Applying TOPSIS to Water Resource Decisions: A Practical Checklist

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Water resource development rarely involves a single objective. A dam site may offer high storage potential but also involve high construction costs, sedimentation risk, ecological disturbance, or social impacts. A treatment technology may achieve excellent pollutant removal while demanding too much energy. TOPSIS helps decision-makers examine such trade-offs systematically by identifying the alternative closest to an ideal solution and farthest from a negative-ideal solution.[^1][^2]

This checklist is useful for students, researchers, engineers, and planners who want to apply TOPSIS correctly and transparently to problems such as dam-site selection, reservoir prioritization, groundwater-recharge planning, irrigation development, water-treatment technology selection, and watershed management. TOPSIS and its hybrid variants have been used in reservoir assessment, regional water-security evaluation, water-quality assessment, and water-management strategy ranking.[^3][^4][^5][^6]

Why use a checklist?

A TOPSIS calculation can look simple once the equations are available. However, an apparently correct ranking can still be misleading if the alternatives are poorly defined, a cost criterion is mistakenly treated as a benefit, criteria overlap, weights are unsupported, or the result is not tested for sensitivity. A checklist therefore does more than prevent calculation errors: it improves transparency, reproducibility, and confidence in the final recommendation.

The TOPSIS idea

TOPSIS evaluates every alternative in relation to two hypothetical reference points. The positive ideal solution contains the most desirable performance for every criterion, while the negative-ideal solution contains the least desirable performance. The preferred alternative should have the smallest distance from the positive ideal and the greatest distance from the negative ideal.[^2][^7][^8]

The standard workflow is:

1. Construct the decision matrix.

2. Normalize the criterion values.

3. Apply criterion weights.

4. determine the positive and negative ideal solutions.

5. Calculate separation distances.

6. Compute the relative closeness coefficient.

7. Rank the alternatives.[^1][^9][^10]

Application checklist

Problem framing

Start by writing one precise decision statement. For example: “Select the most suitable dam site among five candidate locations while considering hydrological, geological, economic, environmental, and social criteria.” Identify the study area, planning period, decision authority, stakeholders, constraints, and intended use of the ranking.

Check:

• Is the decision objective stated clearly?

• Are the alternatives feasible, distinct, and comparable?

• Are legal, environmental, engineering, and budget constraints identified?

• Is the spatial and temporal scope fixed?

Alternative selection

TOPSIS ranks the alternatives included in the model; it does not automatically determine whether an excluded alternative would have been better. Candidate options should therefore be generated through field surveys, GIS screening, hydrological modelling, expert consultation, or preliminary feasibility analysis before ranking begins.

Check:

• Is each alternative described consistently?

• Have clearly infeasible options been screened out?

• Is the number of alternatives sufficient for a meaningful decision?

• Can every alternative be assessed against every selected criterion?

Criteria selection

Criteria should represent all important dimensions of the water resource problem without unnecessary duplication. Depending on the application, these may include water availability, storage capacity, groundwater potential, geology, topography, sediment load, water quality, cost, energy use, ecological impact, land requirements, social acceptance, equity, reliability, and climate resilience. Water-resource vulnerability research has combined water-quantity and water-quality indicators with hydrological, environmental, and socioeconomic data, illustrating the breadth of criteria that may be relevant.[^11]

Check:

• Does each criterion directly support the decision objective?

• Are technical, economic, environmental, and social dimensions represented?

• Are correlated or overlapping criteria identified?

• Is every criterion measurable or scorable?

• Has the criteria set been reviewed by domain experts and stakeholders?

Benefit and cost classification

Every criterion must be classified according to preference direction. A benefit criterion is one for which a higher value is preferred, such as storage capacity, water yield, removal efficiency, or reliability. A cost criterion is one for which a lower value is preferred, such as capital cost, energy consumption, pollutant concentration, environmental damage, or travel distance.[^2][^12]

Check:

• Is the preference direction of each criterion unambiguous?

• Does the classification reflect the actual decision context?

• Have negatively worded indicators been reviewed carefully?

• Is the classification documented beside the decision matrix?

Data collection

Construct the decision matrix with alternatives in rows and criteria in columns. Data may come from field observations, laboratory measurements, GIS and remote-sensing layers, hydrological simulation, government databases, stakeholder surveys, or expert assessment. Document the source, year, unit, spatial resolution, processing method, and uncertainty of every value.

Check:

• Are all data traceable to credible sources?

• Are units consistent within each criterion?

• Are missing values handled transparently?

• Are outliers and data-entry errors checked?

• Do all observations refer to compatible periods and spatial scales?

Criteria weighting

Weights represent the relative influence of criteria on the final ranking. They may be assigned through AHP, expert elicitation, entropy weighting, BWM, equal weighting, or hybrid procedures. Water-resource vulnerability studies have demonstrated that different subjective and objective weighting methods can produce different spatial patterns, especially for water-quality assessments, making the choice of weights an important modelling decision.[^11]

Check:

• Is the weighting method suitable and explained?

• Do all weights sum to 1?

• Are expert participants sufficiently qualified and diverse?

• Is consistency checked when using pairwise comparisons?

• Are alternative weight scenarios prepared for sensitivity analysis?

Normalization

Normalization converts criteria measured in different units into comparable dimensionless values. Under vector normalization,

$$r_{ij}=\frac{x_{ij}}{\sqrt{\sum_{i=1}^{m}x_{ij}^{2}}}$$

where $x_{ij}$ is the performance of alternative $i$ under criterion $j$. Normalization is essential because a criterion expressed using large numerical units could otherwise dominate the distance calculation.[^1][^12]

Check:

• Is one normalization rule applied consistently?

• Is the selected rule appropriate for the data distribution?

• Have zero and negative values been considered?

• Are intermediate normalized values retained for auditing?

Weighted matrix

Multiply each normalized value by the corresponding criterion weight:

$$v_{ij}=w_jr_{ij}$$

The resulting weighted normalized matrix represents both the performance of alternatives and the importance assigned to each criterion.[^13][^12]

Check:

• Is the correct weight applied to each column?

• Do criterion labels remain aligned during spreadsheet calculations?

• Are formulas copied correctly for all alternatives?

• Has the weighted matrix been independently checked?

Ideal solutions

For each benefit criterion, the positive ideal is the maximum weighted value and the negative ideal is the minimum. For each cost criterion, the positive ideal is the minimum weighted value and the negative ideal is the maximum.[^2][^7][^12]

Check:

• Are benefit and cost rules applied in the correct direction?

• Does the positive-ideal profile make engineering sense?

• Does the negative-ideal profile represent the least desirable combination?

• Are the ideal values taken from the weighted normalized matrix?

Separation measures

Calculate each alternative’s Euclidean distance from the positive and negative ideal solutions:

$$D_i^{+}=\sqrt{\sum_{j=1}^{n}(v_{ij}-v_j^{+})^2}$$

$$D_i^{-}=\sqrt{\sum_{j=1}^{n}(v_{ij}-v_j^{-})^2}$$

These distances show how close each alternative is to the best attainable criterion profile and how far it is from the worst profile.[^1][^9][^12]

Check:

• Are distances calculated across all criteria?

• Are squared differences summed before taking the square root?

• Are positive- and negative-ideal distances stored separately?

• Have the calculations been checked using a second tool or manual example?

Closeness and ranking

Compute the relative closeness coefficient:

$$C_i^{*}=\frac{D_i^{-}}{D_i^{+}+D_i^{-}}$$

The coefficient ranges from 0 to 1, and a higher value indicates a stronger preference. Alternatives are ranked in descending order of $C_i^{*}$.[^1][^12][^10]

Check:

• Does every coefficient lie between 0 and 1?

• Are alternatives ranked from highest to lowest coefficient?

• Are ties or very small score differences reported?

• Is the ranking interpreted as decision support rather than an unquestionable answer?

Sensitivity analysis

A final ranking should not be accepted without testing its stability. Change important criterion weights, apply alternative weighting methods, or adjust uncertain performance values and then recompute the rankings. Sensitivity analysis is commonly performed by perturbing weights and checking whether rankings remain stable.[^14][^15][^16]

Check:

• Has each influential weight been increased and decreased?

• Do weights remain normalized after each change?

• Does the best alternative remain first across plausible scenarios?

• Are rank reversals and critical weight thresholds reported?

• Have close-ranking alternatives received additional investigation?

Validation and reporting

Compare the ranking with expert judgment, field observations, previous studies, engineering feasibility, or the output of another MCDM method. Report assumptions, data limitations, excluded criteria, normalization and weighting choices, closeness coefficients, sensitivity results, and stakeholder concerns. A transparent report allows another analyst to reproduce the result and understand why a particular alternative was preferred.

Check:

• Has the result been reviewed by domain experts?

• Is the top-ranked option practically feasible?

• Are uncertainty and limitations stated clearly?

• Are decision matrices and intermediate calculations available?

• Can another researcher reproduce the complete ranking?

Common mistakes

The most common problems are reversing benefit and cost criteria, using weights that do not sum to 1, mixing units without normalization, selecting redundant criteria, rounding intermediate values too early, ignoring data uncertainty, and presenting rankings without sensitivity analysis. Another concern is rank reversal: adding or removing an alternative can sometimes change the relative ordering of existing alternatives, so the final set of alternatives and normalization approach should be justified.[^13]

Final takeaway

TOPSIS is valuable because it converts a complex multi-criteria problem into an understandable ranking, but the quality of that ranking depends on the quality of problem formulation, data, weights, calculations, and validation. A structured checklist keeps attention on these decisions instead of treating TOPSIS as a purely mechanical formula. Used carefully, it can provide a transparent and defensible foundation for selecting water-resource projects, sites, technologies, and management strategies.

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References

1. Original Research Article A comprehensive guide to the TOPSIS ...

2. MULTI-CRITERIA DECISION MAKING MODELS BY APPLYING THE TOPSIS ...

3. Ranking water-scarcity management strategies using the TOPSIS ... - TOPSIS is frequently used to rank water management strategies, such as water conservation initiative...

4. A TOPSIS-Based Multicriteria Approach for Reservoir Assessment - Water management in the Brazilian semi-arid region has been, for decades, a challenge for institutio...

5. Regional Water Resources Security Evaluation Based on a Hybrid Fuzzy BWM-TOPSIS Method - Nowadays, water resource security is becoming increasingly prominent, and this problem is a primary ...

6. Assessment of Water Quality using Fuzzy-AHP and TOPSIS

7. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056

8. Decision

9. [PDF] TOPSIS Techniques on Picture Fuzzy Soft Sets - Engineering Letters

10. Table 4. - Nurse turnover intention poses a significant challenge to healthcare systems, particularly in hospit...

11. Multi-Criteria Assessment of Spatial Robust Water Resource Vulnerability Using the TOPSIS Method Coupled with Objective and Subjective Weights in the Han River Basin - This study developed a multi-criteria approach to spatially assess the robust water resource vulnera...

12. Research Article

13. Resolving Rank Reversal in TOPSIS: A Comprehensive ... - This paper examines ranking reversal (RR) in Multiple Criteria Decision Making (MCDM) using the Tech...

14. A Generalised Fuzzy TOPSIS with Improved Closeness Coefficient

15. An integrated TOPSIS framework with Full-Range Weight ...

16. A dual hesitant fuzzy entropy-TOPSIS framework for multi ... - The rapid evolution of E-learning platforms in dental education is a multi-criteria decision problem...

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