Multidimensional Sustainability Framework

• Multidimensional Sustainability Frameworks are integrative systems that evaluate environmental, social, economic, and technical dimensions holistically without allowing one dimension to compensate for another.
• They employ structured indicator hierarchies and methodologies like SSP-AHP and Fuzzy-AHP to rigorously guide decision-making and policy design.
• Applied across sectors such as healthcare, infrastructure, and blockchain, these frameworks emphasize non-substitutability to achieve balanced sustainable development.

A multidimensional sustainability framework is a methodological structure that integrates multiple, non-reducible aspects of sustainability—typically including, but not limited to, environmental, social, economic, and sometimes technical dimensions—into a single, coherent system for evaluation, measurement, or decision-making. Such frameworks explicitly reject the notion that high performance in one sustainability area can simply compensate for poor performance in another, emphasizing non-substitutability and the need for holistic progress across all dimensions. The development and operationalization of these frameworks respond to the complexity and interdependence of contemporary sustainability challenges, supporting the design of integrated assessment tools, policy mechanisms, and empirical studies across sectors such as infrastructure, healthcare, governance, and software engineering.

1. Conceptual Foundations of Multidimensional Sustainability Frameworks

The core premise of multidimensional sustainability frameworks is that sustainability is not a univariate phenomenon. Instead, it is woven from several concurrent, equally essential dimensions. Early conceptualizations focused on the "three pillars" model—environmental, social, and economic sustainability (Eckstein et al., 2021); subsequent research extends this to include technical or governance dimensions as appropriate to specific domains (McGuire et al., 2023). The fundamental principle is non-compensability: an entity (e.g., a country, organization, or project) that excels in economic efficiency but suffers from severe environmental or social deficits is not "sustainable" overall.

Frameworks operationalize this logic by:

• Explicitly defining each dimension with its own set of indicators or criteria.
• Structuring these indicators hierarchically or as groups—sometimes with explicit weighting, but under "strong sustainability," with mechanisms that prevent full compensability (Wątróbski et al., 2023).
• Employing normalization, scoring, and aggregation methods that respect dimension boundaries and analytic rigor (Farahdel et al., 7 Mar 2024).

2. Methodological Approaches and Formalization

Multiple mathematical and algorithmic tools underpin multidimensional sustainability frameworks:

a) Indicator Selection and Hierarchy: Indicators are chosen using a combination of literature review, stakeholder interviews, and standard-based criteria sets (e.g., GRI, ISO) (Farahdel et al., 7 Mar 2024). Indicators are then organized in a hierarchical manner (dimensions → domains → sub-domains → metrics), as seen in SSP-AHP frameworks for healthcare (Wątróbski et al., 2023) and SCAIS for AI systems (Rohde et al., 2023).

b) Scoring, Weighting, and Aggregation:

• Strong Sustainability Paradigm (SSP-AHP): This extends the Analytical Hierarchy Process by adding a sustainability coefficient that penalizes unbalanced performance, ensuring that high achievement in one domain cannot fully offset poor achievement in another. The normalization formula for a "profit-type" criterion is:

$$r_{ij} = \frac{x_{ij} - \min_{i}(x_{ij})}{\max_{i}(x_{ij}) - \min_{i}(x_{ij})}$$

And the utility of alternative $i$ is:

$U_i = \sum_{j=1}^n b_{ij} w_j$

where $b_{ij}$ adjusts for deviation via a sustainability coefficient $s$:

$b_{ij} = r_{ij} - s \cdot d_{ij}$

(Wątróbski et al., 2023)

• Fuzzy-AHP and Hybrid MCDM Methods: Fuzzy Analytic Hierarchy Process and hybrid models accommodate uncertainty and interdependencies, integrating methods such as DEMATEL and VIKOR for causal mapping and compromise ranking (Farahdel et al., 7 Mar 2024).
• Dynamic/Multivariate Learning: Multivariate tree boosting and spatiotemporal clustering approaches can model correlated sustainability outcomes simultaneously and identify clusters or trajectories in multidimensional sustainability space (Obringer et al., 2019, Morelli et al., 30 May 2024).

3. Domain-Specific Implementations

a) Environmental and Multidimensional Poverty Measurement

A major application in poverty studies extends the welfare-rights framework to include not only social and economic deprivation but also environmental deprivation—partitioned into sub-indicators for ecosystem health (e.g., water, energy, biodiversity poverty), environmental health (e.g., respiratory and spatial health, waste management), and vulnerability to climate change. Each is measured via binary thresholds on availability, quality, and access, and aggregated with other dimensions using well-defined logical structures (OR/AND) (Pérez-Cirera et al., 2017):

• Water poverty indicator:

$$WAT\_POV\_I = \begin{cases} 1, & \text{if } Wat_{avail}=1 \text{ or } Wat_{effacc}=1 \text{ or } Wat_{qual}=1 \ 0, & \text{otherwise.} \end{cases}$$

4. Trade-off Management, Interdependencies, and Non-Substitutability

Multidimensional frameworks recognize and rigorously handle trade-offs and interdependencies between indicators. For example:

• Trade-off Mapping: In software architecture, the Sustainability Impact Score (SIS) framework explicitly quantifies positive and negative impacts of quality attribute (QA) trade-offs across technical, social, economic, and environmental dimensions. Impacts are weighted by risk and importance to assess overall sustainability support or harm, formalized as:

$$SIS_{dim_1, dim_2} = \sum_{i,j} (Priority_{dim_1,i} + Priority_{dim_2,j}) \times Impact_{ij}$$

Normalized for comparability (Fatima et al., 28 Jan 2025).

• Interdependency Analysis: DEMATEL and related approaches construct direct-relation and total-relation matrices to reveal cause-effect relationships between indicators, which is essential in dynamic SAF applications (Farahdel et al., 7 Mar 2024).
• Non-Substitutability Enforcement: The use of sustainability coefficients in methods such as SSP-AHP penalizes alternatives that are imbalanced, favoring well-rounded sustainability profiles over skewed ones (Wątróbski et al., 2023).

5. Applications and Case Studies across Sectors

Multidimensional sustainability frameworks have been operationalized in a range of empirical contexts:

• Urban and Infrastructure Systems: Multivariate modeling predicts and links multiple interdependent outcomes (e.g., damage rate, death rate, recovery time) under environmental stressors (e.g., tsunamis, hurricanes) to identify key environmental predictors and intervention trade-offs (Obringer et al., 2019, Kays et al., 2022).
• Healthcare Systems: Social sustainability is decomposed into equity, quality, responsiveness, financial coverage, and adaptability, with indicators benchmarked using non-compensatory multicriteria analysis (SSP-AHP), showing Nordic countries consistently outperforming in balanced sustainability (Wątróbski et al., 2023).
• Software and AI: Sustainable software engineering frameworks separate product and process sustainability, emphasizing stratification (micro–macro levels) and multisystemic emergence, while AI sustainability is addressed via the SCAIS indicator set spanning governance, social, ecological, and economic impacts (McGuire et al., 2023, Rohde et al., 2023, Samarawickrama, 2022).
• Blockchain/Web3: Blockchain-based carbon offset platforms embody multidimensionality via physical–technological–societal layers, with distinct utilities (recording/tracking, verification, trading, dissemination) and non-reducible criteria for economic, technical, and environmental sustainability (Zhou et al., 2023, Meneguzzo et al., 15 Apr 2025).
• Economic Complexity and Development: Aligning product-level complexity with environmental and social outcome indices (PSPI, PEPI) reveals that while high-income countries’ diversification pathways are often environmentally aligned, developing countries’ accessible options are less so, highlighting the necessity and difficulty of pursuing "unrelated diversification" for sustainable development (Wettinck et al., 22 Sep 2025).

Domain	Dimensions Integrated	Notable Methods/Models
Poverty	Social, Economic, Environmental	Binary sub-indicators, Rights-based
Healthcare	Equity, Quality, Responsiveness,	SSP-AHP, Hierarchical weighting
	Financial, Adaptability
Software/AI	Social, Economic, Environmental,	SCAIS, Process–Product distinction
	Technical, Governance	Stratified, Multisystemic models
Infrastructure	Environmental, Social, Economic,	Multivariate modeling, Interdependency mapping
	Resilience
Economic Dev.	Complexity, Social, Environmental	PCI, PSPI, PEPI, Alignment slopes

6. Challenges, Limitations, and Research Frontiers

Despite their promise, existing multidimensional sustainability frameworks face limitations:

• Empirical Imbalance: Many fields are biased toward conceptual/theoretical or product-centric studies, with few controlled experiments rigorously quantifying process interventions (McGuire et al., 2023).
• Static Methods: Traditional aggregation and interdependency mapping methods (AHP, DEMATEL) often lack adaptive dynamism required for rapidly evolving organizational contexts (Farahdel et al., 7 Mar 2024).
• Subjectivity in Weighting/Normalization: Fuzzy and hybrid MCDM models address subjectivity and uncertainty in expert judgments, but require substantial expertise for implementation and tuning (Farahdel et al., 7 Mar 2024).
• Scalability and Sector-Specificity: Adapting models across sectors—supply chain, software, decentralized governance—demands sector-specific indicator sets and constant recalibration.
• Policy Implications: For lower-income countries and under-resourced systems, opportunity alignment is naturally skewed toward less sustainable diversification paths, suggesting the need for policy support for unrelated or leapfrogging strategies (Wettinck et al., 22 Sep 2025).

7. Synthesis and Outlook

Multidimensional sustainability frameworks underpin contemporary assessment and decision-making for sustainable development. By integrating multiple domains, enforcing non-substitutability, and formalizing trade-off analysis, these frameworks enable rigorous measurement, benchmarking, and strategy formulation across a range of domains. Ongoing research is focused on dynamic, adaptive models (potentially embedding AI/ML), deeper empirical validation, and expanded indicator structures to reflect evolving technical, governance, and policy landscapes. Progress in these areas promises to further refine the science and practice of sustainability assessment at global, organizational, and system levels.