(m^{2}n)\) but can be limited to shortlisted alternatives.