Application of Fuzzy Risk Allocation Decision Model for Improving the Nigerian Public–Private Partnership Mass Housing Project Procurement

Abstract

Public–Private Partnership (PPP) procurement is a relatively new approach in Nigeria’s housing sector. This study introduces a Fuzzy Risk Allocation Decision Model (FRADM) designed to address the complex and subjective nature of risk allocation in PPP-procured Mass Housing Projects (MHPs). A structured quantitative approach involving 40 purposively selected PPP housing experts was employed. Using a fuzzy synthetic evaluation (FSE) technique, critical risk factors were assessed based on partners’ risk management capabilities and allocation criteria. Constants (Ci) normalized the risk-carrying capacity indices (RCCIs) of both public and private sectors. Results show that risk attitude ranks highest among nine allocation criteria (MIS = 6.21), with the private sector demonstrating higher overall risk management capability. For instance, the availability of finance risk is optimally shared 53.48% to the private and 46.52% to the public sector. The FRADM was validated as reliable, practical, and replicable. Implications point to enhanced transparency, equitable risk-sharing, and support for SDG 11. The model is a strategic tool for decision-makers in PPP housing delivery in Nigeria and can inform similar efforts in other emerging economies. Further research should examine applications across other infrastructure sectors.

1. Introduction

Sustainable Development Goal (SDG) 11 and its Target 1 stressed the necessity for inclusive, safe, resilient, and sustainable urban environments, promoting universal access to adequate, safe, and affordable housing by 2030. However, in many developing economies such as Nigeria, the housing deficit remains a critical challenge, estimated at over 20 million units due to rapid urbanization, population growth, and inadequate financial and institutional frameworks [1,2,3]. Conventional procurement approaches have proved insufficient in addressing this vast housing gap. Consequently, Public–Private Partnerships (PPPs) have emerged as a strategic procurement method to address the housing deficit [3,4].

PPPs in mass housing enable governments to leverage private sector resources, expertise, and innovation, facilitating the delivery of affordable housing with shared responsibilities and risks [3,4]. In recent years, there has been a noticeable shift in national housing policy frameworks toward PPP-driven mass housing schemes, reflecting global best practices in collaborative infrastructure delivery. Studies such as Nwangwu [3] and Owolabi et al. [5] opined that PPPs offer significant potential for addressing Nigeria’s urban housing crises through structured financing, long-term asset management, and risk-sharing arrangements. However, the success of PPPs in mass housing largely hinges on effective risk allocation strategies. Risk, being inherently subjective and multifaceted, is often poorly allocated in PPP contracts, leading to disputes, cost overruns, and project delays [2,6]. As noted by Nubor [7], misallocation of project risk severely undermines project delivery outcomes, especially when risks are transferred to partners ill-equipped to manage such risk. This challenge is especially prevalent in Nigeria, where PPP housing schemes frequently suffer from irrational and undocumented risk-sharing practices [2,8].

Although extensive research has been conducted on PPP risk allocation models in infrastructural sectors such as water, transportation, and energy [6,9], there is a significant vacuum in the literature regarding PPP Mass Housing Projects (MHPs). These projects differ from conventional infrastructure due to social dimensions, land use acts, and stakeholders’ involvement, exposing the scheme to risk such as affordability gaps, political intervention, and legal uncertainties [1,10]. Moreover, literature underscores the need for context-specific, adaptable risk allocation models that account for housing sector peculiarities [1,2,6,8,10]. Given Nigeria’s renewed commitment to PPP mass housing, evidenced by the Federal Government’s approval of several PPP housing initiatives since 2020, there is an urgent need to adopt a structured and transparent decision-support tool to optimize risk allocation in PPP mass housing [2,6,8,9]. Accordingly, this study is guided by the following research questions viz (a) how can critical risks in PPP mass housing projects be equitably allocated between partners and (b) how effective is a fuzzy synthetic evaluation model in supporting risk allocation decision-making in the Nigerian context? And the objectives of this study are to (a) develop a Fuzzy Risk Allocation Decision Model (FRADM) tailored to Nigeria’s PPP-MHPs, (b) evaluate the relative risk management capabilities of public and private partners, and (c) validate the practicability and reliability of the FRADM for guiding risk allocation decisions. The developed model integrates multi-criteria decision-making techniques with expert judgments to improve objectivity, minimize bias, and ensure that each risk is allocated to the party most capable of managing it, thereby enhancing the efficiency and long-term sustainability of the scheme.

2. Literature Review

2.1. Challenges of Risk Allocation in PPP Mass Housing Procurement

Over the past decade, PPPs have gained traction across developing countries as governments look for new ways to address acute housing shortages. These partnerships aim to draw from private sector funding and technical know-how, especially in the delivery of affordable housing. But while the model holds promise, implementation has often been difficult due to thorny issues around governance and risk [11,12].

The risks inherent in PPP projects are often specific to the different types of each PPP initiative [11]. As such, the effectiveness of PPPs is largely determined by how well resources, risks, and benefits are shared among the parties involved [13]. These risks generally manifest across several phases of construction, such as operations, finance, commerce, and the political landscape. Financial risk, for instance, often stems from inaccurate projections regarding inflation, fluctuations in interest rates, and shifts in foreign exchange markets. In the construction phase, projects are vulnerable to unforeseen delays and escalating costs, while operationally, issues such as accidents or acts of vandalism introduce additional risk and uncertainty. Commercial risks are frequently linked to flawed assumptions about expenditure or traffic flow forecasts.

Other risk factors may include political instability, weak regulatory quality, corruption, and absence of government support; all contribute to investor hesitation and reduced private sector engagement in PPPs, irrespective of PPP procurement types [14].

The complexity of PPP mass housing projects arises from the intersection of long-term contractual obligations, community needs, as well as the above-mentioned risk and uncertainty; therefore, risk allocation remains one of the most contentious elements in these projects, especially in many African countries, including Nigeria, thus limiting sustainable investment in housing schemes [2,11,14]. Several studies emphasize that affordable PPP housing should be approached as a multi-attribute decision process; unfortunately, considerations such as long-term sustainability, transparency in risk sharing, and the preservation of community values are often underplayed, defeating the developmental objectives of housing as a public good. Moreover, risk attitudes and capacities vary significantly across partners in PPPs. While governments may be better positioned to mitigate macroeconomic and political risks such as land acquisition bottlenecks, policy shifts, or inflation—the private sector typically demonstrates stronger capacity in areas like construction performance, cost control, and innovation [15,16,17]. Without a transparent and analytical framework that captures these asymmetries, decision-makers’ risk would undermine the collaborative intent of PPPs in housing procurement.

2.2. Risk Allocation Criteria in PPP Contracts

Effective risk allocation is critical to the success of any PPP initiative. Central to this is the transfer of risks to the parties best equipped to manage them. Olojede et al. [10] noted that a well-structured allocation framework will not only safeguard public and private sector interests but also enhance overall project performance; thus, risk allocation criteria provide valuable insights into how risks should be assessed and shared, emphasizing the importance of collaborative and informed decision-making [18,19].

Key criteria include the ability to anticipate and evaluate risks, allowing the responsible party to implement preventive measures [18]. Lam et al. [20] emphasized the importance of minimizing, monitoring, and controlling risks proactively, rather than reacting only after they occur. Similarly, Li et al. [21] argued that the capacity to manage the consequences of realized risks is vital, such as when a private partner mitigates financial disruptions through flexible payment models. Ameyaw and Chan [16] suggested that when risks cannot be eliminated, they should be absorbed, diversified, or managed to reduce their impact. Cost-efficiency is another essential criterion; Lam et al. [20] maintained that risks should be assumed at the lowest reasonable cost and distributed fairly among project stakeholders. In some cases, taking on risk can be advantageous, enhancing an investor’s reputation, operational efficiency, or financial returns [1,2]. For instance, a private partner demonstrating strong risk management in a mass housing PPP may gain credibility and future opportunities.

Assigning risks to those best positioned to absorb potential losses is equally crucial. Xu et al. [18] advocated for risk distribution based on the ability to mitigate severity, reduce costs, and avoid service delays. However, risk-taking should come at a fair price. Ameyaw and Chan [16] stressed the importance of reasonable and acceptable risk premiums. Governments, for example, must assess whether it is more cost-effective to bear certain risks themselves, such as foreign exchange volatility, rather than compensate private operators charging excessive premiums. Risk attitude also plays a vital role. Risks should be allocated based on each party’s risk tolerance. For instance, governments may assume expropriation risks. Adopting such principles in PPP housing projects promotes fair and efficient risk-sharing, thereby enhancing project sustainability and long-term success [15,22] (see

Table 1. Determinant of equitable risk allocation in PPP procurement.

ID	Definition	Risk Allocation Criteria (RAC)	Reference
1	Ability to minimize the loss if a risk occurs	Minimize the risk if it occurs	[2,15,16,18,19,20]
2	Ability to foresee the probability of risk occurrence and eliminate the severity of risk consequences	Foresee and assess the risk	[2,9,11,15,16,18,20]
3	Ability to avoid, minimize, monitor, and control the chance of risk occurrence	Control the chance of risk occurrence	[2,9,11,15,16,18,20,21]
4	Ability to bear the risk at the lowest price	Bear the risk at the lowest price	[2,9,15,16,18,19,20]
5	Ability to sustain the consequences of the risk	Sustained the consequence	[2,9,11,15,16,18,20,22]
6	Ability to get a reasonable and acceptable premium	Obtained a reasonable premium	[9,11,15,16,18,20,21,22]
7	Ability to enhance the risk undertaker’s credibility, reputation, and efficient risk management	Obtained benefit from risk	[2,9,11,15,16,18,19,20]
8	Ability to assume direct loss	Assumed and managed the direct loss	[2,15,16,18,20,21,22]
9	Risk should be allocated to the party who prefers to assume the risk (risk-neutral, risk-averse, or risk–prone)	risk attitude	[9,15,16,18,19,20,22]

Source: Adapted from Ameyaw [15].

).

2.3. Theoretical Risk Allocation Frameworks Used by Researchers

A theoretical framework is a set of interrelated hypotheses aimed at explaining or advancing knowledge within defined boundaries [23]. Takona [24] also described a theoretical framework as a structured representation of key concepts and their assumed interconnections. Leo-Olagbaye et al. [25] emphasized the need for reviewing and adapting existing models to align with a doctoral thesis’s research focus.

Relevant frameworks for this study include the PPP risk allocation model by [21], which categorizes risks among public, private, and third-party stakeholders. Khazaeni et al. [6] proposed a fuzzy TOPSIS decision model incorporating uncertainty and expert judgment. Awodele [26] developed a conceptual framework for risk management in Nigeria’s private finance market using empirical data. Most central to this study is the framework by Ameyaw [15] and Kukah et al. [9], which applies a fuzzy-based, Delphi-guided approach to allocate risks in PPP infrastructure projects based on each party’s capacity to manage them.

2.4. Conceptual Framework for PPP Mass Housing Risk Allocation Optimization

A conceptual framework describes what is occurring with the things being studied and why, in addition to what one is interested in investigating [24]. A graphical model developed by Ameyaw [15] and Kukah et al. [9] to allocate risk in the PPP water and power schemes in Ghana was adopted and improved upon for this study using a Fuzzy synthetic evaluation approach with the introduction of SEM analysis to allocate the critical risk factors and effects on project delivery. According to Ameyaw [15], the model depicted in Figure 1 is a systematic approach where the output of the preceding step is fed into the subsequent steps. It facilitates addressing the subjective and imprecise nature of the risk allocation procedure. The following steps are into consideration in the decision-making process: (i) establishing basic criteria; (ii) defining a set of grade alternatives for the criteria that are expressed in linguistic terms; (iii) establishing a set of weighting by calculating the weight function of the evaluation risk; (iv) develop a fuzzy evaluation matrix for the factors; and (v) applying the weightings in (iii) and matrix to determine the final fuzzy evaluation.

3. Methods

An earlier study assessed the overall risk exposure in Nigeria’s PPP mass housing projects (MHPs), identifying 31 critical risk factors (CRFs) out of 63 for allocation among key stakeholders [1]. Based on this premise, the present study applied risk allocation criteria (RAC) to develop a fuzzy-based decision model, drawing on insights from purposively selected industry experts (see

Table 2. Profile of respondents.

Expert	Position	Industry Experience	PPP Experience	Sector	Organization
Team A 1	Company Secretary	10	5	Private	C2Q Properties
Team A 2	Director	18	10	Private	Prince & Princess
Team A 3	Partner	10	8	Private	Citel Properties
Team A 4	Partner	15	10	Private	B.T.O Properties
Team A 5	Director	8	5	Private	Greenhouse International
Team A 6	Project Engineer	12	6	Private	Arbato Homes & Properties
Team A 7	Senior Partner	16	6	Private	Danbata Holdings
Team A 8	Partner	10	8	Private	Carrillion Nigeria Limited
Team A 9	Partner	10	9	Private	Slec Nigeria LTD
Team A 10	Director	8	5	Private	AROFED Resources LTD
Team A 11	Principal Partner	10	6	Private	Arbico PLC
Team A 12	Director	18	9	Private	Cappa & D’alberto PLC
Team A 13	Partner	10	8	Private	Telisol LTD
Team A 14	Partner	12	10	Private	Riozpet Integrated Services
Team A 15	Project QS	8	6	Private	LesJay Construction Company
Team A 16	Principal Engineer	10	6	Private	Julius Berger Nig PLC
Team A 17	Director	18	9	Private	Costain West Africa
Team A 18	Partner	10	8	Private	ReynoildsConstructionCompany
Team A 19	Project QS	12	10	Private	Arab Contractors
Team A 20	Project QS	8	6	Private	Setraco PLC
Team B 1	Director	20	11	Public	FMW &H
Team B 2	Director	12	6	Public	FHA
Team B 3	Deputy Director	12	5	Public	FCTA
Team B 4	Assistant Director	12	5	Public	FLB
Team B 5	Assistant Director	14	5	Public	FCDA
Team B 6	Assistant Director	20	11	Public	FMW &H
Team B 7	Assistant Director	12	6	Public	FHA
Team B 8	Principal Qs	12	5	Public	FCTA
Team B 9	Principal Qs	12	5	Public	FLB
Team B 10	Principal Engineer	14	5	Public	FCDA
Team B 11	Principal Qs	20	11	Public	FMW &H
Team B 12	Principal Engineer	12	6	Public	FHA
Team B 13	Principal Qs	12	5	Public	FCTA
Team B 14	Principal Engineer	12	5	Public	FLB
Team B 15	Principal Engineer	14	5	Public	FCDA
Team B 16	Architect	20	11	Public	FMW &H
Team B 17	Principal Engineer	12	6	Public	FHA
Team B 18	Quantity Surveyor I	12	5	Public	FCTA
Team B 19	Principal Builder	12	5	Public	FLB
Team B 20	Principal Engineer	14	5	Public	FCDA

FMW &H = Federal Ministry of Works & Housing; FHA = Federal Housing Authority; FC TA/DA = Federal Capital Territory, Abuja/Development Authority; FLB = Federal Loans Board.

). The composition of the two expert panels is outlined in the table, while

Table 3. Evaluation framework/linguistic terms for input variables.

Scale	Linguistic Term	Input Variables	Range of RM Capability	Constant (Ci)
1	Very low	ui1	0–0.25	0.125 (C1)
2	Low	ui2	0–0.50	0.250 (C2)
3	Moderate	ui3	0.25–0.75	0.500 (C3)
4	High	ui4	0.50–1.00	0.750 (C4)
5	Very high	ui5	0.75–1.00	0.875 (C5)

presents the grading matrix used to assess both risk transfer proportions and management capabilities.

Each panel from the Public and Private sectors comprised 20 professionals actively engaged in PPP-MHPs in Lagos and Abuja, and due to the relatively recent adoption of PPP in Nigeria’s housing sector, a snowball sampling approach was used to identify participants with relevant experience and organizational roles. Their input was considered both credible and essential to the study’s objectives.

The study employed an exponential non-discriminative snowball sampling method, wherein the initial participant referred multiple others. In simpler terms, the researcher engaged a primary respondent, who then connected several additional participants. As Adeoye [27] noted, all referrals should be included to reach a broader and more representative sample. To normalize the Membership Functions (MFs) and the Risk Carrying Capability Index (RCCI) for both parties, a constant (Ci) was derived using the Risk Management Capability (RMC) scale ranging from 0 to 1, as detailed in Table 3.

The model employs the Fuzzy Synthetic Evaluation (FSE) method to simultaneously assess multiple risk allocation criteria (RACs), accommodating the subjective and imprecise nature of PPP housing [15]. Following the identification of nine RACs, the 31 critical risk factors (CRFs) were evaluated and distributed between the public and private sectors using a five-point scale, where 1 indicates extremely low capability and 5 represents very high capability.

Respondents previously engaged in the study were re-contacted via email to validate the findings and assess the proposed risk allocation model for PPP mass housing projects (MHPs) in Lagos and Abuja. Over a three-week period, 20 responses were collected. The validation questionnaire included information on respondent profiles, the identified critical risk factors (CRFs), and the model’s output based on the Risk-Carrying Capability Indices (RCCIs) of both parties. A five-point Likert scale (1 = poor, 5 = excellent) was used to score each item. Respondents evaluated seven dimensions to assess the model’s relevance and practicality as follows: (a) appropriateness of input variables in reflecting the public/private partner’s risk management capacity, (b) reasonableness of variable rankings, (c) realism of risk allocation ratios for actual PPP-MHPs, (d) applicability of the fuzzy model in guiding decision-making, (e) ease of understanding and use by practitioners, (f) clarity and replicability of implementation procedures for both researchers and professionals, and (g) the model’s overall suitability for risk allocation in PPP-driven housing projects.

4. Results

Table 4. Risk allocation criteria for PPP-MHPs.

ID	Risk Allocation Criteria (RAC)	Mean	Std. Deviation	Ranking
9	Risk attitude	6.21	0.613	1
1	Minimize the risk if it occurs	6.18	0.895	2
3	Control the chance of risk occurrence	6.12	0.615	3
2	Foresee and assess the risk	6.10	0.509	4
6	Obtained a reasonable premium	6.00	0.537	5
4	Bear the risk at the lowest price	5.69	0.615	6
8	Assumed and managed direct loss	5.43	0.948	7
5	Sustained the consequence	5.34	0.648	8
7	Obtained benefit from risk	5.19	0.695	9

presents the mean rankings of the risk allocation criteria used in PPP-MHPs in Nigeria, based on a 7-point Likert scale. Among the evaluated criteria, partners’ risk attitude received the highest mean score (6.21), indicating its perceived importance in risk allocation. This was followed by the capacity to manage the likelihood of risk occurrence (6.18) and the ability to mitigate risks once they arise (6.12). In contrast, the capacity to bear the consequences of risk and to benefit from risk ranked lower, with mean scores of 5.34 and 5.19, respectively. Despite these variations, all criteria were considered relevant, with mean values ranging between 5.19 and 6.21, underscoring their collective significance in allocating perceived risks within PPP-MHPs.

4.1. Application of the Fuzzy Risk Allocation Decision Model (FRADM)

A single salient risk factor (Availability of Finance, also referred to as RF1) was selected from among the 31 established critical risk factors to illustrate the operation of the fuzzy allocation decision model.

Table 5. Input variables and their weighting functions.

ID	Risk Allocation Principles/Criteria (RAP/C)	Mean	Weighting Function
U1	Risk attitude	6.21	0.119
U2	Minimize the risk if it occurs	6.18	0.118
U3	Control the chance of risk occurrence	6.12	0.117
U4	Foresee and assess the risk	6.10	0.115
U5	Obtained a reasonable premium	6.00	0.116
U6	Bear the risk at the lowest price	5.69	0.109
U7	Assumed and managed the direct loss	5.43	0.104
U8	Sustained the consequence	5.34	0.103
U9	Obtained benefit from risk	5.19	0.099
	Total Mean Value	52.26	∑wi =1.00

,

Table 6. RCCI of the government for the availability of finance (RF1).

ID	Risk Allocation Criteria (RAC)	Weighting wi	MFs of Input Variables (RAP/C)	MF of RCCI (gov)
u1	Risk attitude	0.119	(0.00,0.00,0.40,0.60,0.00)
u2	Minimize the risk if it occurs	0.118	(0.00,0.20,0.60,0.20,0.00)
u3	Control the chance of risk occurrence	0.117	(0.00,0.20,0.40,0.40,0.00)
u4	Foresee and assess the risk	0.115	(0.00,0.00,1.00,0.00,0.00)	(0.00,0.08,0.55,0.34,0.03)
u5	Obtained a reasonable premium	0.116	(0.00,0.00,1.00,0.00,0.00)
u6	Bear the risk at the lowest price	0.109	(0.00,0.20,0.00,0.60,0.20)
u7	Assumed and managed direct loss	0.104	(0.00,0.00,0.20,0.80,0.00)
u8	Sustained the consequence	0.103	(0.00,0.00,0.20,0.80,0.00)
u9	Obtained benefit from risk	0.099	(0.00,0.00,0.80,0.20,0.00)

and

Table 7. RCCI of private for the availability of finance (RF1).

ID	Risk Allocation Criteria (RAC)	Weighting wi	MFs of Input Variables (RAP/C)	MF of RCCI (Private)
u1	Risk attitude	0.119	(0.00,0.00,0.20,0.80,0.00)
u2	Minimize the risk if it occurs	0.118	(0.00,0.00,0.20,0.80,0.00)
u3	Control the chance of risk occurrence	0.117	(0.00,0.00,0.60,0.40,0.00)
u4	Foresee and assess the risk	0.115	(0.00,0.00,0.20,0.80,0.00)	(0.00,0.00,0.35,0.65,0.00)
u5	Obtained a reasonable premium	0.116	(0.00,0.00,0.40,0.60,0.00)
u6	Bear the risk at the lowest price	0.109	(0.00,0.00,0.20,0.80,0.00)
u7	Assumed and managed direct loss	0.104	(0.00,0.00,0.20,0.80,0.00)
u8	Sustained the consequence	0.103	(0.00,0.00,0.80,0.20,0.00)
u9	Obtained benefit from risk	0.099	(0.00,0.00,0.40,0.60,0.00)

display the findings of the remaining 30 CRFs.

4.1.1. Determining the Input Variables’ (IVs’) Weighting Function

In step 1, the Nine (9) Risk Allocation Principles have been established and defined as input variables; therefore, given that the overall mean of IVs is 52.26, the weighting function of the variables is calculated. For instance, the weighting function of “Risk attitude (U1)” is normalized and obtained as follows:

$$\mathrm{W}{u}_1= {\displaystyle \frac{6.21}{6.21+6.18+6.12+6.10+6.00+5.69+5.43+5.34+5.19}=6.21/52.26=0.119}$$

Using this approach, Table 5 reports the weighting function of the other input variables.

4.1.2. Determining the Input Variables’ Membership Function

The membership function for an assessed risk factor’s input variable was determined by the combined expertise of each team. The survey indicates that Team A (Public) evaluated u1 (Risk Attitude) for RF1 in the following manner: 0% indicates very low capability, 40% indicates moderate capability, 60% indicates high capability, and 0% indicates very high capability. As a result, Team A’s membership function (MF) of u1 for RF1 is computed as follows:

$$MF{u}_{1\left(A\right)}={\displaystyle \frac{0.00}{very low}}+{\displaystyle \frac{0.00}{low}}+{\displaystyle \frac{0.40}{moderate}}+{\displaystyle \frac{0.60}{high}}+{\displaystyle \frac{0.00}{very high}}={\displaystyle \frac{0.00}{1}}+{\displaystyle \frac{0.00}{2}}+{\displaystyle \frac{0.40}{3}}+{\displaystyle \frac{0.60}{4}}+{\displaystyle \frac{0.00}{5}}$$

It is possible to rewrite the MF of MFu1 (A) as (0.00, 0.00, 0.40, 0.60, and 0.00). The MF of the remaining input variables (u₂–u₉) is calculated and reported using the same approach, and the fuzzy matrix for RF1 is presented as follows:

	MFu1	(0.00,0.00,0.40,0.60,0.00)
	MFu2	(0.00,0.20,0.60,0.20,0.00)
	MFu3	(0.00,0.20,0.40,0.40,0.00)
	MFu4	(0.00,0.00,1.00,0.00,0.00)
R(A) =	MFu5	(0.00,0.00,1.00,0.00,0.00)
	MFu6	(0.00,0.20,0.00,0.60,0.20)
	MFu7	(0.00,0.00,0.20,0.80,0.00)
	MFu8	(0.00,0.00,0.40,0.80,0.00)
	MFu9	(0.00,0.00,0.80,0.20,0.00)

Similarly, Team B’s (Private) evaluation of the memberships function of the input variables for RF1 is expressed as follows: 0% denoting very low capability, 20% denoting moderate capability, 80% denoting high capability, and 0% denoting very high capability, Team B’s membership function (MF) of u₁ for RF1 is calculated as follows:

$$MF{u}_{1\left(B\right)}={\displaystyle \frac{0.00}{very low}}+{\displaystyle \frac{0.00}{low}}+{\displaystyle \frac{0.20}{moderate}}+{\displaystyle \frac{0.80}{high}}+{\displaystyle \frac{0.00}{very high}}={\displaystyle \frac{0.00}{1}}+{\displaystyle \frac{0.00}{2}}+{\displaystyle \frac{0.20}{3}}+{\displaystyle \frac{0.80}{4}}+{\displaystyle \frac{0.00}{5}}$$

The MF of MFu1(B) is thus rewritten as follows: (0.00, 0.00, 0.20, 0.80, and 0.00); the fuzzy matrix for the remaining input variables (u₂–u₉) for RF1 by Team B is expressed as follows:

	MFu1	(0.00,0.00,0.20,0.80,0.00)
	MFu2	(0.00,0.00,0.20,0.80,0.00)
	MFu3	(0.00,0.00,0.60,0.40,0.00)
	MFu4	(0.00,0.00,0.20,0.80,0.00)
R(B) =	MFu5	(0.00,0.00,0.40,0.60,0.00)
	MFu6	(0.00,0.00,0.20,0.80,0.00)
	MFu7	(0.00,0.00,0.20,0.80,0.00)
	MFu8	(0.00,0.00,0.80,0.20,0.00)
	MFu9	(0.00,0.00,0.40,0.60,0.00)

These matrixes are presented in Table 6 and Table 7, respectively.

4.1.3. Determining the Public/Private Partners’ RCCI Membership Functions

Determining the membership function RCCI for both sectors follows after calculating the membership function of the input variable. The MF of the Public Partner’s RCCI for RF1 is thus computed using the fuzzy matrix (RA) and the weighting function (wi) that was calculated through the fuzzy composite operation.

$$D_1=w_i\circ R_i=(d_{1,},d_2\dots \dots \dots d_n)$$

									MFu1
									MFu2
									MFu3
									MFu4
									MFu5
DRRCCIgov = Wi * R(A) = (Wu1, Wu2, Wu3, Wu4, Wu5, Wu6, Wu7, Wu8, Wu9) X									MFu6
									MFu7
									MFu8
									MFu9

						(0.00,0.00,0.40,0.60,0.00)
						(0.00,0.20,0.60,0.20,0.00)
						(0.00,0.20,0.40,0.40,0.00)
						(0.00,0.00,1.00,0.00,0.00)
DRRCCIgov = (0.119,0.118,0.117,0.115,0.116,0.109,0.104,0.103,0.099) X						(0.00,0.00,1.00,0.00,0.00)
						(0.00,0.20,0.00,0.60,0.20)
						(0.00,0.00,0.20,0.80,0.00)
						(0.00,0.00,0.20,0.80,0.00)
						(0.00,0.00,0.80,0.20,0.00)

= (0.00,0.08,0.55,0.34,0.03)

The result is shown in

Table 8. RCCI and RMC of government and private partners for the CRFs.

		Membership Functions of Risk Carrying Capacity Index (RCCI)
ID	Critical Risk Factors	Government	Private
RF1	Availability of finance	(0.00,0.08,0.55,0.34,0.03)	(0.00,0.00,0.35,0.65,0.00)
RF2	High finance cost	(0.00,0.27,0.45,0.28,0.00)	(0.00,0.04,0.28,0.68,0.00)
RF3	Unstable value of local currency	(0.00,0.21,0.31,0.48,0.00)	(0.00,0.46,0.54,0.00,0.00)
RF4	Lack of creditworthiness	(0.16,0.66,0.16,0.02,0.00)	(0.00,0.13,0.37,0.50,0.00)
RF5	Influential economic events (boom/recession)	(0.00,0.05,0.48,0.47,0.00)	(0.00,0.21,0.60,0.19,0.00)
RF6	High bidding cost	(0.14,0.53,0.24,0.09,0.00)	(0.00,0.10,0.44,0.46,0.00)
RF7	Poor financial market	(0.00,0.22,0.41,0.37,0.00)	(0.00,0.53,0.47,0.00,0.00)
RF8	Financial attraction to project investors	(0.00,0.57,0.38,0.05,0.00)	(0.00,0.00,0.32,0.68,0.00)
RF9	Interest rate volatility	(0.00,0.17,0.38,0.45,0.00)	(0.00,0.34,0.64,0.02,0.00)
RF10	Inflation rate volatility	(0.00,0.10,0.45,0.45,0.00)	(0.00,0.27,0.69,0.04,0.00)
RF11	Corruption and lack of respect for the law	(0.03,0.29,0.37,0.31,0.00)	(0.00,0.31,0.60,0.09,0.00)
RF12	Non-involvement of the host community	(0.00,0.23,0.39,0.38,0.00)	(0.00,0.14,0.56,0.30,0.00)
RF13	Poor execution of housing policies	(0.00,0.18,0.31,0.51,0.00)	(0.00,0.22,0.51,0.27,0.00)
RF14	Wrong perception of housing need by low-income earners	(0.00,0.27,0.44,0.29,0.00)	(0.00,0.11,0.51,0.38,0.00)
RF15	Illegal title to land	(0.00,0.51,0.42,0.07,0.00)	(0.00,0.02,0.67,0.13,0.00)
RF16	The poor decision-making process	(0.00,0.09,0.49,0.42,0.00)	(0.00,0.39,0.40,0.21,0.00)
RF17	Change in government	(0.00,0.13,0.35,0.52,0.00)	(0.00,0.38,0.33,0.29,0.00)
RF18	Land grabbing/encroachment	(0.00,0.70,0.27,0.03,0.00)	(0.00,0.18,0.36,0.46,0.00)
RF19	Public opposition to the mass housing projects	(0.00,0.51,0.42,0.07,0.00)	(0.00,0.38,0.51,0.11,0.00)
RF20	Inadequate experience in PPP	(0.00,0.39,0.50,0.11,0.00)	(0.00,0.22,0.52,0.26,0.00)
RF21	Inadequate distribution of responsibility and risks	(0.00,0.06,0.58,0.36,0.00)	(0.00,0.21,0.60,0.18,0.00)
RF22	Risk regarding pricing of product/service	(0.00,0.71,0.29,0.00,0.00)	(0.00,0.00,0.45,0.55,0.00)
RF23	Lack of commitment from public/private partners	(0.00,0.21,0.64,0.15,0.00)	(0.00,0.21,0.44,0.35,0.00)
RF24	Inadequate distribution of authority between partners	(0.00,0.00,0.58,0.42,0.00)	(0.00,0.07,0.74,0.19,0.00)
RF25	Land acquisition and site availability	(0.00,0.30,0.49,0.21,0.00)	(0.00,0.49,0.44,0.07,0.00)
RF26	Level of demand for the mass housing projects	(0.00,0.07,0.47,0.46,0.00)	(0.00,0.32,0.45,0.23,0.00)
RF27	Prolonged negotiation period before initiation	(0.00,0.20,0.47,0.33,0.00)	(0.00,0.22,0.54,0.24,0.00)
RF28	Delay in project approvals and permits	(0.00,0.11,0.37,0.52,0.00)	(0.00,0.54,0.44,0.02,0.00)
RF29	Construction time delay	(0.00,0.69,0.29,0.02,0.00)	(0.00,0.14,0.38,0.48,0.00)
RF30	Construction cost overrun	(0.00,0.69,0.27,0.04,0.00)	(0.00,0.06,0.31,0.63,0.00)
RF31	Force majeure	(0.00,0.50,0.44,0.06,0.00)	(0.00,0.34,0.66,0.00,0.00)

.

In the same way, the Private Partner determines the MF of RCCI for RF1 as follows:

	(0.00,0.00,0.20,0.80,0.00)
	(0.00,0.00,0.20,0.80,0.00)
	(0.00,0.00,0.60,0.40,0.00)
	(0.00,0.00,0.20,0.80,0.00)
DRRCCIPrivate = (0.119,0.118,0.117,0.115,0.116,0.109,0.104,0.103,0.099) X	(0.00,0.00,0.40,0.60,0.00)
	(0.00,0.00,0.20,0.80,0.00)
	(0.00,0.00,0.20,0.80,0.00)
	(0.00,0.00,0.80,0.20,0.00)
	(0.00,0.00,0.40,0.60,0.00)

= (0.00,0.00,0.35,0.65,0.00)

The MF of RCCI of the other important risk factors, established by both parties using the same approach, is shown in Table 8.

4.1.4. Determine the Public and Private Sectors’ RCCI and RCM

By taking into account the scale intervals constant, the MF Public DRRCCI_gov and Private DRRCCI_Private are normalized. The Public Partner RCCI has been normalized for RF1 (finance risk) as follows:

$$DRRCCIgov={\sum }_{i-1}^{5}DRRCCIgov \mathrm{X} {\mathrm{C}}^{\mathrm{T}}=(0.00, 0.08, 0.55, 0.34, 0.03)\times (0.125, 0.250, 0.500, 0.750, 0.875)=0.58$$

The defuzzified risk management capability level for RF1 is given as follows:

$$RMCgov={\sum }_{i-1}^{5}DRRCCIgov. x \mathrm{V}=(0.00, 0.08, 0.55, 0.34, 0.03)\times (1, 2, 3, 4, 5)=3.3 (\mathrm{Moderate})$$

Similarly, the RCCI for RF1 is normalized for the Private Partners as follows:

$$D\mathrm{R}\mathrm{R}\mathrm{C}\mathrm{C}\mathrm{I}Private={\sum }_{i-1}^{5}DRRCCIPrivate \mathrm{X} {\mathrm{C}}^{\mathrm{T}}=(0.00, 0.00, 0.35, 0.65, 0.00)\times (0.125, 0.250, 0.500, 0.750, 0.875)=0.66$$

The defuzzified risk management capability level for RF1 by Private Partners is given as follows:

$$RMCprivate={\sum }_{i-1}^{5}DRRCCIPrivate. x \mathrm{V} =(0.00, 0.00, 0.35, 0.65, 0.00)\times (1, 2, 3, 4, 5)=3.6 (\mathrm{High})$$

The scale interval of RMC is interpreted as follows: RMC < 1.5 denotes extremely low-risk management capability; 1.5 ≤ RMC < 2.5 indicates low-risk management capability; 2.5 ≤ RMC < 3.5 signifies moderate risk management capability; 3.5 ≤ RMC < 4.5 represents high-risk management capability; and RMC ≥ 4.2 reflects very high-risk management capability. The outcomes of the remaining CRFs’ RCCI and RMC are computed for both the public and private sectors utilizing the same technique as previously outlined.

4.1.5. Quantify Risk Allocation Proportion

Ameyaw [15] asserted that public and private partners possess distinct capabilities for managing risk associated with a certain risk factor. This study relies on prior research indicating that risk should be allocated to the party capable of managing its consequences. The risk allocation proportions are expressed as a percentage of the RCCI for both parties. The proportion of RF1 (Availability of Finance) that the government assumes is quantified as follows:

$$P_u={\displaystyle \frac{RCC{I}_{gov.}}{RCC{I}_{gov.}+RCC{I}_{prvate}}}\times 100\% = P_u={\displaystyle \frac{0.58}{0.58+0.66}}\times 100\%=46.52\%$$

Similarly, the percentage of RF1 that the private bears is given as follows:

$$P_r={\displaystyle \frac{RCC{I}_{\mathrm{Pr}i}}{RCC{I}_{gov.}+RCC{I}_{prvate}}}\times 100\% = P_r={\displaystyle \frac{0.66}{0.58+0.66}}\times 100\%=53.48\%$$

4.2. Validation of Fuzzy Risk Allocation Decision Model

To validate the proposed model in Figure 1 and the result in

Table 9. Summary of model results.

ID	Critical Risk Factors	Risk Management Capability (RMC) Level				RCCIs and Proportion of Risk Allocation (%)
		Government		Private		Government		Private
		Index	Linguistic	Index	Linguistic	RCCI	%	RCCI	%
CRF1	Availability of finance	3.32	Moderate	3.65	High	0.58	46.52	0.66	53.48
CRF2	High finance cost	3.01	Moderate	3.64	High	0.50	43.23	0.66	56.77
CRF3	Unstable value of local currency	3.27	Moderate	2.54	Moderate	0.57	59.58	0.39	40.42
CRF4	Lack of creditworthiness	2.04	Low	3.37	Moderate	0.28	33.33	0.56	66.67
CRF5	Influential economic events (boom/recession)	3.42	Moderate	2.98	Moderate	0.61	57.76	0.44	42.24
CRF6	High bidding cost	2.28	Low	3.36	Moderate	0.34	37.40	0.57	62.60
CRF7	Poor financial market	3.15	Moderate	2.47	Moderate	0.54	69.58	0.24	30.42
CRF8	Financial attraction to project investors	2.48	Moderate	3.68	High	0.37	35.58	0.67	64.42
CRF9	Interest rate volatility	3.28	Moderate	2.68	Moderate	0.57	62.98	0.34	37.02
CRF10	Inflation rate volatility	3.35	Moderate	2.77	Moderate	0.59	57.04	0.44	42.96
CRF11	Corruption and lack of respect for the law	2.96	Moderate	2.78	Moderate	0.49	52.60	0.45	47.40
CRF12	Non-involvement of the host community	3.15	Moderate	3.16	Moderate	0.54	49.88	0.54	50.12
CRF13	Poor execution of housing policies	3.33	Moderate	3.05	Moderate	0.58	53.20	0.51	46.80
CRF14	Wrong perception of housing needs by low-income earners	3.02	Moderate	3.27	Moderate	0.51	47.09	0.57	52.91
CRF15	Illegal title to land	2.56	Moderate	2.57	Moderate	0.39	47.13	0.44	52.87
CRF16	Poor decision-making process	3.33	Moderate	2.82	Moderate	0.58	56.14	0.46	43.86
CRF17	Change in government	3.39	Moderate	2.91	Moderate	0.60	55.58	0.48	44.42
CRF18	Land grabbing/encroachment	2.33	Moderate	3.28	Moderate	0.33	36.84	0.57	63.16
CRF19	Public opposition to the mass housing projects	2.56	Moderate	2.73	Moderate	0.39	47.42	0.43	52.58
CRF20	Inadequate experience in PPP	2.72	Moderate	3.04	Moderate	0.43	45.74	0.51	54.26
CRF21	Inadequate distribution of responsibility and risks	3.30	Moderate	2.94	Moderate	0.58	54.12	0.49	45.88
CRF22	Risk regarding the pricing of the product/service	2.29	Low	3.55	High	0.32	33.59	0.64	66.41
CRF23	Lack of commitment from public/private partners	2.94	Moderate	3.14	Moderate	0.49	47.55	0.54	52.45
CRF24	Inadequate distribution of authority between partners	3.42	Moderate	3.12	Moderate	0.61	53.30	0.53	46.70
CRF25	Land acquisition and site availability	2.91	Moderate	2.58	Moderate	0.48	54.73	0.40	45.27
CRF26	Level of demand for the mass housing projects	3.39	Moderate	2.91	Moderate	0.60	55.58	0.48	44.42
CRF27	Prolonged negotiation period before initiation	3.13	Moderate	3.02	Moderate	0.53	51.33	0.51	48.67
CRF28	Delays in project approvals and permits	3.41	Moderate	2.48	Moderate	0.60	61.95	0.37	38.05
CRF29	Construction time delay	2.33	Moderate	3.34	Moderate	0.33	36.24	0.59	63.76
CRF30	Construction cost overrun	2.35	Moderate	3.57	High	0.34	34.44	0.64	65.56
CRF31	Force majeure	2.56	Moderate	2.66	Moderate	0.39	48.45	0.42	51.55

, respondents assessed seven key aspects, including its appropriateness, practicality, applicability, reliability, and overall suitability. As shown in

Table 10. Validation results for the risk allocation model.

No	Factors	Average	Good	Very Good	Excellent	Mean
a	Are the input variables (risk allocation principles) appropriate, such that they reflect the risk management capability of a Public/Private Partner?	0	3	10	7	4.20
b	Are the importance rankings of the input variables reasonable?	0	2	13	5	4.15
c	Are the risk allocation proportions reasonable and practical in a typical PPP Mass Housing Project’s delivery in Nigeria?	1	5	14	0	3.65
d	Is the fuzzy synthetic evaluation risk allocation model practical and applicable enough to enable PPP practitioners to apply it to support risk allocation decision-making?	2	3	12	3	3.80
e	Is the fuzzy synthetic evaluation risk allocation model easy to understand and use by practitioners	1	0	13	6	4.20
f	Are the steps involved in applying the model logical, such that the model can be replicated by researchers and practitioners	0	3	11	6	4.15
g	Overall suitability to be adopted in practice for risk allocation decision-making in PPP-procured Mass Housing Projects	0	3	13	4	4.05

, there was strong consensus on the relevance of the risk allocation criteria (RAC), with a mean score of 4.20, affirming accurate reflection of public and private partners’ risk management capacities. The prioritization of these criteria was also well supported by a high mean of 4.15, suggesting broader applicability across various PPP projects.

A mean score of 3.65 for risk allocation proportions indicates agreement that risk sharing should be tailored to individual projects and is feasible in Nigeria’s PPP-MHP context. Respondents also affirmed the model’s utility in decision-making, as reflected in the 3.80 mean score for its practical application. The FSE-based model was rated favorably overall, achieving a validation score of 4.20, indicating substantial expert support. The procedural logic of the model was considered replicable, earning a mean of 4.15, suggesting that both academics and practitioners could apply it across other PPP infrastructure projects. Finally, the model’s overall suitability for risk allocation in PPP-MHPs received a mean score of 4.05, confirming expert confidence in its effectiveness and relevance to the sector.

5. Discussion

Table 9 presents the model output derived using the Fuzzy Synthetic Evaluation (FSE) method, which determines the risk allocation ratios between public and private partners in PPP mass housing projects. The Fuzzy Risk Allocation Decision Model (FRADM) results indicate that risk distribution differs notably between the two sectors. Evaluations were based on a five-point scale, where 1 represents extremely poor capability and 5 represents very good capability. Each risk factor is fully allocated (100%), with proportions ranging from 0% (no responsibility) to 50% (shared responsibility) and up to 100% (full responsibility by one party). A party assuming at least 50% of a risk factor is considered primarily responsible for its management.

The Risk-Carrying Capability Index (RCCI), also ranging from 0 to 1, quantifies each party’s ability to manage specific risks. Higher RCCI values indicate stronger risk-bearing capacity. The findings reveal that the public sector can moderately manage 15 risk factors, each with a minimum 50% allocation. The private sector demonstrates moderate capability for 11 risk factors and high capability for 5, all exceeding the 50% threshold. Given the inherent complexity and risk of PPP-MHPs, it is evident that no single party can assume all risks. Effective collaboration and shared responsibility are essential for achieving the objectives of PPP housing initiatives and advancing SDG Goal 11.

5.1. Risks Allocated to the Public Sector in the PPP Mass Housing Scheme

These risks are inherently tied to the public sector due to its regulatory and leadership roles in PPPs. As shown in Table 4, the sector’s capacity reflects its risk attitude and ability to mitigate and manage potential risk occurrences, and the top 10 risk variables allocated to the sector are discussed as follows:

Currency fluctuation presents a major risk (RCCI = 0.57; allocation = 58.58%) to this sector, thereby increasing project costs and deterring private investment. The government’s recent monetary policies, such as currency redesign to curb excessive cash outside the banking system, are aimed at stabilizing the naira and improving investment conditions in the housing sector [28,29,30]. Economic cycles, including booms and recessions (RCCI = 0.61; allocation = 57.76%), can also be best managed by the public sector. Nigeria’s past experiences with both cycles have influenced household welfare and sectoral stability [31,32,33]. Policy responses like the Economic Recovery and Growth Plan (ERGP) reflect efforts to buffer adverse impacts and build economic resilience [34].

Financial market instability (RCCI = 0.54; allocation = 69.58%) significantly affects PPPs. Nigeria’s underdeveloped financial systems increase market risk, influence investor confidence, and limit credit access [35,36,37]. Enhancing financial infrastructure, especially through better credit mechanisms, remains key to improving housing finance. Interest rate volatility (RCCI = 0.57; allocation = 62.98%) impacts borrowing costs for private developers, while inflation (RCCI = 0.59; allocation = 57.04%) affects cost predictability in construction. Monetary policy adjustments are essential for stabilizing investment conditions in the sector [38,39,40].

Corruption and weak legal compliance (RCCI = 0.49; allocation = 52.60%) undermine PPP execution. This includes inconsistent law enforcement and unethical behavior, often deterring private investment. Effective public sector leadership and adherence to legal frameworks are critical to reducing these risks [2,41,42]. Ineffective execution of housing policies (RCCI = 0.58; allocation = 53.20%) remains a persistent challenge. Despite policy frameworks, poor implementation has hindered sectoral outcomes. Targeted awareness campaigns and stakeholder engagement could improve uptake and performance [2,43]. Flawed decision-making (RCCI = 0.58; allocation = 56.14%) impacts PPP outcomes. Weak institutional performance in areas such as permitting and enforcement constrains infrastructure growth [44,45]. Institutional reform is necessary to reduce bureaucratic delays and promote investor confidence. Changes in government (RCCI = 0.60; allocation = 55.58%) may disrupt long-term housing initiatives due to policy shifts. Strengthening autonomous bodies like the ICRC could enhance policy continuity and protect PPP projects from political fluctuations [2,46].

5.2. Risks Allocated to the Private Sector in the PPP Mass Housing Scheme

These risks are uniquely suited to the private sector, given its operational flexibility, financial expertise, and capacity to manage uncertainties. As shown in Table 4, allocations are guided by the sector’s risk attitude, mitigation ability, and likelihood control.

The availability of finance risk (RCCI = 0.66; allocation = 53.48%) is assigned to the private sector, reflecting its stronger capacity to mobilize capital. Given limited public funds, it is expected that private entities source project financing [14,42]. Similarly, high financing costs (RCCI = 0.66; allocation = 56.77%) fall under private responsibility due to their experience in financial planning and cost control. Lack of creditworthiness (RCCI = 0.56; allocation = 66.67%) is also a private sector risk, as securing loans hinges on financial stability and repayment reliability [2,47]. High bidding costs (RCCI = 0.57; allocation = 62.60%) are attributed to private partners who bear tendering expenses and manage procurement processes efficiently [13,42]. Although some studies argue that the public sector is better positioned to support project viability through incentives [13,42], this study allocates the risk of financial attractiveness (RCCI = 0.67; allocation = 64.42%) to the private sector. For PPP housing, relatively short contract durations offer quicker returns, aligning with private investment goals.

Misinterpretation of housing needs by low-income earners (RCCI = 0.57; allocation = 52.91%) is linked to the private sector’s role in stakeholder engagement. Their responsibility lies in informing end-users of project benefits and clarifying misconceptions related to location and design [2]. Illegal land titles (RCCI = 0.44; allocation = 52.87%) and encroachment (RCCI = 0.57; allocation = 63.13%) are attributed to private entities, particularly when access to land is gained through unofficial channels. This practice often leads to speculation and conflicts among developers, threatening project continuity [2,42]. Liu and Fong [48] argued that the private sector’s motivation, efficiency, and risk-handling expertise make it better suited to manage these risks in a cost-effective manner.

6. Conclusions

The study presents a robust methodology for assessing and assigning risks in PPP mass housing schemes, ensuring that they are allocated to the parties most capable of managing them. Findings reveal that the private sector assumes a larger share of risk due to its expertise, technological capacity, and managerial efficiency, which collectively enhance project delivery. Conversely, public sector risks stem largely from policy, regulatory, and macroeconomic conditions.

As Yuan and Zhang [49] noted, equitable risk distribution is essential for PPP success. This research introduces a Fuzzy Risk Allocation Decision Model (FRADM), which transforms subjective expert opinions and qualitative risk allocation criteria into quantitative outputs using fuzzy set theory. The FRADM offers a transparent and systematic framework for risk allocation, strengthening decision-making in PPP-MHPs. It recommends that stakeholders rigorously assess each party’s risk-handling capabilities prior to allocation to improve accountability and project outcomes. Adopting the nine risk allocation criteria enhances the model’s accuracy and efficiency, offering a credible alternative to subjective, preference-driven approaches. It also functions as a practical negotiation tool, enabling balanced and adaptive risk-sharing between public and private partners. Implementation of this model can reduce project delays and uncertainties while improving the long-term viability of PPP housing schemes globally.

6.1. Practical Implications and Lessons from Global PPP Practice

This study provides valuable insights for PPP stakeholders in Nigeria, especially in optimizing risk allocation for mass housing delivery. Drawing lessons from global experiences such as PPP housing initiatives in India, South Africa, and Malaysia, this emphasizes the need for structured decision-making models like the FRADM to support project viability. In India’s Rajiv Awas Yojana, for instance, clear frameworks for land risk and affordability gaps contributed to improved outcomes. Likewise, South Africa’s Social Housing Program incorporated private innovation with state guarantees, mirroring some of the shared-risk principles applied in this study.

For Nigeria, the FRADM demonstrates how evidence-based tools can improve collaboration, transparency, and long-term sustainability in PPP housing schemes. PPP stakeholders are encouraged to adopt the nine risk allocation criteria and fuzzy logic mechanisms for equitable risk-sharing. This approach not only supports improved project delivery but also aligns closely with national housing goals and SDG 11 on sustainable cities.

6.2. Study Limitations

This study is not without limitations. Firstly, it focuses exclusively on PPP mass housing projects in Nigeria, limiting the generalizability of findings to other infrastructure sectors. Secondly, the fuzzy model relies on expert judgments, which, while validated, are inherently subjective. Finally, the model has not yet been tested in live project environments, which may affect its operational robustness. Future research should explore longitudinal case studies across diverse PPP sectors and regions to further validate and refine the FRADM.