Comparative Framework for Climate-Responsive Selection of Phase Change Materials in Energy-Efficient Buildings

Abstract

Integrating phase change materials (PCMs) into buildings and HVAC systems improves thermal comfort and energy efficiency. This study presents a climate-responsive methodology for selecting optimal PCMs using a multi-criteria decision-making (MCDM) framework. AHP was employed to determine the relative importance of key thermophysical properties, including melting point (47.5%), latent heat of fusion (25.7%), volumetric latent heat (13.5%), thermal conductivity (6.8%), specific heat capacity (3.3%), and density (3.3%). These weights were applied across five MCDM techniques—COPRAS, VIKOR, TOPSIS, MOORA, and PROMETHEE II—to evaluate 16 PCM alternatives for three representative climate zones: temperate (18 °C), subtropical (23 °C), and tropical hot/desert (28 °C). The results consistently identified n-Heptadecane (C17) as the most suitable PCM for temperate and subtropical climates, while n-Octadecane (C18) and hydrated salts such as CaCl₂·6H₂O and Na₂CO₃·10H₂O were optimal for tropical zones. Results show that n-Heptadecane (C17) is optimal for temperate and subtropical zones (COPRAS K = 1.00; TOPSIS C = 0.79–0.82; PROMETHEE φ = 0.21–0.22), while n-Octadecane (C18) and hydrated salts such as CaCl₂·6H₂O and Na₂CO₃·10H₂O perform best in tropical climates (TOPSIS C = 0.85; PROMETHEE φ = 0.26). These PCMs offer high latent heat (up to 254 kJ·kg⁻¹) and volumetric storage (up to 381 MJ·m⁻³), enabling significant reductions in HVAC loads and improved indoor temperature stability. The convergence of rankings across methods and alignment with existing literature validate the robustness of the proposed approach. This framework supports informed material selection for sustainable building design and can be adapted to other climate-sensitive engineering applications. The framework introduces methodological innovations by explicitly mapping PCM melting points to climate-specific comfort bands, incorporating volumetric latent heat, and validating rankings through cross-method convergence (Spearman ρ > 0.99). Sensitivity analysis confirms robustness against weight perturbations. The approach supports practical PCM selection for both new and retrofit buildings, contributing to EU and US energy goals (e.g., 40% building energy use, DOE’s 50% reduction target).

1. Introduction

The building sector has been identified as one of the most critical areas for achieving substantial reductions in greenhouse gas emissions worldwide. In the European Union (EU), buildings account for approximately 40% of total energy consumption and 36% of carbon dioxide (CO₂) emissions, highlighting their significant impact on the region’s overall environmental footprint [1]. This challenge is further underscored by the stark contrast in energy performance between new and existing buildings: while recently constructed buildings typically require less than 3 to 5 L of heating oil per square meter annually, older buildings consume an average of about 25 L per square meter per year [2]. This disparity illustrates the urgent need for retrofitting and upgrading the existing building stock to improve energy efficiency and reduce emissions.

Similarly, in the United States, the Department of Energy (DOE) has prioritized advancements in building energy performance as a key strategy for national sustainability goals. Through the development and promotion of efficient, affordable, and high-impact technologies, systems, and practices, the DOE aims to transform the building sector [3]. The long-term objective of the DOE’s Building Technologies Office is to achieve a 50% reduction in energy use compared to 2010 levels, reflecting a strong commitment to innovation and continuous improvement in building design and operation [4].

These ambitious targets in both the EU and the US underscore the necessity for innovative solutions that can address the dual challenges of energy efficiency and occupant comfort. Among the various strategies being explored, the integration of advanced materials—such as phase change materials (PCMs)—into building envelopes and systems offers significant potential for reducing energy demand and greenhouse gas emissions, while simultaneously enhancing indoor environmental quality [5,6].

Thermal comfort in buildings is a fundamental factor influencing both quality of life and energy efficiency, particularly in the context of increasing demand for sustainable solutions. Phase change materials (PCMs) have emerged as a promising technology for passive indoor temperature management due to their ability to store and release thermal energy during phase transitions, such as melting and solidification. By absorbing excess heat when ambient temperatures rise and releasing it as temperatures fall, PCMs can help maintain indoor environments within comfortable ranges, thereby reducing reliance on active heating and cooling systems [7,8,9].

The use of PCMs in building applications has gained increasing attention over the past decades as an effective strategy to enhance the performance of heating, ventilation, and air conditioning (HVAC) systems. By leveraging their latent heat storage capabilities, PCMs can help regulate indoor temperatures, reduce peak energy loads, and improve overall energy efficiency [6,7,10].

Several studies have explored the integration of PCMs into HVAC systems and building envelopes. Rastogi et al. developed a methodology for selecting and evaluating phase change materials (PCMs) for integration with HVAC systems in residential buildings. Their study focused on identifying suitable PCMs based on melting point, thermal properties, and compatibility with building operation schedules. The results demonstrated that appropriately selected PCMs can significantly reduce indoor temperature fluctuations and lower peak cooling and heating loads. This leads to improved thermal comfort and energy savings, especially when the PCM’s phase transition temperature closely matches the desired indoor comfort range [11]. Turnpenny et al. investigated a novel ventilation cooling system that incorporates PCMs and heat pipes. Their experimental setup involved using nighttime ventilation to solidify the PCM, which then absorbed heat during the day, thus reducing the need for active air conditioning. The study found that this system could store substantial amounts of latent heat and provide effective passive cooling, particularly in climates with significant diurnal temperature swings. The approach was shown to be suitable for retrofitting existing buildings and offered both energy and environmental benefits by reducing reliance on conventional air conditioning [12]. Parameshwaran et al. explored the use of advanced PCM systems with variable volume for enhancing the energy efficiency of modern buildings. Their research highlighted the integration of PCM-based thermal energy storage with variable air volume (VAV) air conditioning systems. The findings indicated that such systems could dynamically adjust to changing thermal loads, resulting in reduced energy consumption for cooling and improved indoor comfort. The study also emphasized the importance of selecting PCMs with suitable thermal properties and phase transition temperatures for optimal performance [13]. Sun et al. conducted a comprehensive economic and energy performance analysis of buildings equipped with PCM wallboards. Their research assessed the impact of PCM integration on energy consumption, cost savings, and payback periods across different climate zones. The results showed that PCM wallboards could effectively reduce heating and cooling energy demands, with the economic viability depending on local energy prices and climate conditions. In some cases, the payback period for PCM investment was found to be favorable, making it a promising solution for both new and existing buildings [14].

However, the optimal selection of a PCM is highly dependent on local climatic conditions. The phase transition temperature of the material must closely align with the prevailing comfort temperature of the specific region to maximize its effectiveness. If the melting point of the PCM is not well matched to the local climate, its capacity to moderate indoor temperatures and contribute to energy savings is significantly diminished [15,16].

The selection of the most appropriate phase change material (PCM) is a critical step in the design and development of energy-efficient buildings. The process involves comparing candidate materials, ranking them, and ultimately choosing the optimal option—a stage that is fundamental to the overall success of the material selection process. To achieve a robust selection, it is essential to identify and prioritize the criteria that most significantly influence the engineering application. This approach enables the elimination of unsuitable alternatives and supports the selection of the most appropriate PCM using straightforward and logical methods [17,18]. The suitability of a PCM for a specific application depends on a range of factors, particularly its physical and thermochemical properties, such as melting point, latent heat of fusion, thermal conductivity, chemical stability, and compatibility with other building materials. Additionally, considerations such as cost, availability, environmental impact, and long-term performance are increasingly important in sustainable building design. Given the complexity and the number of variables involved, the material selection process can be effectively structured as a multi-criteria decision-making (MCDM) problem. This systematic approach allows for the simultaneous evaluation of multiple, often conflicting, criteria, ensuring a comprehensive and efficient assessment of candidate materials. By applying MCDM techniques, designers and engineers can objectively rank and select PCMs that best meet the specific requirements of the building and its climatic context, thereby optimizing both thermal comfort and energy performance [19,20,21].

Several studies have explored PCM selection and integration. Nadeem et al. [22] apply the Analytic Hierarchy Process (AHP) to rank different PCMs for building applications. The method evaluates both thermal and non-thermal properties, such as latent heat, thermal conductivity, melting point, and density. The AHP helps decision makers systematically compare alternatives and select the most suitable PCM for building envelopes. Kumar et al. [23] describe a hybrid approach combining AHP (for weighting criteria) and TOPSIS (for ranking alternatives) to select PCMs for thermal energy storage in buildings. The study details the evaluation steps and parameters, demonstrating how these multi-criteria decision-making (MCDM) techniques help identify the most appropriate PCM for thermal comfort applications. Wang et al. [2] compare 33 different MCDM algorithms for selecting the optimal PCM for thermal energy storage heat exchangers. Six materials and five thermophysical properties are evaluated. The study validates the results using the Pearson correlation and highlights the robustness of MCDM methods for PCM selection. Jha et al. [5] analyze the selection of bio-based PCMs for walls and roofs using both MCDM methods and energy simulations. The Ashby approach is used to determine figures of merit and rank the performance of different PCMs under various environmental conditions [24].

Previous studies on PCM selection using MCDM techniques have laid important groundwork but exhibit notable limitations. Nadeem et al. [22] applied AHP to rank PCMs based on thermal properties but did not incorporate climate-specific scoring or validate results across multiple methods. Kumar et al. [23] introduced a hybrid AHP–TOPSIS approach, yet omitted volumetric latent heat and regional comfort alignment. Wang et al. [2] compared 33 MCDM algorithms for heat exchangers, focusing on method robustness but not on climate responsiveness. Jha et al. [5] combined MCDM with simulations for bio-based PCMs, without multi-zone analysis. Mehling et al. [24] reviewed PCM degradation but did not integrate MCDM frameworks. In contrast, this study introduces a climate-zoned PCM ranking methodology using five MCDM techniques, explicitly mapping melting points to regional set-points and validating convergence across methods, addressing key gaps in prior literature.

This article presents a review and methodological proposal for the selection of phase change materials based on the annual mean temperature of various climatic regions. Representative zones with average temperatures of 18 °C (e.g., Madrid, Lisboa, Los Ángeles), 23 °C (e.g., Miami, Panamá, Brisbane), and 28 °C (e.g., Bangkok, Manila, Dubai) are identified, and the criteria for PCM selection in each case are discussed, taking into account not only thermal comfort but also technical feasibility and economic considerations.

Although the use of 18 °C, 23 °C, and 28 °C represents a simplified climatic proxy, each temperature corresponds directly to standardized comfort bands from EN 16798-1 and ASHRAE 55 [25], ensuring physical and practical relevance. This approach provides a transparent baseline for PCM comparison across cool, temperate, and warm climates while remaining compatible with more detailed adaptive comfort modeling that may be used in future work.

2. Materials and Methods

2.1. Definition of the Decision-Making Problem for Material Selection

The selection of phase change materials (PCMs) for building applications is a complex decision-making problem that requires the simultaneous consideration of multiple performance criteria. PCMs are utilized for their ability to absorb and release latent heat during phase transitions, thereby maintaining indoor temperatures within a desired comfort range. For effective integration into building envelopes or HVAC systems, the melting point of the PCM should closely match the target indoor comfort temperature, contributing to a more stable and comfortable indoor environment [7,15,25].

To ensure optimal performance and safety, the selection process must evaluate a range of thermal, physical, chemical, and economic properties. Based on the literature, the key criteria for PCM selection include the following:

• High latent heat of fusion (per unit volume and mass) and high specific heat capacity to maximize energy storage and minimize the required material volume.
• Melting point appropriately matched to the intended application, climate, and building location.
• Chemical stability and low corrosion potential to ensure long-term durability.
• Non-toxicity and safety, particularly in the event of fire or accidental release.
• Reproducible phase transitions without material degradation over repeated cycles.
• Minimal volume changes during solidification to prevent structural issues.
• High thermal conductivity, enabling rapid heat transfer and efficient thermal response.
• Abundance and low cost to ensure economic feasibility and scalability.

There are other key practical attributes such as cycling stability, subcooling behavior, volume change, phase segregation, compatibility, flammability/toxicity, corrosion potential, and cost/availability, which are critical for the building applications of PCMs. This decision model focused primarily on quantitative thermophysical parameters to enable reproducibility and objective comparison across all materials.

Among these, the most critical properties are the melting point (Tm), latent heat of fusion (ΔHfus), specific heat capacity (Cp), thermal conductivity (k), and density (ρ). It has been taken into account that the materials display an average cost/availability. The ideal PCM should combine high energy storage capacity, suitable melting point, good thermal conductivity, chemical and physical stability, safety, and affordability. The decision-making process, therefore, involves systematically evaluating candidate materials against these criteria to identify the most suitable PCM for the specific building application [23,26,27].

Table 1. Material properties for the PCM alternatives in buildings [6].

PCM	Category	Tm (°C)	ΔHfus (kJ/kg)	ρ (kg/m3)	Vol. Latent Heat (MJ/m3)	Cp (kJ/kg·K)	k (W/m·K)
n-Heptadecane (C17)	Paraffin	22	225	770	~173	2.1	0.20
n-Octadecane (C18)	Paraffin	28	244	775	~189	2.1	0.20
n-Nonadecane (C19)	Paraffin	32	250	780	~195	2.1	0.20
Rubitherm RT27	Commercial paraffin blend	27	120	770	~92	2.0	0.20
Rubitherm RT31	Commercial paraffin blend	31	115	777	~89	2.0	0.20
Capric acid (C10)	Fatty acid	31.6	150	940	~141	2.1	0.18
Capric–Lauric eutectic	Fatty acid eutectic	24	160	900	~144	2.1	0.18
Fatty acid eutectic (C10–C12–C14)	Fatty acid eutectic	35	150	880	~132	2.0	0.18
1-Dodecanol	Fatty alcohol	24	160	813	~130	2.0	0.17
PEG-600	PEG (low MW)	20	120	1100	~132	1.9	0.25
Glauber’s salt (Na2SO4·10H2O)	Salt hydrate	32.4	254	1500	~381	1.4	0.60
CaCl2·6H2O	Salt hydrate	29	190	1700	~323	1.3	0.60
Na2HPO4·12H2O	Salt hydrate	35	200	1600	~320	1.4	0.50
Na2CO3·10H2O	Salt hydrate	32	190	1450	~276	1.4	0.60
Form-stable paraffin/HDPE	Composite	25	120	900	~108	1.9	0.25
Organic ester mixture	Commercial ester PCM	25	140	900	~126	2.0	0.18

shows the material properties for the PCM alternatives in buildings.

In this study, the mean melting point was prioritized as the main criterion, considering that the MCDM methods used (COPRAS, VIKOR, TOPSIS, MOORA, PROMETHEE II) require unique values per criterion. However, we are aware that a wide melting range can dilute the thermal control capability in sensitive applications.

2.2. Multi-Criteria Decision-Making Methods

AHP, COPRAS, VIKOR, TOPSIS, MOORA and PROMETHEE II are the MCDM methods that have been used and are explained below. Using AHP for weight selection ensures that the most relevant criteria are emphasized, based on expert judgment. Applying multiple MCDM methods allows for a comprehensive, unbiased, and validated selection of the optimal PCM for different climate zones and building applications.

2.2.1. Analytic Hierarchy Process (AHP)

The Analytic Hierarchy Process (AHP), introduced by Thomas Saaty, is a structured technique used to determine the relative importance of alternatives in decision-making scenarios. This method is particularly effective for complex problems involving multiple criteria. AHP operates through three main components: establishing a hierarchical structure, conducting pairwise comparisons among criteria, and evaluating the consistency of the judgments made [28].

In the hierarchy setup, each alternative is assigned a value reflecting its relevance to the decision context. The structure typically includes three levels: the overall goal, the criteria influencing the decision, and the set of alternatives under consideration.

The next step involves comparing the criteria to each another to assign relative weights. These weights are derived from expert judgment or technical knowledge, and Saaty proposed a scale from 1 to 9 to quantify the importance of one criterion over another. Intermediate values such as 2, 4, 6, and 8 are used for finer distinctions.

The pairwise comparisons are organized into a square matrix (A), where each element represents the relative importance of one criterion compared to another. The principal eigenvector of this matrix yields the priority weights for each criterion.

$$A=\left(\begin{array}{ccc}{a}_{11}& \dots & a_{1n}\\ ⋮& \ddots & ⋮\\ a_{n1}& \dots & a_{nn}\end{array}\right) a_{ii}=1, a_{ji}={\displaystyle \frac{1}{a_{ij}}}, a_{ij}\ne 0$$

(1)

Afterwards, from matrix A it is determined the relative priority among properties. The eigenvector w is the weight importance and it corresponds with the largest eigenvector (max):

$$(A-{\lambda }_{max})w = 0$$

(2)

To ensure the reliability of the comparisons, AHP includes a consistency check. The consistency index (CI) and consistency ratio (CR) are calculated using the largest eigenvalue of the matrix. If the CR exceeds 0.1, the comparisons should be revised to improve consistency. In Equations (3) and (4) is shown the consistency indexes required to validate the results.

$$CI={\displaystyle \frac{({\lambda }_{max}-n)}{n-1}}$$

(3)

$$CR={\displaystyle \frac{CI}{RI}}$$

(4)

where

n: number of selection criteria;

RI: random index;

CI: consistency index;

CR: consistency relationship;

max (A): largest eigenvalue.

CR should be greater than 0.1; otherwise, the importance coefficient (1–9) has to be reset and the CR recalculated [22].

It is important to emphasize which criteria are going to be considered as positive and negative during the development of the MCDM method [26]; this consideration is shown in

Table 2. Definition of positive and negative criteria.

Material	Tm (°C)	ΔHfus (kJ/kg)	ρ (kg/m3)	Vol. Latent Heat (VLH) (MJ/m3)	Cp (kJ/kg·K)	k (W/m·K)
	proximity to a zone target	+	+	+	+	+

, which will be used for all methods that require this consideration.

2.2.2. COPRAS Method

The COPRAS (Complex Proportional Assessment) method is a multi-criteria decision-making technique that evaluates alternatives by considering both beneficial and non-beneficial criteria. It identifies the most suitable option by calculating the relative significance and utility of each alternative based on its performance across all criteria. This approach facilitates a clear understanding of how each alternative compares to others in terms of overall effectiveness. Goswami et al. [29] develop the algorithm using the following steps:

Step 1: Calculate the normalized decision matrix $x_{ij}^{*}$.

$${ x}_{ij}^{*}={\displaystyle \frac{x_{ij}}{\sum _{i=1}^m{x}_{ij}}}$$

(5)

Step 2: Calculate the weighted normalized decision matrix Dij.

$${\mathrm{D}}_{\mathrm{ij}}=x_{ij}^{*}·{\mathrm{w}}_{\mathrm{j}}=\left[\begin{array}{cccc}{w_{1}r}_{11}& w_2{r}_{12}& \dots & {w_{n}r}_{1n}\\ {w_{1}r}_{21}& w_2{r}_{22}& \dots & w_n{r}_{2n}\\ ⋮& ⋮& \ddots & ⋮\\ {w_{1}r}_{m1}& w_2{r}_{m2}& \dots & w_n{r}_{mn}\end{array}\right]$$

(6)

Step 3: Calculate S_i+ and S_i− of the normalized weighted values.

$$S_{i+}=\sum _{k=1}^k{D}_{ij}$$

(7)

$$S_{i-}=\sum _{k=1}^k{D}_{ij}$$

(8)

Step 4: Determine the relative importance of the $Q_i$ alternatives.

$${ Q}_i=S_{i+}+{\displaystyle \frac{\sum _{j=1}^m{S}_{i-}}{S_{i-}\sum _{j=1}^m\frac{1}{S_{i-}}}}$$

(9)

Step 5: Calculate $P_i$ of each alternative, using following Equation (9).

$$P_i={\displaystyle \frac{Q_i}{Q_{max}}}\times 100$$

(10)

where $Q_{max}$ is the maximum value of relative importance.

This structured approach allows decision makers to rank alternatives effectively and select the one that offers the highest utility, balancing both positive contributions and negative impacts.

2.2.3. VIKOR Method

The VIKOR method (Višekriterijumsko Kompromisno Rangiranje) is a multi-criteria decision-making technique designed to identify a compromise solution that is closest to the ideal, especially when dealing with conflicting criteria. Unlike methods that seek a perfect solution, VIKOR aims to find an alternative that represents a balanced trade-off acceptable to all stakeholders. It comprises the following steps used by Radovanović et al. in ref. [30].

Step 1: Normalize decision matrix X_ij.

$$X_{ij}=\left[\begin{array}{cccc}{x}_{11}& x_{12}& \dots & x_{1n}\\ x_{21}& x_{22}& \dots & x_{2n}\\ \dots & \dots & \dots & \dots \\ x_{m1}& x_{m2}& \dots & x_{mn}\end{array}\right]$$

(11)

Step 2: Calculate weighted normalized decision matrix f_ij.

$${\mathrm{f}}_{\mathrm{ij}}={\displaystyle \frac{X_{ij}}{\sqrt{\sum _{i=1}^m{X_{ij}}^2}}}$$

(12)

Step 3: Determine the best $f_i^{*}$ and the worst $f_i^{-}$-value of all the criterion.

$$f_i^{*}={\mathrm{m}\mathrm{a}\mathrm{x}}_{\mathrm{j}} {\mathrm{f}}_{\mathrm{i}\mathrm{j}}$$

(13)

$$f_i^{-}={max}_j {\mathrm{f}}_{ij}$$

(14)

Step 4: Calculate the distance to the positive ideal solution S_i and negative ideal solution $R_i$.

$${\mathrm{S}}_{\mathrm{i}}=\sum _j^n{W}_{i }(f_i^{*}-f_{ij})/(f_i^{*}-f_i^{-})$$

(15)

$$R_i={\mathrm{Max}}_{\mathrm{j}} [W_i{f}_i^{*}-f_{ij})/(f_i^{*}-f_i^{-})]$$

(16)

Step 5: Calculate the values (I_i); for i = 1…, I, is defined by Equation (17).

$${\mathrm{I}}_{\mathrm{i}}=\mathrm{v} \left[{\displaystyle \frac{S_i-S^{*}}{S^{-}-S^{*}}}\right]+(1-\mathrm{v}) \left[{\displaystyle \frac{R_i-R^{*}}{R^{-}-R^{*}}}\right]$$

(17)

2.2.4. TOPSIS Method

The Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is a widely used multi-criteria decision-making method that ranks alternatives based on their proximity to an ideal solution. The fundamental principle of TOPSIS is that the best option should be closest to the positive ideal solution (PIS) and furthest from the negative ideal solution (NIS).

The method involves calculating the geometric distances of each alternative from both the PIS and NIS. These distances are then used to compute a relative closeness index, which ranges from 0 to 1. A higher index indicates a better alternative. This approach facilitates clear and rational decision making by quantifying how close each option is to the optimal solution.

According to the procedure outlined by Taherdoost et al. [31], the TOPSIS method consists of the following steps:

Step 1: Construct the normalized decision matrix r_ij, which standardizes the data to eliminate unit differences.

$$r_{ij}=\left[\begin{array}{cccc}{r}_{11}& r_{12}& \dots & r_{1n}\\ r_{21}& r_{22}& \dots & r_{2n}\\ \dots & \dots & \dots & \dots \\ r_{m1}& r_{m2}& \dots & r_{mn}\end{array}\right]$$

(18)

Step 2: Normalize the decision matrix to ensure comparability across criteria.

$${\mathrm{R}}_{\mathrm{ij}}={\displaystyle \frac{r_{ij}}{\sqrt{\sum _{i=1}^m{r_{ij}}^2}}}$$

(19)

Step 3: Generate the weighted normalized decision matrix (Vij) using the assigned weights for each criterion (20).

$${\mathrm{V}}_{\mathrm{i}\mathrm{j}}={\mathrm{W}}_{\mathrm{i}}*{\mathrm{R}}_{\mathrm{i}\mathrm{j}}$$

(20)

$$\mathit{Vij}=\left[\begin{array}{cccc}{W}_1{r}_{11}& {W_{2}r}_{12}& \dots & W_n{r}_{1n}\\ W_2{r}_{21}& {W_{2}r}_{22}& \dots & W_n{r}_{2n}\\ \dots & \dots & \dots & \dots \\ {W_{n}r}_{m1}& W_n{r}_{m2}& \dots & W_n{r}_{mn}\end{array}\right]$$

(21)

Step 4: Identify the positive ideal and negative ideal solutions based on the best and worst values for each criterion $A^{*}$ and $A^{-}$.

$$A^{*}=\left\{\underset{i}{\max } v_{ij}│j\in J),(\underset{i}{\min } v_{ij}│j\in J^{\prime })\right\}=\left\{{v_1}^{*}, {v_2}^{*},\dots , {v_n}^{*}\right\}$$

(22)

$$A^{-}=\left\{\underset{i}{\max } v_{ij}│j\in J),(\underset{i}{\min } v_{ij}│j\in J^{\prime })\right\}=\left\{{v_1}^{-}, {v_2}^{-},\dots , {v_n}^{-}\right\}$$

(23)

Step 5: Calculate the separation measures, which represent the distances of each alternative from the ideal and anti-ideal solutions ${S_i}^{*}$ and ${S_i}^{-}$.

$${S_i}^{*}=\sqrt{\sum _{j=1}^n{\left(v_{ij}-{v_j}^{*}\right)}^2}$$

(24)

$${S_i}^{-}=\sqrt{\sum _{j=1}^n{\left(v_{ij}-{v_j}^{-}\right)}^2}$$

(25)

Step 6: Determine the relative closeness coefficient for each alternative, which serves as the basis for ranking

$${C_i}^{*}={\displaystyle \frac{{S_i}^{-}}{{S_i}^{-}+{S_i}^{*}}}$$

(26)

This structured approach enables decision makers to evaluate and rank alternatives effectively, ensuring that the selected option aligns closely with the desired performance characteristics.

2.2.5. MOORA Method

The MOORA (Multi-Objective Optimization on the Basis of Ratio Analysis) method is a practical and reliable approach for addressing multi-criteria decision-making problems. It is particularly valued for its simplicity and effectiveness in comparing alternatives across both favorable and unfavorable criteria [32]. The procedure involves the following steps:

Step 1: Determine the decision matrix Xij.

$${\mathrm{X}}_{\mathrm{ij}} \left[\begin{array}{cccc}{X}_{11}& X_{12}& \dots & X_{1n}\\ X_{21}& X_{22}& \dots & X_{2n}\\ \dots & \dots & \dots & \dots \\ X& X_{m2}& \dots & X_{mn}\end{array}\right]$$

(27)

Step 2: Calculate the radius matrix of the form $\overline{X_{ij}}$ = $\left[\overline{x_{ij}}\right]$.

$$\overline{{ X}_{ij}}={\displaystyle \frac{X_{ij}}{\sqrt{\sum _{i=1}^m{X_{ij}}^2} }}$$

(28)

Step 3: Weight the vector calculus of each of the criteria.

$$W=\left|\begin{array}{ccccc}{W}_1& W_2& W_3& \dots ..& W_n\end{array}\right|$$

(29)

Step 4: Normalize the weighted matrix.

Step 5: Calculate the aggregation function to evaluate each alternative S(x_i) using Equation.

$$\mathrm{S}({\mathrm{x}}_{\mathrm{i}})={\sum }_{i=1}^h\overline{X_{ij}}-{\sum }_{i=h+1}^n\overline{X_{ij}}$$

(30)

This method allows for a clear and objective ranking of alternatives, making it especially useful in engineering, sustainability, and material selection contexts.

2.2.6. PROMETHEE Method

The PROMETHEE Method (Preference Ranking Organization Method for Enrichment Evaluations) is especially useful when multiple alternatives need to be evaluated based on several criteria and a preference ranking among them is desired [33].

The steps of the PROMETHEE II method, which is most commonly used, are as follows:

• Define the alternatives and criteria.
• Assign weights to the criteria.
• Select preference functions: for each criterion, a preference function $Pj(a,b)$ is defined, which measures how much alternative $a$ is preferred over $b.$
• Calculate the aggregated preference indices for each alternatives $(a,b).$

  $$\mathsf{\pi }(\mathrm{a},\mathrm{b})=\sum \mathrm{wj}·\mathrm{Pj}(\mathrm{a},\mathrm{b})$$

  (31)
• Calculate the preference flows.

Positive flow: how much an alternative dominates the others.

$${\phi }^{+}(a)=(1/(m-1)) \sum \pi (a,b)$$

(32)

Negative flow: how much an alternative is dominated by the others.

$${\phi }^{-}(a)=(1/(m-1)) \sum \pi (b,a)$$

(33)

Net Flow:

$$\phi \left(a\right) = {\phi }^{+}\left(a\right) - {\phi }^{-}\left(a\right)$$

(34)

6.

Rank the alternatives:

In PROMETHEE II, alternatives are ranked according to their net flow φ(a). The higher the value, the better the alternative.

3. Results

The results presented in this section stem from the application of a structured MCDM framework aimed at selecting the most suitable PCMs for building applications across different climatic zones. To ensure a comprehensive and unbiased evaluation, five MCDM methods—TOPSIS, VIKOR, COPRAS, MOORA, and PROMETHEE II—were employed. These methods offer diverse analytical perspectives, ranging from proximity to ideal solutions to preference-based rankings. To establish a consistent basis for comparison, the AHP was first applied to determine the relative importance of the selection criteria. This weighting process incorporated expert judgment and consistency validation, resulting in a prioritization that reflects the critical influence of thermal properties such as melting point, latent heat of fusion, and volumetric latent heat.

3.1. AHP Method Results

To obtain the criteria weighting, the comparison among properties has been performed for every alternative, as showed in Table 1. The property identification appears as (Tm), (ΔHfus), (ρ), (Cp), (VLH), and (k) (W/m·K). The scale of relative importance used in the AHP method are 1, equal importance; 3, moderate importance; 5, strong importance; 7, very strong importance; and 9, extreme importance. Rankings of 2, 4, 6, and 8 indicate intermediate importance.

Table 3. Comparison among criteria of PCMs in AHP method.

Tm (°C)	ΔHfus	VLH	k	Cp	ρ
1	3	5	7	9	9
0.333333	1	3	5	7	7
0.2	0.333333	1	3	5	5
0.142857	0.2	0.333333	1	3	3
0.111111	0.142857	0.2	0.333333	1	1
0.111111	0.142857	0.2	0.333333	1	1

Scale

Each criterion was compared using Saaty’s scale of relative importance (1–9), which quantifies how much more one criterion influences the decision over another. The resulting comparison matrix (Table 3) reflects the authors’ expert evaluations, with melting point (Tm) identified as the most critical property for PCM selection, particularly due to its alignment with regional comfort temperatures.

The consistency of the pairwise comparisons was verified using the Consistency Index (CI) and Consistency Ratio (CR). The calculated values CI = 0.010 and CR = 0.044 are both below the acceptable threshold of 0.1, confirming the reliability of the judgments.

From the normalized matrix, the priority weights for each criterion were derived using the principal eigenvector method. The final weight distribution is shown in

Table 4. Criteria weighting by the AHP.

Tm (°C)	ΔHfus	VLH	k	Cp	ρ
47.5%	25.7%	13.5%	6.8%	3.3%	3.3%

. These weights were subsequently used across all MCDM methods to ensure consistency in the evaluation of PCM alternatives. The dominance of Tm in the weighting reflects its pivotal role in ensuring thermal comfort across different climate zones, while ΔHfus and VLH contribute significantly to the energy storage capacity of the materials.

3.2. COPRAS Method Results

The COPRAS method was applied to evaluate and rank phase change materials (PCMs) for building applications across three climatic zones, considering both beneficial and non-beneficial criteria. In the temperate zone (~18 °C,

Table 5. Full ranking of COPRAS results (descending order by C) for Zone 1, temperate (~18 °C) (e.g., Madrid, Lisbon, Los Angeles).

Pos	Material	S	K
1	n-Heptadecane (C17)	0.363514	1.000000
2	PEG-600	0.341757	0.940250
3	Capric–Lauric eutectic	0.309021	0.850404
4	1-Dodecanol	0.305781	0.841369
5	Organic ester mixture	0.293201	0.806351
6	Form-stable paraffin/HDPE	0.292470	0.804582
7	Rubitherm RT27	0.281010	0.772924
8	Rubitherm RT31	0.276407	0.760795
9	n-Nonadecane (C19)	0.274168	0.754285
10	n-Octadecane (C18)	0.269168	0.740634
11	Fatty acid eutectic (C10–C12–C14)	0.256204	0.704901
12	Capric acid (C10)	0.255267	0.702144
13	Na2CO3·10H2O	0.254930	0.700882
14	Na2HPO4·12H2O	0.250071	0.687907
15	CaCl2·6H2O	0.243456	0.669775
16	Glauber’s salt (Na2SO4·10H2O)	0.206488	0.568086

), n-Heptadecane (C17) achieved the highest utility value (K = 1.000), confirming its suitability due to its low melting point and strong thermal storage properties. PEG-600 and Capric–Lauric eutectic followed closely, reflecting their favorable energy storage capacities and compatibility with cooler climates. In the subtropical zone (~23 °C,

Table 6. Full ranking of COPRAS results (descending order by C) for Zone 2, subtropical/moderate tropical (~23 °C) (e.g., Miami, Panama, Brisbane).

Pos	Material	S	K
1	n-Heptadecane (C17)	0.363920	1.000000
2	Capric–Lauric eutectic	0.328651	0.903356
3	1-Dodecanol	0.327533	0.900040
4	Organic ester mixture	0.314678	0.864993
5	Form-stable paraffin/HDPE	0.311834	0.857031
6	PEG-600	0.307821	0.846096
7	Rubitherm RT27	0.296525	0.815010
8	Rubitherm RT31	0.292999	0.804150
9	n-Nonadecane (C19)	0.291222	0.800140
10	n-Octadecane (C18)	0.286023	0.786195
11	Na2CO3·10H2O	0.284905	0.783212
12	Capric acid (C10)	0.281968	0.774588
13	Fatty acid eutectic (C10–C12–C14)	0.271365	0.745867
14	Na2HPO4·12H2O	0.268593	0.738270
15	CaCl2·6H2O	0.263166	0.723406
16	Glauber’s salt (Na2SO4·10H2O)	0.241365	0.663362

), n-Heptadecane again ranked first, demonstrating consistent performance across criteria, while Capric–Lauric eutectic and 1-Dodecanol also performed well due to their melting points aligning with the target comfort range. In the tropical hot/desert zone (~28 °C,

Table 7. Full ranking of COPRAS results (descending order by C) for Zone 23, tropical hot/desert (~28 °C) (e.g., Bangkok, Manila, Dubai).

Pos	Material	S	K
1	n-Octadecane (C18)	0.370865	1.000000
2	CaCl2·6H2O	0.362522	0.977449
3	Na2CO3·10H2O	0.342808	0.924328
4	Na2HPO4·12H2O	0.340702	0.919152
5	Glauber’s salt (Na2SO4·10H2O)	0.333831	0.900154
6	Rubitherm RT31	0.319247	0.860951
7	n-Nonadecane (C19)	0.312725	0.843160
8	Rubitherm RT27	0.310591	0.837629
9	Organic ester mixture	0.293391	0.790618
10	Form-stable paraffin/HDPE	0.292997	0.789257
11	Capric acid (C10)	0.289896	0.781752
12	Fatty acid eutectic (C10–C12–C14)	0.288453	0.777505
13	PEG-600	0.241584	0.651639
14	1-Dodecanol	0.233789	0.630533
15	n-Heptadecane (C17)	0.228171	0.615165
16	Capric–Lauric eutectic	0.214559	0.578701

), n-Octadecane (C18) emerged as the top-ranked PCM (K = 1.000), with its melting point precisely matching the climatic requirements and offering high latent heat. Hydrated salts such as CaCl₂·6H₂O and Na₂CO₃·10H₂O also ranked highly in this zone, benefiting from their high volumetric latent heat and density. These results underscore the effectiveness of COPRAS in identifying optimal PCMs by balancing thermal performance, material properties, and climate-specific requirements.

3.3. VIKOR Method Results

The VIKOR method was employed to identify the most suitable phase change materials (PCMs) for building applications across three distinct climatic zones, emphasizing a compromise solution that balances performance across multiple criteria. In the temperate zone (~18 °C

Table 8. Full ranking of VIKOR results (descending order by C) for Zone 1, temperate (~18 °C) (e.g., Madrid, Lisbon, Los Angeles).

Pos	Material	S	R	Q
1	n-Heptadecane (C17)	0.309372	0.096164	0
2	Capric–Lauric eutectic	0.504843	0.173799	0.273128
3	1-Dodecanol	0.520109	0.173799	0.286457
4	PEG-600	0.447764	0.247755	0.320904
5	n-Octadecane (C18)	0.456668	0.253333	0.33604
6	CaCl2·6H2O	0.463146	0.285	0.383491
7	Organic ester mixture	0.585935	0.210777	0.392735
8	Form-stable paraffin/HDPE	0.62429	0.247755	0.475028
9	Glauber’s salt (Na2SO4·10H2O)	0.428638	0.392667	0.495464
10	Rubitherm RT27	0.703416	0.247755	0.544112
11	n-Nonadecane (C19)	0.56929	0.38	0.601548
12	Na2CO3·10H2O	0.584621	0.38	0.614934
13	Capric acid (C10)	0.763966	0.367333	0.754801
14	Rubitherm RT31	0.840466	0.348333	0.796516
15	Na2HPO4·12H2O	0.651281	0.475	0.798519
16	Fatty acid eutectic (C10–C12–C14)	0.882048	0.475	1

), n-Heptadecane (C17) emerged as the optimal PCM (Q = 0), owing to its melting point closely aligned with the target indoor comfort range and its favorable latent heat and density properties. For subtropical climates (~23 °C,

Table 9. Full ranking of VIKOR results (descending order by C) for Zone 2, subtropical/moderate tropical (~23 °C) (e.g., Miami, Panama, Brisbane).

Pos	Material	S	R	Q
1	n-Heptadecane (C17)	0.246039	0.096164	0
2	n-Octadecane (C18)	0.376062	0.172727	0.203268
3	Capric–Lauric eutectic	0.378176	0.173799	0.206344
4	1-Dodecanol	0.393442	0.173799	0.218346
5	CaCl2·6H2O	0.394055	0.215909	0.274406
6	Organic ester mixture	0.470783	0.210777	0.327953
7	Form-stable paraffin/HDPE	0.509139	0.247755	0.406912
8	PEG-600	0.534128	0.247755	0.426557
9	Glauber’s salt (Na2SO4·10H2O)	0.398699	0.362727	0.471833
10	Rubitherm RT27	0.611295	0.247755	0.487222
11	n-Nonadecane (C19)	0.534744	0.345455	0.555988
12	Na2CO3·10H2O	0.550076	0.345455	0.568041
13	Capric acid (C10)	0.724815	0.328182	0.682615
14	Rubitherm RT31	0.794405	0.302273	0.703128
15	Na2HPO4·12H2O	0.651281	0.475	0.818582
16	Fatty acid eutectic (C10–C12–C14)	0.882048	0.475	1

), n-Heptadecane again ranked highest, demonstrating robust performance across criteria, despite a slightly lower melting point than the target. In contrast, for tropical hot/desert climates (~28 °C,

Table 10. Full ranking of VIKOR results (descending order by C) for Zone 23, tropical hot/desert (~28 °C) (e.g., Bangkok, Manila, Dubai).

Pos	Material	S	R	Q
1	n-Octadecane (C18)	0.2033	0.0888	0
2	CaCl2·6H2O	0.2375	0.1183	0.0620
3	Rubitherm RT27	0.2972	0.2613	0.2885
4	Organic ester mixture	0.4268	0.2375	0.3478
5	Form-stable paraffin/HDPE	0.4421	0.2375	0.3585
6	n-Nonadecane (C19)	0.6057	0.2108	0.4376
7	Capric acid (C10)	0.5411	0.2478	0.4406
8	Fatty acid eutectic (C10–C12–C14)	0.6104	0.2138	0.4447
9	Rubitherm RT31	0.6157	0.2375	0.4791
10	Na2CO3·10H2O	0.6309	0.2375	0.4897
11	Na2HPO4·12H2O	0.6441	0.2478	0.5121
12	Glauber’s salt (Na2SO4·10H2O)	0.6703	0.2570	0.5423
13	PEG-600	0.6023	0.3563	0.6235
14	1-Dodecanol	0.5919	0.4156	0.6932
15	n-Heptadecane (C17)	0.8227	0.4156	0.8536
16	Capric–Lauric eutectic	0.9228	0.4750	1

), n-Octadecane (C18) was identified as the best compromise solution (Q = 0.846), with a melting point precisely matching the target and strong thermal storage capacity. Notably, hydrated salts such as CaCl₂·6H₂O also performed well in warmer zones due to their high volumetric latent heat and density, despite lower thermal conductivity. These results highlight the importance of aligning PCM thermal properties with regional climatic conditions and demonstrate the effectiveness of VIKOR in balancing trade-offs among conflicting criteria to support informed material selection.

3.4. TOPSIS Method Results

The TOPSIS method was utilized to rank phase change materials (PCMs) based on their proximity to the ideal solution, considering multiple thermal and physical criteria. In the temperate zone (~18 °C,

Table 11. Full ranking of TOPSIS results (descending order by C) for Zone 1, temperate (~18 °C) (e.g., Madrid, Lisbon, Los Angeles).

Pos	Material	D+	D−	C
1	n-Heptadecane (C17)	0.051137	0.196209	0.793257
2	PEG-600	0.065568	0.221410	0.771521
3	Capric–Lauric eutectic	0.081353	0.163312	0.667492
4	1-Dodecanol	0.082675	0.163188	0.663736
5	Organic ester mixture	0.096667	0.147912	0.604762
6	Form-stable paraffin/HDPE	0.096905	0.145649	0.601238
7	Rubitherm RT27	0.106691	0.127684	0.544612
8	Rubitherm RT31	0.111636	0.120286	0.518133
9	n-Nonadecane (C19)	0.114662	0.118561	0.508089
10	n-Octadecane (C18)	0.120605	0.111009	0.479587
11	Fatty acid eutectic (C10–C12–C14)	0.134365	0.096341	0.417530
12	Capric acid (C10)	0.134719	0.095442	0.414872
13	Na2CO3·10H2O	0.137317	0.092015	0.401177
14	Na2HPO4·12H2O	0.140574	0.087539	0.383020
15	CaCl2·6H2O	0.143521	0.082747	0.366244
16	Glauber’s salt (Na2SO4·10H2O)	0.154961	0.051579	0.249314

), n-Heptadecane (C17) achieved the highest closeness coefficient (C = 0.793), indicating its superior alignment with the desired performance profile for cooler climates. PEG-600 followed closely, benefiting from its low melting point and high density, while Capric–Lauric eutectic and 1-Dodecanol also performed well due to their balanced thermal properties. In the subtropical zone (~23 °C,

Table 12. Full ranking of TOPSIS results (descending order by C) for Zone 2, subtropical/moderate tropical (~23 °C) (e.g., Miami, Panama, Brisbane).

Pos	Material	D+	D−	C
1	n-Heptadecane (C17)	0.041773	0.184487	0.815376
2	Capric–Lauric eutectic	0.056020	0.180689	0.763340
3	1-Dodecanol	0.057922	0.180577	0.757139
4	Organic ester mixture	0.064604	0.163763	0.717104
5	Form-stable paraffin/HDPE	0.070172	0.163488	0.699682
6	PEG-600	0.075247	0.156129	0.674258
7	Rubitherm RT27	0.086618	0.139041	0.615740
8	Rubitherm RT31	0.089618	0.131854	0.595136
9	n-Nonadecane (C19)	0.093349	0.128602	0.579343
10	n-Octadecane (C18)	0.103606	0.115662	0.527562
11	Capric acid (C10)	0.112608	0.104306	0.480850
12	Fatty acid eutectic (C10–C12–C14)	0.113386	0.102753	0.475084
13	Na2CO3·10H2O	0.103696	0.119890	0.535123
14	Na2HPO4·12H2O	0.117436	0.101544	0.463479
15	CaCl2·6H2O	0.111421	0.106926	0.489759
16	Glauber’s salt (Na2SO4·10H2O)	0.119137	0.071677	0.375235

), n-Heptadecane remained the top-ranked material (C = 0.815), reaffirming its versatility across moderate climates. Capric–Lauric eutectic and 1-Dodecanol continued to show strong performance, with melting points near the target temperature and favorable latent heat values. In the tropical hot/desert zone (~28 °C,

Table 13. Full ranking of TOPSIS results (descending order by C) for Zone 3, tropical hot/desert (~28 °C) (e.g., Bangkok, Manila, Dubai).

Pos	Material	D+	D−	C
1	n-Octadecane (C18)	0.038419	0.212015	0.846591
2	CaCl2·6H2O	0.035884	0.187908	0.839656
3	Rubitherm RT27	0.075337	0.180546	0.705581
4	Organic ester mixture	0.099454	0.129423	0.565470
5	Form-stable paraffin/HDPE	0.103158	0.129076	0.555800
6	n-Nonadecane (C19)	0.087222	0.163628	0.652445
7	Capric acid (C10)	0.100588	0.151987	0.601546
8	Fatty acid eutectic (C10–C12–C14)	0.095666	0.141126	0.595081
9	Rubitherm RT31	0.083267	0.147554	0.639434
10	Na2CO3·10H2O	0.068894	0.166497	0.707697
11	Na2HPO4·12H2O	0.069617	0.163620	0.701408
12	Glauber’s salt (Na2SO4·10H2O)	0.058245	0.124675	0.681342
13	PEG-600	0.122096	0.077555	0.388966
14	1-Dodecanol	0.127950	0.070787	0.356201
15	n-Heptadecane (C17)	0.130648	0.066652	0.338028
16	Capric–Lauric eutectic	0.143736	0.044907	0.238641

), n-Octadecane (C18) emerged as the optimal PCM (C = 0.847), with its melting point precisely matching the climatic requirements and offering high latent heat of fusion. Hydrated salts such as CaCl₂·6H₂O and Na₂CO₃·10H₂O also ranked highly due to their exceptional volumetric latent heat and density, despite lower specific heat capacities. These results demonstrate TOPSIS’s effectiveness in identifying PCMs that closely approximate ideal thermal performance for specific climate zones.

3.5. PROMETHEE Method Results

The PROMETHEE II method was applied to rank phase change materials (PCMs) based on net preference flows, offering a comprehensive view of how each alternative dominates or is dominated by others across multiple criteria. In the temperate zone (~18 °C,

Table 14. Full ranking of PROMETHEE results (descending order by C) for Zone 1, temperate (~18 °C) (e.g., Madrid, Lisbon, Los Angeles).

Pos	Material	φ+	φ−	φ
1	n-Heptadecane (C17)	0.529310	0.321391	0.207919
2	PEG-600	0.500103	0.322986	0.177117
3	Capric–Lauric eutectic	0.435630	0.308201	0.127429
4	1-Dodecanol	0.431029	0.315261	0.115768
5	Organic ester mixture	0.412854	0.330486	0.082368
6	Form-stable paraffin/HDPE	0.407731	0.328642	0.079089
7	Rubitherm RT27	0.369968	0.333616	0.036352
8	Rubitherm RT31	0.362686	0.336040	0.026647
9	n-Nonadecane (C19)	0.359037	0.338463	0.020574
10	n-Octadecane (C18)	0.351289	0.341199	0.010090
11	Fatty acid eutectic (C10–C12–C14)	0.334060	0.351772	−0.017713
12	Capric acid (C10)	0.333077	0.353606	−0.020529
13	Na2CO3·10H2O	0.332761	0.356431	−0.023670
14	Na2HPO4·12H2O	0.326285	0.363651	−0.037366
15	CaCl2·6H2O	0.317229	0.376412	−0.059183
16	Glauber’s salt (Na2SO4·10H2O)	0.262166	0.471361	−0.209195

), n-Heptadecane (C17) achieved the highest net flow (φ = 0.208), confirming its superior performance due to its low melting point and strong thermal storage properties. PEG-600 and Capric–Lauric eutectic followed closely, reflecting their favorable thermal conductivity and compatibility with cooler climates. In the subtropical zone (~23 °C,

Table 15. Full ranking of PROMETHEE results (descending order by C) for Zone 2, subtropical/moderate tropical (~23 °C) (e.g., Miami, Panama, Brisbane).

Pos	Material	φ+	φ−	φ
1	n-Heptadecane (C17)	0.532666	0.314323	0.218343
2	Capric–Lauric eutectic	0.484479	0.318226	0.166253
3	1-Dodecanol	0.482546	0.317940	0.164606
4	Organic ester mixture	0.455346	0.331133	0.124213
5	Form-stable paraffin/HDPE	0.451280	0.331004	0.120276
6	PEG-600	0.448683	0.335328	0.113355
7	Rubitherm RT27	0.415163	0.345130	0.070033
8	Rubitherm RT31	0.404719	0.350521	0.054198
9	n-Nonadecane (C19)	0.401248	0.353160	0.048088
10	n-Octadecane (C18)	0.388964	0.363500	0.025463
11	Na2CO3·10H2O	0.370687	0.388919	−0.018232
12	Capric acid (C10)	0.378020	0.397390	−0.019370
13	Fatty acid eutectic (C10–C12–C14)	0.367438	0.409452	−0.042014
14	Na2HPO4·12H2O	0.352012	0.423882	−0.071870
15	CaCl2·6H2O	0.340652	0.437101	−0.096450
16	Glauber’s salt (Na2SO4·10H2O)	0.323064	0.456306	−0.133242

), n-Heptadecane again ranked first (φ = 0.218), demonstrating consistent dominance across criteria. Capric–Lauric eutectic and 1-Dodecanol also performed well, with melting points near the target temperature and balanced thermal properties. In the tropical hot/desert zone (~28 °C,

Table 16. Full ranking of PROMETHEE results (descending order by C) for Zone 23, tropical hot/desert (~28 °C) (e.g., Bangkok, Manila, Dubai).

Pos	Material	φ+	φ−	φ
1	n-Octadecane (C18)	0.547603	0.283488	0.264115
2	CaCl2·6H2O	0.531435	0.308198	0.223237
3	Na2CO3·10H2O	0.497408	0.333614	0.163793
4	Na2HPO4·12H2O	0.491107	0.339311	0.151796
5	Glauber’s salt (Na2SO4·10H2O)	0.474999	0.352047	0.122952
6	Rubitherm RT31	0.449452	0.361591	0.087861
7	n-Nonadecane (C19)	0.443042	0.367633	0.075409
8	Rubitherm RT27	0.442594	0.372679	0.069915
9	Organic ester mixture	0.397920	0.375103	0.022818
10	Form-stable paraffin/HDPE	0.397482	0.375668	0.021814
11	Capric acid (C10)	0.393613	0.381821	0.011792
12	Fatty acid eutectic (C10–C12–C14)	0.392445	0.382955	0.009490
13	PEG-600	0.328873	0.447772	−0.118899
14	1-Dodecanol	0.318332	0.456727	−0.138395
15	n-Heptadecane (C17)	0.310879	0.465060	−0.154181
16	Capric–Lauric eutectic	0.292257	0.477768	−0.185511

), n-Octadecane (C18) emerged as the top-ranked PCM (φ = 0.264), with its melting point precisely matching the climatic requirements and offering high latent heat. Hydrated salts such as CaCl₂·6H₂O and Na₂CO₃·10H₂O also showed strong performance, benefiting from their high volumetric latent heat and density. These results highlight PROMETHEE II’s ability to provide nuanced rankings by capturing both the strengths and weaknesses of each PCM relative to that of the others.

3.6. MOORA Method Results

The MOORA (Multi-Objective Optimization on the Basis of Ratio Analysis) method was applied to rank phase change materials (PCMs) by aggregating weighted normalized performance scores across multiple criteria. In the temperate zone (~18 °C,

Table 17. Full ranking of MOORA results (descending order by C) for Zone 1, temperate (~18 °C) (e.g., Madrid, Lisbon, Los Angeles).

Rank	Material	r_Tm	r_ΔHfus	r_VLH	r_k	r_Cp	r_rho	wr_Tm	wr_ΔHfus	wr_VLH	wr_k	wr_Cp	wr_rho	MOORA_score
1	n-Heptadecane (C17)	0.035801	0.038218	0.044022	0.030555	0.087654	0.047210	0.017061	0.009810	0.005942	0.002079	0.002893	0.001558	0.039443
2	PEG-600	0.032546	0.038218	0.070239	0.030555	0.066989	0.084860	0.015481	0.009810	0.009488	0.002079	0.002210	0.002801	0.041868
3	Capric–Lauric eutectic	0.052531	0.049610	0.057492	0.030555	0.073141	0.072803	0.024999	0.012739	0.007761	0.002079	0.002414	0.002403	0.052395
4	1-Dodecanol	0.052531	0.049610	0.051937	0.030555	0.066089	0.069512	0.024999	0.012739	0.007010	0.002079	0.002182	0.002295	0.051305
5	Organic ester mixture	0.052531	0.043384	0.057492	0.030555	0.063457	0.067213	0.024999	0.011822	0.007761	0.002079	0.002094	0.002217	0.050972
6	Form-stable paraffin/HDPE	0.048291	0.038218	0.057492	0.030555	0.054840	0.084860	0.022975	0.009810	0.007761	0.002079	0.001810	0.002801	0.047236
7	Rubitherm RT27	0.056303	0.038218	0.044022	0.030555	0.048964	0.064241	0.026771	0.009810	0.005942	0.002079	0.001617	0.002121	0.048342
8	Rubitherm RT31	0.061424	0.036364	0.044771	0.030555	0.047303	0.072945	0.029181	0.009352	0.006049	0.002079	0.001560	0.002405	0.050626
9	n-Nonadecane (C19)	0.067520	0.040106	0.045520	0.030555	0.048964	0.072803	0.032095	0.010308	0.006145	0.002079	0.001617	0.002403	0.054648
10	n-Octadecane (C18)	0.056303	0.039327	0.045520	0.030555	0.048964	0.072803	0.026771	0.010091	0.006145	0.002079	0.001617	0.002403	0.049106
11	Fatty acid eutectic (C10–C12–C14)	0.035801	0.036364	0.042393	0.030555	0.044209	0.084860	0.017061	0.009352	0.005723	0.002079	0.001459	0.002801	0.038475
12	Capric acid (C10)	0.032546	0.044945	0.045520	0.030555	0.048964	0.072803	0.015481	0.011555	0.006145	0.002079	0.001617	0.002403	0.039279
13	Na2CO3·10H2O	0.067520	0.044945	0.105578	0.030555	0.195856	0.079906	0.032095	0.011555	0.014244	0.002079	0.006462	0.002637	0.069071
14	Na2HPO4·12H2O	0.061424	0.047379	0.116971	0.030555	0.226087	0.067213	0.029181	0.012178	0.015791	0.002079	0.007460	0.002217	0.069106
15	CaCl2·6H2O	0.058562	0.043384	0.125337	0.030555	0.019401	0.060389	0.027845	0.011822	0.016925	0.002079	0.000641	0.001993	0.061305
16	Glauber’s salt (Na2SO4·10H2O)	0.048291	0.057962	0.226435	0.030555	0.455200	0.111447	0.022975	0.014884	0.030569	0.002079	0.012004	0.003677	0.086187

), PEG-600 achieved the highest MOORA score, followed closely by n-Heptadecane (C17) and Capric–Lauric eutectic. These materials demonstrated strong performance in terms of melting point, volumetric latent heat, and density, aligning well with the thermal requirements of cooler climates. In the subtropical zone (~23 °C,

Table 18. Full ranking of MOORA results (descending order by C) for Zone 2, subtropical/moderate tropical (~23 °C) (e.g., Miami, Panama, Brisbane).

Rank	Material	r_Tm	r_ΔHfus	r_VLH	r_k	r_Cp	r_rho	wr_Tm	wr_ΔHfus	wr_VLH	wr_k	wr_Cp	wr_rho	MOORA_score
1	n-Heptadecane (C17)	0.040041	0.038218	0.044022	0.030555	0.087654	0.047210	0.019020	0.009810	0.005942	0.002079	0.002893	0.001558	0.041301
2	Capric–Lauric eutectic	0.079394	0.049610	0.057492	0.030555	0.073141	0.072803	0.037707	0.012739	0.007761	0.002079	0.002414	0.002403	0.065103
3	1-Dodecanol	0.079394	0.049610	0.051937	0.030555	0.066089	0.069512	0.037707	0.012739	0.007010	0.002079	0.002182	0.002295	0.063013
4	Organic ester mixture	0.079394	0.043384	0.057492	0.030555	0.063457	0.067213	0.037707	0.011822	0.007761	0.002079	0.002094	0.002217	0.063679
5	Form-stable paraffin/HDPE	0.075180	0.038218	0.057492	0.030555	0.054840	0.084860	0.035714	0.009810	0.007761	0.002079	0.001810	0.002801	0.060975
6	PEG-600	0.063622	0.038218	0.070239	0.030555	0.066989	0.084860	0.030266	0.009810	0.009488	0.002079	0.002210	0.002801	0.056654
7	Rubitherm RT27	0.101713	0.038218	0.044022	0.030555	0.048964	0.064241	0.048349	0.009810	0.005942	0.002079	0.001617	0.002121	0.070018
8	Rubitherm RT31	0.122956	0.036364	0.044771	0.030555	0.047303	0.072945	0.058533	0.009352	0.006049	0.002079	0.001560	0.002405	0.079978
9	n-Nonadecane (C19)	0.163090	0.040106	0.045520	0.030555	0.048964	0.072803	0.077599	0.010308	0.006145	0.002079	0.001617	0.002403	0.100151
10	n-Octadecane (C18)	0.136130	0.039327	0.045520	0.030555	0.048964	0.072803	0.064719	0.010091	0.006145	0.002079	0.001617	0.002403	0.087055
11	Na2CO3·10H2O	0.163090	0.044945	0.105578	0.030555	0.195856	0.079906	0.077599	0.011555	0.014244	0.002079	0.006462	0.002637	0.114575
12	Capric acid (C10)	0.163090	0.044945	0.053571	0.030555	0.048964	0.072803	0.077599	0.011555	0.007246	0.002079	0.001617	0.002403	0.102499
13	Fatty acid eutectic (C10–C12–C14)	0.079394	0.036364	0.050000	0.030555	0.044209	0.084860	0.037707	0.009352	0.006750	0.002079	0.001459	0.002801	0.060148
14	Na2HPO4·12H2O	0.122956	0.047379	0.116971	0.030555	0.226087	0.067213	0.058533	0.012178	0.015791	0.002079	0.007460	0.002217	0.098258
15	CaCl2·6H2O	0.122956	0.043384	0.125337	0.030555	0.019401	0.060389	0.058533	0.011822	0.016925	0.002079	0.000641	0.001993	0.093995
16	Glauber’s salt (Na2SO4·10H2O)	0.079394	0.057962	0.226435	0.030555	0.455200	0.111447	0.037707	0.014884	0.030569	0.002079	0.012004	0.003677	0.101920

), Capric–Lauric eutectic and 1-Dodecanol emerged as top performers, with melting points near the target comfort range and balanced thermal properties. The organic ester mixture and form-stable paraffin/HDPE also ranked highly due to their favorable latent heat and thermal conductivity. In the tropical hot/desert zone (~28 °C,

Table 19. Full ranking of MOORA results (descending order by C) for Zone 23, tropical hot/desert (~28 °C) (e.g., Bangkok, Manila, Dubai).

Rank	Material	r_Tm	r_ΔHfus	r_VLH	r_k	r_Cp	r_rho	wr_Tm	wr_ΔHfus	wr_VLH	wr_k	wr_Cp	wr_rho	MOORA_score
1	n-Octadecane (C18)	0.163090	0.039327	0.045520	0.030555	0.048964	0.072803	0.077599	0.010091	0.006145	0.002079	0.001617	0.002403	0.100
2	CaCl2·6H2O	0.101713	0.043384	0.125337	0.030555	0.019401	0.060389	0.048349	0.011822	0.016925	0.002079	0.000641	0.001993	0.081738
3	Na2CO3·10H2O	0.131944	0.044945	0.105578	0.030555	0.195856	0.079906	0.062796	0.011555	0.014244	0.002079	0.006462	0.002637	0.100774
4	Na2HPO4·12H2O	0.131944	0.047379	0.116971	0.030555	0.226087	0.067213	0.062796	0.012178	0.015791	0.002079	0.007460	0.002217	0.102221
5	Glauber’s salt (Na2SO4·10H2O)	0.094841	0.057962	0.226435	0.030555	0.455200	0.111447	0.045100	0.014884	0.030569	0.002079	0.012004	0.003677	0.108313
6	Rubitherm RT31	0.058560	0.036364	0.044771	0.030555	0.047303	0.072945	0.027893	0.009352	0.006049	0.002079	0.001560	0.002405	0.049338
7	n-Nonadecane (C19)	0.045709	0.040106	0.045520	0.030555	0.048964	0.072803	0.021770	0.010308	0.006145	0.002079	0.001617	0.002403	0.044322
8	Rubitherm RT27	0.060028	0.038218	0.044022	0.030555	0.048964	0.064241	0.028213	0.009810	0.005942	0.002079	0.001617	0.002121	0.049783
9	Organic ester mixture	0.060028	0.043384	0.057492	0.030555	0.063457	0.067213	0.028213	0.011822	0.007761	0.002079	0.002094	0.002217	0.054186
10	Form-stable paraffin/HDPE	0.060028	0.038218	0.057492	0.030555	0.054840	0.084860	0.028213	0.009810	0.007761	0.002079	0.001810	0.002801	0.052675
11	Capric acid (C10)	0.064517	0.044945	0.053571	0.030555	0.048964	0.072803	0.030644	0.011555	0.007246	0.002079	0.001617	0.002403	0.055544
12	Fatty acid eutectic (C10–C12–C14)	0.056535	0.036364	0.050000	0.030555	0.044209	0.084860	0.026926	0.009352	0.006750	0.002079	0.001459	0.002801	0.049367
13	PEG-600	0.036360	0.038218	0.070239	0.030555	0.066989	0.084860	0.017309	0.009810	0.009488	0.002079	0.002210	0.002801	0.043698
14	1-Dodecanol	0.036360	0.049610	0.051937	0.030555	0.066089	0.069512	0.017309	0.012739	0.007010	0.002079	0.002182	0.002295	0.043615
15	n-Heptadecane (C17)	0.036360	0.038218	0.044022	0.030555	0.087654	0.047210	0.017309	0.009810	0.005942	0.002079	0.002893	0.001558	0.039591
16	Capric–Lauric eutectic	0.030284	0.049610	0.057492	0.030555	0.073141	0.072803	0.014391	0.012739	0.007761	0.002079	0.002414	0.002403	0.041786

), n-Octadecane (C18) led the rankings, supported by its ideal melting point and high latent heat of fusion. Hydrated salts such as Na₂CO₃·10H₂O and Na₂HPO₄·12H₂O also performed well, benefiting from their high volumetric latent heat and density. These results confirm MOORA’s effectiveness in identifying PCMs that offer optimal thermal performance across diverse climatic conditions through a straightforward and robust evaluation framework.

4. Discussion

This study introduces a climate-responsive PCM selection framework that integrates AHP-derived weights with five MCDM methods (COPRAS, VIKOR, TOPSIS, MOORA, PROMETHEE II). Unlike prior works, it explicitly maps PCM melting points to three climate zone set-points (18 °C, 23 °C, 28 °C), incorporates volumetric latent heat as a key criterion, and performs a cross-method convergence analysis to validate ranking robustness. This multi-zonal, multi-method approach provides a replicable and adaptable model for PCM selection in sustainable building design. The mapping of the PCM melting point to climate zones is based on the assumption that optimal indoor comfort ranges align with average outdoor temperatures. Thus, PCMs with melting points near 18 °C, 23 °C, and 28 °C are considered ideal for temperate, subtropical, and tropical zones, respectively.

The comparative evaluation of phase change materials (PCMs) using five multi-criteria decision-making (MCDM) methods—COPRAS, VIKOR, TOPSIS, MOORA, and PROMETHEE II—demonstrated consistent rankings across climate zones, reinforcing the robustness of the AHP-derived weighting scheme and validating the methodological framework. Across all methods, n-Heptadecane (C17) was consistently identified as the most suitable PCM for temperate and subtropical climates, while n-Octadecane (C18) dominated in tropical hot/desert zones. These findings align with the conclusions of Rastogi et al. [11], who emphasized the importance of matching the PCM melting point with regional comfort ranges to optimize thermal regulation and energy savings.

The strong performance of Capric–Lauric eutectic and 1-Dodecanol in subtropical zones is consistent with the work of Kumar and Singh [23], who demonstrated the effectiveness of hybrid AHP–TOPSIS models in identifying PCMs with balanced thermal and physical properties. Similarly, the favorable rankings of fatty acid eutectics support the work of Jha et al. [5], who highlighted the potential of bio-based PCMs for sustainable building envelopes, particularly in warm climates.

In tropical zones, the high rankings of hydrated salts such as CaCl₂·6H₂O, Na₂CO₃·10H₂O, and Na₂HPO₄·12H₂O reflect their superior volumetric latent heat and density, despite their lower specific heat capacities. These results corroborate the work of Mehling et al. [24], who emphasized the importance of volumetric energy density and thermal conductivity in PCM selection for high-temperature applications. The findings also align with the review by Wang et al. [2], which compared 33 MCDM algorithms and confirmed the reliability of such methods in selecting optimal PCMs for thermal energy storage systems.

The consistent top rankings of PEG-600 in temperate zones across the MOORA and PROMETHEE II methods further validate the conclusions of Parameshwaran et al. [13], who demonstrated the effectiveness of PEG-based systems in variable air volume HVAC applications. Additionally, the performance of commercial blends such as Rubitherm RT27 and RT31 across all zones supports the findings of Sun et al. [14], who showed their economic viability and thermal efficiency under diverse climate conditions.

PEG-600 demonstrated consistently high performance in the temperate zone across multiple MCDM methods. In the MOORA and PROMETHEE II evaluations, PEG-600 achieved an average normalized score of 0.953, with a 95% confidence interval of ±0.001, based on weight perturbation analysis. This statistical robustness supports its suitability for cooler climates, where its low melting point and high density contribute to effective thermal regulation. The proximity of PEG-600’s score to that of the top-ranked PCM (C17) further reinforces its inclusion in the acceptable set for temperate applications.

A summary and interpretation of the Spearman rank correlation matrices between the five MCDM methods (COPRAS, VIKOR, TOPSIS, MOORA, PROMETHEE) for each climate zone is provided below. For a temperate zone of 18 °C (

Table 20. Spearman rank correlation matrix between COPRAS, VIKOR, TOPSIS, MOORA, and PROMETHEE for each climate zone at 18 °C.

	COPRAS	VIKOR	TOPSIS	MOORA	PROMETHEE
COPRAS	1	0.8059	0.9912	0.9912	0.8059
VIKOR	0.8059	1	0.8618	0.8618	1
TOPSIS	0.9912	0.8618	1	1	0.8618
MOORA	0.9912	0.8618	1	1	0.8618
PROMETHEE	0.8059	1	0.8618	0.8618	1

), TOPSIS and MOORA show perfect agreement (ρ = 1.000). COPRAS is highly correlated with TOPSIS and MOORA (ρ ≈ 0.99), but less so with VIKOR and PROMETHEE (ρ ≈ 0.81). VIKOR and PROMETHEE are perfectly aligned (ρ = 1.000), suggesting similar ranking behavior.

For temperate zones at 23 °C (

Table 21. Spearman rank correlation matrix between COPRAS, VIKOR, TOPSIS, MOORA, and PROMETHEE for each climate zone at 23 °C.

	COPRAS	VIKOR	TOPSIS	MOORA	PROMETHEE
COPRAS	1	0.9206	0.9941	0.9941	0.9206
VIKOR	0.9206	1	0.9471	0.9471	1
TOPSIS	0.9941	0.9471	1	1	0.9471
MOORA	0.9941	0.9471	1	1	0.9471
PROMETHEE	0.9206	1	0.9471	0.9471	1

), TOPSIS and MOORA again show perfect agreement. All methods are very strongly correlated (ρ > 0.92), indicating high consistency in PCM rankings across methods in this zone.

For temperate zones at 23 °C (

Table 22. Spearman rank correlation matrix between COPRAS, VIKOR, TOPSIS, MOORA, and PROMETHEE for each climate zone at 28 °C.

	COPRAS	VIKOR	TOPSIS	MOORA	PROMETHEE
COPRAS	1	0.8118	0.9971	0.9971	0.8118
VIKOR	0.8118	1	0.8147	0.8147	1
TOPSIS	0.9971	0.8147	1	1	0.8147
MOORA	0.9971	0.8147	1	1	0.8147
PROMETHEE	0.8118	1	0.8147	0.8147	1

), TOPSIS and MOORA again perfectly agree. COPRAS is highly aligned with TOPSIS and MOORA (ρ ≈ 0.997). VIKOR and PROMETHEE are again perfectly correlated (ρ = 1.000) but show slightly lower agreement with COPRAS, TOPSIS, and MOORA.

Overall, the convergence of results across MCDM methods and their alignment with prior studies confirm the validity of the proposed framework. The integration of thermal, physical, and economic criteria ensures a comprehensive assessment of PCM suitability, offering a reliable decision-making tool for climate-responsive building design.

In addition to the thermophysical properties considered in the MCDM model, it has been taken into account that materials based on hydrated salts, such as CaCl₂·6H₂O and Na₂CO₃·10H₂O, exhibit additional characteristics relevant to their implementation in building systems. Specifically, their hygroscopic nature can lead to the absorption of ambient moisture, which affects the material’s stability and thermal storage capacity. Furthermore, the risk of leakage during the fusion process necessitates appropriate encapsulation solutions to prevent loss of active mass and structural damage. Although these variables have not been explicitly modeled in the decision matrix, they are recognized as critical factors in system design. The use of airtight encapsulations, corrosion-resistant materials, and thermal cycling tests is recommended to ensure the technical feasibility and durability of these PCMs in real-world applications.

A complete decision matrix for each climate zone (including values after any transformations), the exact normalization routine per method, and the scripts/spreadsheets are provided in Appendix A.

5. Conclusions

This study presents a comprehensive and climate-responsive framework for selecting phase change materials (PCMs) for building applications using a multi-criteria decision-making (MCDM) approach. By integrating the Analytic Hierarchy Process (AHP) for criteria weighting with five distinct MCDM methods—COPRAS, VIKOR, TOPSIS, MOORA, and PROMETHEE II—the methodology ensures a robust, transparent, and adaptable evaluation of PCM alternatives across diverse climatic zones.

The use of multiple decision models not only enhances the reliability of the selection process but also provides a multidimensional perspective on material performance, capturing trade-offs between thermal, physical, and economic properties. This approach enables designers and engineers to make informed decisions tailored to specific environmental conditions and building requirements.

The robustness of PCM rankings was evaluated by applying five distinct MCDM methods—COPRAS, VIKOR, TOPSIS, MOORA, and PROMETHEE II—using a consistent set of AHP-derived weights. Across all climate zones, the top-ranked materials (e.g., n-Heptadecane for temperate and subtropical zones; n-Octadecane and CaCl₂·6H₂O for tropical zones) showed strong convergence in the rankings, indicating high agreement among methods. This cross-method consistency suggests that the selection framework is resilient to methodological biases. Furthermore, sensitivity analysis of the AHP weighting matrix confirmed that moderate perturbations in criteria weights did not significantly alter the top-ranked PCMs, reinforcing the stability of the decision outcomes. These findings validate the reliability of the proposed approach for climate-responsive PCM selection in building applications.

Beyond its technical rigor, the framework contributes to the broader goals of sustainable building design by promoting materials that enhance energy efficiency and occupant comfort. It also offers a replicable model for future studies aiming to optimize material selection in other domains in which multiple performance criteria must be balanced.

The methodology proposed in this study can be adopted as a practical and replicable template for PCM selection in climate-responsive building applications. The process is as follows: (1) the local thermal comfort band is defined based on established standards such as EN 16798-1 or ASHRAE 55; (2) a shortlist of PCM candidates is compiled based on melting point compatibility and availability; (3) a decision matrix is populated with thermophysical and operational data sourced from literature and vendor datasheets; (4) AHP is applied to derive weights for each criterion, although these can be adapted to reflect stakeholder-specific priorities; (5) multiple MCDM methods are executed to rank the alternatives, and a consensus ranking is reported to ensure robustness; finally, (6) sensitivity analysis and system-level constraints—such as encapsulation feasibility, cost, and long-term stability—are considered to validate the practical suitability of the selected PCMs. This structured approach supports informed decision making and can be tailored to diverse climatic contexts and building typologies.

Despite the robustness of the proposed methodology, several limitations should be acknowledged. First, the property data used in the decision matrices were sourced from a combination of vendor datasheets and literature, which may vary in regards to measurement conditions, formats, and precision, introducing heterogeneity that could affect comparability. Second, important operational attributes such as thermal cycling stability and subcooling behavior were not included in the current model due to limited standardized data, although they are critical for long-term performance. Third, the study does not incorporate dynamic building simulations to validate the real-world impact of PCM integration on thermal comfort or energy savings. Lastly, regional variability in PCM availability and pricing was not modeled, which may influence practical feasibility across different markets. Future work should address these aspects by integrating dynamic simulation tools (e.g., EnergyPlus or Modelica), conducting life cycle assessments (LCA), and performing sensitivity analyses on installed costs and supply constraints to enhance the applicability of the framework in diverse building contexts.

Future work may extend this methodology by incorporating lifecycle assessments, dynamic building simulations, and real-world validation to further refine PCM selection and integration strategies.