Maturity model for evaluating building maintenance practice: A fuzzy-DEMATEL approach

Abstract The purpose of this study is to develop a performance measurement model based on maturity dimensions or criteria and KPIs identified through an extensive literature review. Using the Decision-Making Trial and Evaluation Laboratory (DEMATEL) method, a maturity model is developed by analyzing 12 criteria/dimensions and 51 KPIs. The importance of each criterion and KPI is analysed through focus group discussions with experts. A fuzzy method is used to resolve the fuzziness and uncertainty of the expert judgments. The fuzzy DEMATEL method is used to analyse the data, and the values of R+C and R-C are computed. In order to visualize the complex relationships, identify the most important criteria of building maintenance and analyse their mutual influence, a cause-effect diagram is created by mapping all sets of coordinates. Accordingly, C8 (culture and leadership), C1 (maintenance policy and strategy), C6 (design life), and C5 (maintenance information management) are assigned to the cause group. These four criteria are identified as the most critical criteria because they can influence the remaining criteria categorized in the effect group. For negative values of (R-C), C2, C3, C4, C7, C9, C10, C11, and C12 are categorized in the effect group. A five-level hierarchical model was developed to measure maturity performance based on the weighted average of the criteria and KPIs of the fuzzy DEMATE outcomes. The current model covers multiple measurement dimensions/perspectives as a measurement criterion for building maintenance maturity. The model is important for decision makers to identify weaknesses and strengths and incrementally improve the weaknesses in a continuous improvement approach. The new model can help decision makers determine the current state of maintenance maturity and plan actions to improve efficiency and effectiveness to create sustainable and productive building assets.


Introduction
In the built environment, there is a growing need among owners and public organizations for the importance of facility management to core business operations.Various strategies are being employed to optimize business objectives and real-world problems.These strategies are due to the rapidly changing work and business environment, such as: the demand for better service, limited financial resources, higher standards and regulations for health and safety.Despite the considerable investment in the development of new infrastructure in Ethiopia, the maintenance of these investments and existing facilities is neglected, which becomes a critical problem.
Higher institutions including public universities play a leading role towards attaining national developmental goals other than teaching and learning, research and community services.This is due to the fact that public universities are integral part of a nation's capacity scheme in transferring up-to-date and international knowledge and fostering an active and thinking citizen (Odediran et al., 2015).In this sense, an appropriate and conducive environment that integrates operational facility management practices is necessary to achieve the university's core objectives.According to Anker Jensen (2011) and Price (2003), the performance of a university's core business can be measured by the efficiency of its facilities management (FM) and asset management (AM), as deficient facilities are a barrier to achieving the university's core goals.
Since 2005, the Ethiopian federal government has made significant investments in the expansion of existing universities and the establishment of new ones as part of a University Capacity Building Programme (UCBP), which is an integral part of the country's Growth and Transformation Plan (GTP).The investments are accompanied by the construction of infrastructure such as dormitories, classrooms, libraries, canteens, sports fields, etc.These extensive expansions and new constructions are aimed at meeting the demand for higher education by providing equal educational opportunities to the majority of underserved regions, producing highly qualified graduates and ultimately achieving the strategic plan (MoF, 2021).
In addition, private and public organizations throughout Ethiopia are investing heavily in the construction of facilities such as real estate, business and educational institutions, hospitals, etc.However, once a construction project is completed, there is very little awareness and knowledge of how to manage the facilities that have been built.This is evident in practices such as improper use of a facility, lack of experts and low level of certified professionals in the field, mixing of general service and facility management, lack of timely maintenance (culture of replacing or restoring an element when it breaks), provision of soft services such as cleaning and security, and lack of standards and low level of enforcement.There is also a lack of established benchmarks for determining the most appropriate procurement approach for maintenance work.
The need for improved maintenance management to utilize existing real estate, especially in public educational institutions, is becoming a major concern.This is primarily due to the fact that owners and managers of public facilities in developing countries place more emphasis on developing new facilities than on optimizing existing ones.However, implementing strategies for the entire life cycle of a facility, especially the maintenance and operation phase, is crucial as it accounts for the bulk of investments compared to planning, designing, building or manufacturing a project and converting it into an asset.A strategic approach to the life cycle can lead to significant cost and time savings, as there is no such thing as a maintenance-free building, as it will deteriorate over time through normal wear and tear or usage (Lateef, 2010).Maintaining a building therefore requires strategies to effectively and efficiently manage the facilities and achieve the strategic goals of the organization.Moreover, the demand for better service has increased in recent decades despite limited resources, such as insufficient funding.As a result of higher standards and regulations for health and safety, private and public organizations are forced to create a place that is comfortable, conducive and productive to achieve the required level of service and become competitive in the market (Amos et al., 2019).Therefore, owners of private and public organizations recognize the importance of facility management and adapt various strategies.However, the local practice of building maintenance is still far behind the expected level of practice in the study context.Therefore, the gradual and continuous improvement of building maintenance performance is of utmost importance to ensure the long-term benefits of public assets in the study context.
One way to ensure long-term benefits and achieve business goals is to gradually improve existing practices.To this end, the development of a maturity model or a performance measurement maturity model is crucial.A maintenance performance measurement maturity model is a conceptual model composed of individual components that define the performance area of interest (Anker Jensen, 2011;De Souza & Gomes, 2015;PMI, 2017).
In practise, there are various types of performance measurement models that have been developed, especially in the field of manufacturing, information systems, supply chain management and other assets (Chemweno et al., 2015).However, there are few studies on the development of a maturity model for performance measurement in building maintenance specifically in the context of the study.Therefore, this study identifies relevant performance criteria and key performance indicators (KPIs) as a measure of performance and their respective weights to progressively measure and improve maintenance practises until an optimal level is reached.Considering the level of awareness of building maintenance management and recognising its importance in Ethiopia's development and the research gap, this study aims to develop a maturity model for building maintenance performance measurement.

Performance measurement in facility management
Facilities management (FM) involves the efficient coordination and optimisation of an organisation's physical environment, assets, services and resources in support of its key business objectives.The performance of FM is a key indicator of an organisation's ability to manage its facilities and deliver value to its stakeholders.Organisational maintenance management performance can be measured using quantitative and qualitative criteria to examine the extent to which facility and organisational objectives are being met in practise (Koleoso et al., 2017;Shohet & Nobili, 2017) to ensure effectiveness and efficiency.Maturity models are used to assess organisational capabilities in relation to specific dimensions or criteria.
Maturity models are used to assess the capabilities of an organisation against specific dimensions or criteria.The need for performance measurement in FM is highlighted by many researchers; for example (Amaratunga & Baldry, 2003;Amos et al., 2019) to ensure the economic health of the organization.

Maturity model
Maturity model serves as an indicator of the level of knowledge of processes, people and tools in an organisation.It helps assess the current state of the organisation's capabilities and identify areas for improvement in order to set future goals for process improvement.
A maturity model is one of the techniques used to evaluate the effectiveness of activities carried out in an organization and to determine the competencies that need to be learned next to improve performance.
As outlined in (Meng et al., 2011) the maturity model is also a method for determining how well an organization manages its business processes.It refers to how well an organization or system can improve itself.Maturity is thus inextricably linked to the possibility of success or failure.Immature organizations are characterized by management improvising without making critical connections between different knowledge areas.However, most maturity models are descriptive and do not inform an organization how to improve.Instead, they describe essential attributes that should characterize an organization at a particular maturity level.
There are numerous primary process categories and maturity levels in various industries such as information systems (IS), project management (PM), knowledge management (KM) and supply chain management (SCM) are just a few.One of the most notable works that have laid the foundation for maturity models is the Quality Management Maturity Grid by Crosby (1979) (Berztiss, 2005;Chemweno et al., 2015;Oliveira & Lopes, 2020), which establishes a model based on five incremental maturity levels for quality management.
Various authors and institutions have presented a five-stage maturity model that aims to enhance continuous improvement capabilities.This makes it easier for companies to plan and improve the process maturity of organizations by developing strategies to increase their continuous improvement capabilities.A maturity model for quality management is included in the standard ISO 9004:2009 (2009).Maturity models have been developed by researchers (Amaratunga et al., 2002;Banyani et al., 2015;Kwak & Ibbs, 2002;Pathirage et al., 2008;Van Der Lei et al., 2012) from various fields such as project management, asset management and facility management.Some examples of the models related to the present study are summarized in Table 1.
Since most of the literatures studied are based on the five-stage maturity model (Bessant et al., 2001;Fryer et al., 2013;Paulk et al., 2011), the present study uses a five-stage maturity model as shown in Figure 1.(Paulk et al., 2011) Maturity models for performance measurement therefore have the potential to form the basis for achieving organizational excellence, as they can clearly show the level at which the organization is in relation to the various perspectives or criteria.The criterion for measuring the maintenance performance of buildings in this study is based on the maintenance process and the organisational perspective as an evaluation criterion for developing a measurement model.

Multi-Criteria Decision Making (MCDM) and Multi-Attribute Decision Making (MADM)
The difference between MCDM and MADM lies in their scope.MCDM focuses on multi-criteria decision-making, whereas MADM is a part of MCDM that incorporates multiple attributes and focuses on a dynamic, time-critical, uncertain and ambiguous environment (Ali & Ansari, 2022;Li et al., 2021;Shen et al., 2021;Zavadskas & Kazimieras, 2016).MCDM often involves a systematic process of evaluation, ranking and selection of alternatives based on predetermined criteria and decision rules (Cuong, 2013;Shen et al., 2021;Siddique et al., 2021).Multi-attribute decisionmaking is a decision-making process that involves evaluating and selecting the best alternative among several options based on different attributes or criteria (Akram et al., 2021;Sorourkhah & Edalatpanah, 2022).The objective of MADM is to find an optimal solution that systematically and quantitatively considers all relevant attributes and criteria.Different approaches or methods can be used in MADM (Filabadi & Hesamian, 2021;Qiu et al., 2023;Soltanifar & Ghousi, 2022).
Another approach is multi-attribute decision-making, which focuses on evaluating alternatives based on multiple attributes.This involves considering multiple attributes or criteria and assigning weights to each attribute according to its importance.These weights are then used to calculate a score or rank for each alternative and the alternative with the highest score or rank is selected as the best option (Li, 1999;Zhou et al., 2018).

Intuitionistic fuzzy sets
This fuzzy set was first introduced by Atanassov in 1983 (Atanassov, 1986) and extends classical fuzzy sets by the degree of membership (µ) and non-membership (ν) for each element as well as a degree of inconclusiveness (λ).In contrast to classical fuzzy sets, where an element has a single membership value between 0 and 1, intuitionistic fuzzy sets allow the sum of membership and non-membership to exceed 1, representing more flexible uncertainty and partial knowledge.They are particularly useful in decision-making scenarios with incomplete or uncertain information (Kumar Adak & Darvishi Salookolaei, 2021;Siddique et al., 2021;Yuphaphin et al., 2022).

Pythagorean fuzzy sets (PFS)
Pythagorean fuzzy sets (PFS) are an advanced version of intuitionistic fuzzy sets (IFS) that provide accurate data for decision-making scenarios (Kumar Adak & Darvishi Salookolaei, 2021;Yuphaphin et al., 2022).They can deal with variable alternative values more effectively by using algebraic operations.PFS is also used in multi-attribute decision making, in combination with differential evolutionary algorithms for optimal results (Sang-To et al., 2023;Tran et al., 2023).Recently, Fermatean fuzzy sets have emerged (Senapati & Yager, 2020), offering a more flexible handling of uncertainties in real-life decision-making situations than intuitionistic and Pythagorean fuzzy sets (Ali & Ansari, 2022;Kumar Adak & Darvishi Salookolaei, 2021;Siddique et al., 2021).

Picture fuzzy sets
Picture fuzzy sets are another type of fuzzy set introduced in 2013 and offer a unique way of dealing with uncertainty and imprecision (Cuong, 2013).Unlike traditional fuzzy sets, they consider different types of responses, including affirmative, abstention, negation and rejection.They find application in various fields such as uninorm-based probabilistic algebras and cluster analysis.Their geometric interpretation and correlation coefficients measure the degree of membership and refusal, help represent uncertain information more comprehensively.They resemble neutrosophic sets and bear isomorphism with 3-fuzzy sets (Yuphaphin et al., 2022).

Hesitant fuzzy sets
Hesitant fuzzy sets are a mathematical model that manages uncertainty and indecision in decision-making and are widely used in areas such as bridge safety monitoring (Ali & Ansari, 2022;Fang et al., 2022;Shen et al., 2021); wireless sensor networks (Anees & Zhang, 2021), recommender systems (Cui et al., 2021), and multi-attribute decision-making (Ali & Ansari, 2022;Fang et al., 2022;Shen et al., 2021;Siddique et al., 2021).Hesitant fuzzy sets transform hesitant or probabilistic fuzzy sets into binary connection numbers in a MADM that enables effective ranking of alternatives based on their degrees of dominance.

Neutrosophic sets
Neutrosophic sets are a mathematical concept that extends the framework of fuzzy sets to deal with uncertain, indeterminate and inconsistent information (Ali & Ansari, 2022;Cui et al., 2021).These sets are used to handle deal with uncertainty and ambiguity in data analysis and decisionmaking processes by enabling the representation of truth, indeterminacy and falsity membership functions (Ali & Ansari, 2022;Siddique et al., 2021).They have applications in medical diagnosis (Siddique et al., 2021), image processing (Cuong, 2013;Yuphaphin et al., 2022), pattern recognition (Siddique et al., 2021;Yuphaphin et al., 2022), and decision-making (Shen et al., 2021).

Plithogenic fuzzy set
It is another type of fuzzy set whose elements are characterised by multiple attribute values.Each attribute value has a corresponding degree of membership, which can be fuzzy, intuitionistic fuzzy or neutrosophic, indicating the membership of the element to the set based on certain criteria (Siddique et al., 2021;Yuphaphin et al., 2022).The scope of these fuzzy sets includes multiobjective optimisation (Ali & Ansari, 2022;Cuong, 2013), classification, clustering and decision problems where multiple attributes need to be considered simultaneously (Ali & Ansari, 2022;Kumar Adak & Darvishi Salookolaei, 2021;Shen et al., 2021;Siddique et al., 2021).

Hypersoft fuzzy set
Hypersoft set is an extension of soft-set theory used to treat fuzzy problems.It combines the concepts of soft sets and bipolarity to create a new mathematical model called bipolar hypersoft set (Ali & Ansari, 2022;Siddique et al., 2021).This model consists of two hypersoft sets, one of which provides positive information and the other negative.Another extension of the theory of fuzzy sets is the concept of the bijective hypersoft set, which was developed specifically for attribute-valued sets (Ali & Ansari, 2022;Cuong, 2013;Yuphaphin et al., 2022).The scope of application of these fuzzy sets includes decision making, data analysis, pattern recognition and artificial intelligence (Ali & Ansari, 2022;Cuong, 2013;Kumar Adak & Darvishi Salookolaei, 2021;Shen et al., 2011;Siddique et al., 2021).

Triangular fuzzy sets
Triangular fuzzy sets are a type of fuzzy set in which a triangular shape represents the membership function.This triangular shape allows the representation of uncertainty or imprecision in the membership of an element to the set.Some common methods or approaches used in multiattribute decision making are the analytic hierarchy process, weighted sum model, ELECTRE, PROMETHEE, TOPSIS, fuzzy set theory and grey relational analysis (Ali & Ansari, 2022;Cui et al., 2021;Kumar Adak & Darvishi Salookolaei, 2021;Siddique et al., 2021).In this study, triangular fuzzy sets are used because they are so popular and easy to use.Moreover, fuzzy sets and other mathematical concepts and algorithms are capable of solving real-world problems in engineering in general and in civil infrastructure and facilities in particular.For example, the BCMO-ANN algorithm has been used to solve vibration and function optimization problems for thin-walled structures (Tran et al., 2023); stochastically based coupled model for the identification of engineering failure analyses for beams (Ho et al., 2022); Shrimp and Goby association search algorithm (Sang-To et al., 2023) for solving structural health monitoring optimization problems for large and complex structures.

Research design and sampling
The methodology used in this study consists mainly of three parts: (1) identification of performance measurement criteria through literature review; (2) data collection through a focus group discussion with experts; and (3) data analysis using a combined approach of Fuzzy-DEMATEL, where DEMATEL stands for Decision-Making Trial and Evaluation Laboratory.
A focus group discussion among experts was conducted to make a pairwise comparison between the criteria and KPIs.
The research design for this study is a quantitative method.The approach is used to collect primary data from a group of experts.A DEMATEL questionnaire was developed and used to make a pairwise comparison between the criteria and the KPIs.Accordingly, the opinions of two groups of experts were collected for the analysis.
Purposive sampling method was used to select experts for the expert group as described in Richard Fellows (2008).Purposive sampling methods have been criticised for their bias and lack of randomisation in data collection.However, this flaw can be removed by selecting appropriate data sources from the most trusted and experienced experts, as described in Neuman (2006).Accordingly, the researchers in the present study have used experienced experts who are either heavily involved in one of the phases of a building's life cycle.It is assumed that the data collected by such a group of experienced experts are of high quality and reliable.
Finally, the maturity model for building maintenance was developed based on criteria and KPIs weighted using a fuzzy DEMATEL approach.The development of the model is accompanied by an expert group consisting of academics, practitioners, the university FM and maintenance managers.The overall process followed in this study is shown in (Figure 2).

Figure 2. The overall process of the Study
The main criteria for maintenance management performance measurement and a description of performance indicators compiled from extensive review of previous works are presented in Tables 2 and 3, respectively.
Similarly, based on the main criteria depicted key performance indicators gathered through a comprehensive literature review is presented in Table 3.
Table 3 data compiled from (Abdullah et al., 2020;Besiktepe et al., 2020;Brooks & Brian, 2015;Campbell & Reyes-Picknell, 2015;Cholasuke et al., 2004;Flores-Colen et al., 2010;Fonseca et al., 2021;Hermans et al., 2014;Hirsch et al., 2013;Horenbeek & Pintelon, 2014;ISO 55000, 2014;Johannes et al., 2021;Kumar et al., 2003;Maletič et al., 2020;Manandhar et al., 2019;Mansfield & Pinder, 2008;Matthew et al., 2014;Olanrewaju & Abdul-Aziz, 2015;Queensland, 2018;Reichelt et al., 2008;Shin et al., 2018;Shohet & Nobili, 2017;Tan et al., 2014;PAS-55-1, 2008;Zawawi et al., 2011): The relationship between the input of a maintenance process and an outcome in terms of total contribution to performance and strategic business objectives shall be identified (C111-C115) C 12 Environmental and Social Impact of the Built asset The rating of a building maturity shall take into consideration of environmental and social impact on built asset-related maintenance activities as it is one of the expected outcomes when it comes to public infrastructure (C121 to C123) A fuzzy DEMATEL method was used to determine the importance of the criteria and indicators for measuring the maintenance performance of buildings.Focus group discussions were conducted with selected experts who were deliberately chosen for their relevance.Accordingly, the experts gave their opinion using the DEMATEL questionnaire.The profiles of the experts who participated in the focus group discussion are presented in (Table 4).
A fuzzy DEMATEL approach was used to assess the importance of criteria and indicators for evaluating the maintenance performance of buildings.Selected experts, specifically chosen for their expertise, participated in focus group discussions.These experts provided their insights using the DEMATEL questionnaire.

Procedure for fuzzy DEMATEL analysis
Decision-making trial and evaluation laboratory (DEMATEL) technique was first developed by the Geneva Research Centre of the Battelle Memorial Institute to visualize the structure of complicated The social significance of the building The significance of the asset in terms of cultural heritage significance, community attachment, or other government priorities causal relationships through matrices or digraphs (Chang et al., 2011;Si et al., 2018).Since then it has been widely accepted as one of the most widely used tools to solve the cause and effect relationship among the evaluation criteria or perspectives (Sumrit & Anuntavoranich, 2012).Like many other Multi-criteria decision-making (MCDM) methods, DEMATEL requires decision-makers (DMs) to provide assessments against criteria using assessment scales (Asan et al., 2018).
In this section, we analysed and refined the degree of influence of each of the maintenance criteria and indicators using the fuzzy DEMATEL method.We gathered a group of experts who were divided into two groups for the focus group discussion.These experts were asked to give their professional judgement using the DEMATEL questionnaire.
For simplicity, we denote the building maintenance criteria as C i , and the KPIs for each criterion are denoted as C ij , where i ranges from 1 to 12 and j from 1 to 6.The DEMATEL methods can be summarised in the following steps:

Evaluate the mutual influences between criteria and indicators
This process involves evaluation of the causal links between two criteria and indicators by the experts group.Two sets of expert data from the DEMATEL survey were collected.The scale for the DEMATEL questionnaire ranges from "No influence", "Low influence", "Medium influence", "High influence", and "Very High Influence" are denoted by 0, 1, 2, 3, and 4, respectively.

Construct the direct-relation matrix Z
As shown in equation 1, Z is an n × n matrix generated by a pairwise relationship in terms of influence and direction between criteria and KPIs.The direct-influence matrix by each expert group.The principal diagonal elements are zero and represent the decision-maker's assessment in the group process of the extent to which criterion C i or (KPI) i influences criterion C j or (KPI) j .A non-negative matrix is created for each expert group.Here, n stands for the number of criteria and the number of expert groups, expressed as Z e ¼ z e ij � � nxn and the aggregated group opinion of the experts gives the final matrix for further analysis.The matrix of the direct influence of the group can be obtained from Equation 1 as shown in the matrix.
In the context of this focus group discussion, z ij represents the preference of expert group e, while k denotes the total number of participating expert groups.
Where matrix Z is:

Applying fuzzy theory and fuzzy linguistic scale
The incorporation of membership function in fuzzy theory addresses linguistic variables by recognising and resolving uncertain or fuzzy data in the environment (Li, 1999).It acknowledges the presence of a certain degree of fuzziness in people's thoughts, inference, and perception, and aims to resolve uncertain or fuzzy data in the environment.
Applying the membership function in fuzzy theory allows for managing and resolving uncertain or fuzzy data by acknowledging linguistic variables.This approach concedes that people's thoughts, inferences, and perceptions possess a level of fuzziness.The main target of this function is to reconcile and interpret unclear or ambiguous data that exists within the environment (Anees & Zhang, 2021;Cui et al., 2021;Siddique et al., 2021;Yuphaphin et al., 2022).
A fuzzy linguistic scale can be applied to convert ambiguous evaluation/judgements in to fuzzy triangular numbers X, denoted by a triplet (l, m, u), where l ≤ m ≤ u.A fuzzy triangular Membership function μ x is shoFigure 3) and equation 3. Here, fuzzy numbers denote the fuzzy set on a real line R, and their membership function is a convex fuzzy subset and continuous piecewise (Patel et al., 2021).
As the expert's judgments are subjective, it can have some inaccuracies and vagueness in a reallife situation.Thus, a fuzzy set theory that applies fuzzy number is introduced to minimize the inconsistencies and reduce the vagueness in decision-making (Ali & Ansari, 2022;Uygun & De de, 2016).Therefore, this study applies a fuzzy DEMATEL-method using Triangular Fuzzy Numbers (TFNs) as shown (Table 5).

Normalize the fuzzy numbers using the formula
Normalizing the initial direct-relation fuzzy matrix, normalized direct-relation fuzzy matrix X can be computed from Equations 4-6

Obtain the total-relation fuzzy matrix
Let xij ¼ ðl ij ; m ij ; u ij Þ furthermore define three deferent crisp matrices to which elements can be extracted from X

Calculate the fuzzy total-influence matrix
TFNs usually require to be defuzzified into crisp value for prioritization purpose this can be computed using Equation 10.Accordingly, the Graded mean Integration Representation (GMIR) method is utilized to due to its popularity and familiarity in defuzzification process (Karthick & Uthayakumar, 2021)

Establishing the normalized relation/influence matrix X
The direct influence-matrix X can be generated using equation 13.
Where the matrix X is: From which the elements of the initial matrix can be computed from All elements in the matrix X are complying with 0 � x ij <1; ∑ n j¼1 x ij � 1 and at least one i such that ∑ n j¼1 z ij � R

Construction of total-relation matrix T
The Total Influence Matrix, T, is a key component of the DEMATEL analysis method.It helps to evaluate the cause-effect relationships between different criteria or indicators in this analysis.The values in the Total-Influence Matrix represent the strength of influence between the criteria/ indicators.This can be calculated by using the normalized direct-influence matrix X, the totalinfluence matrix T, is the computed by adding the direct effects and all of the indirect effects by where h ! 1 And I denotes the I identity matrix.

Determination of threshold value (α)
Thus, the complex relationship between factors can be visualized with a casual cause-effect relationship graph (diagraph).The threshold value (α) can be calculated before constructing the cause-and-effect diagram.(α) Can be calculated from the median elements [t ij ] from matrix T according to Equation 15.This calculation aims to eliminate minor effects of elements in the matrix T (Gigović et al., 2016).
Where n is the number of elements in the matrix T, the factors tij greater than (α) are selected and shown in the cause-effect diagram.

Development of the cause-and-effect diagram
The normalized direct-influence matrix, and the total-influence matrix T can be obtained.Then, the value of (R + C) and (R − C) can be determined based on the total-relation matrix, and the cause and effect diagram can also be constructed using these values based on (Abdullah et al., 2020;Patel et al., 2021;Si et al., 2018).The values of R and C can be calculated from The horizontal axis "Prominence" represents the significance of the criterion, and the vertical axis depicts "Relation".Here, the positive value of (R− C) brings criterion into the cause group, whereas the negative value of (R− C) turns into the effect group.

Determination of weights maintenance criteria
The previous sections explained the procedure for analysing experts' opinions using the Fuzzy DEMATEL method.This section shows how the importance or prominence of maintenance Criteria from the focus group study can be analysed.The level of influence in measuring maintenance performances is based on weights for a particular criterion.According to the study by Dalalah et al., (2011);Kobryń, (2017) in DEMATEL method, weights of criteria can be determined using Equation 17.
Where the values ω i can be normalized from Equation 17, where ð∑w i ¼ 1Þ Nevertheless, the approach is not accurate since it is based on the above two equations, the similar weight can be assigned to any two criteria, i and j, in which (Kobryń, 2017) Whereby R-C is less than zero.Different approach can be used to determine the criteria weights using DEMATEL by assuming that the indicators R+C and R-C can be computed from a total-influence matrix resulting from the direct-influence diagram (Kobryń, 2017).
However, it should be noted that if one criterion dominates any criterion, the corresponding ratings of this criterion resulting from a direct-influence graph are equal to zero.This creates substantial difficulties since the corresponding row in direct-influence matrix consists of zeros only.Hence, when a zero is encountered, it is necessary to correct the weight values by adding the minimum results from each average weight to all the averaged weights.Nonetheless, the present study there was no need as a "0" value was not encountered.

Results
The objective of this research is to create a model for measuring building maintenance performance, which is based on a set of criteria and KPIs.Various scholars have demonstrated the applicability of MCDM techniques in decision-making process for construction projects.For instance, Belay et al. (2022) used an AHP-based MCDM method to analyse success factors and improve decision-making process in infrastructure construction projects.Besiktepe et al. (2020) employed Choosing by Advantage (CBA) as an MCDM approach for selecting building maintenance strategies.Furthermore, Ayalew et al. (2022) applied Fuzzy-AHP and Fuzzy TOPSIS to evaluate and select a road maintenance strategy.
There have been few studies that have used DEMATEL in combination with fuzzy logic for decisionmaking problems during the construction and post-construction stages.The reason for selecting DEMATEL over other MCDM approaches in the present study is its effectiveness in capturing and analysing interdependencies and relationships among criteria.Moreover, it also allows for a comprehensive understanding of how factors/criteria influence each other within a complex system.As the identified criteria are interconnected, DEMATEL provides a better solution.
The result of the Fuzzy DEMATEL analysis is presented based on the expert's judgment from a focus group discussion in two groups.

Evaluation of the mutual influences
The evaluation of the mutual influence of criteria and indicators is Tables 6 and 7 from the expert group discussion.

Constructing the direct-influence matrix Z
The direct-relation matrix was calculated as illustrated in Table 8.Here, the arithmetic mean of all experts' responses was computed to develop the direct-relation matrix using Equation 1.Based on experts' judgment determined in, the individual direct-influence fuzzy matrix is acquired for each expert group regarding the influence degree among maintenance criteria is aggregated and shown (Tables 8).

Applying theory fuzzy
The fuzzy direct-relation matrix was generated by converting the direct-relation matrix into fuzzy numbers, using the fuzzy-based linguistic scale as shown in Table 5 and Figure 3 The resultant fuzzy DEMATEL matrix is shown in Table 9.All the twelve criteria were ranked to prioritize the most important criteria for performance evaluation.
Group Direct-Influence De-fuzzified Matrix Z Using Weighted Average Method is claculated.

Establishing the normalized relation/influence matrix X
Table 10.below illustrates the normalized relation/influence matrix X.Using Equations 5-7 and Equation 13, the fuzzy direct-relation matrix was normalized as illustrated in Table 10.
The fuzzy total-relation matrix T was calculated using Equation ( 14), as shown in Table Table 11  and 12

Constructing total-relation matrix T
The crisp total-relation matrix was generated by de-fuzzifying the fuzzy total-relation matrix into crisp values, Equations 16-17, as shown in Table 13 The Total-Influence Matrix in DEMATEL is used to quantify the strength and direction of influence between different factors within a system (Sumrit & Anuntavoranich, 2012).The values in Table 13 indicate the strength of influence between criteria.Each cell in the matrix contains a value indicating the degree of influence of one criterion on another.The values of R+C indicate the degree of importance of one criterion compared to the others, while R-C indicates the influence of each criterion in determining the category as a cause or effect group.
Accordingly, values below the set threshold (0.55) are considered as intangible or insignificant influence between criteria and KPIs.
Table 7. Expert group II judgments for maintenance criteria

Determination of the threshold value
The crisp values of all criteria were calculated using Equations ( 17) Subsequently, R + C and R − C were calculated, where R− C represents the net effects contributing to the entire system by a particular factor and R+ C represents the degree of the criteria's importance in the system.The final result is tabulated as shown in Table 14.The importance of maintenance criteria from the focus group study is further analysed.The final result shows the level of influence in measuring building maintenance performances based on weights.According to studies by (Kobryń, 2017) and (Dalalah et al., 2011); DEMATEL method can also be used to determine the weights of criteria using Equation 17.

Determine weights of each of the criterion and KPI
Accordingly with Equation 17, the weighted values are computed for each criteria and indicator, as shown in Table 15.R+C shows the importance of the dimension/criterion, whereas R-C shows the relation cause.The criteria that belonged in the cause group are C 8 , C 1 , C 6 , and C 5 , while the remaining criteria belong to the effect group.A larger value of R-C denotes a higher influence of the dimension/criteria has on other criteria.

Discussions
As described in the previous section, C8 (culture and leadership), C1 (maintenance policy and strategy), C6 (design life) and C5 (maintenance information management) are the main cause groups of the building maintenance maturity model.Causes are more important than effect since effects are results (Siddique et al., 2021).Thus, the cause group criteria have a high value for maintenance management performance.This suggests that decision-makers should be more concerned with the cause group criteria than with the effect group criteria.Moreover, the analysis of cause groups in the DEMATEL method allows decision-makers to gain a deeper understanding of the underlying factors that contribute to the results (Ali & Ansari, 2022;Shen et al., 2021;Siddique et al., 2021).
In particular to the present study, all criteria are found to be important and should be used as performance measurement criteria in building maintenance since the average weight calculation for all criteria is above 8%.
Culture, learning and growth are critical factors that have an impact on building management practises in Ethiopia.Insufficient awareness of the importance of maintenance among public university managers has had a negative impact on its implementation.Consequently, C8 could be one of the most important criteria for measuring maintenance management performance.Being in a cause group, C 8 (Culture and Leadership) is the critical.This demonstrates that the lack of a maintenance policy in public universities is rooted in the leadership's degree of relevance for maintenance.This is also ingrained in the culture.
On the contrary, it can be observed that the execution of maintenance-related activities in public universities is not guided by a suitable framework and approach.The expert analysis of the DEMATEL questionnaire serves as a valuable indication towards the significance of developing a comprehensive maintenance policy and strategy that aligns with the university's strategic objectives and suits to the expectations of the public in terms of corporate image.
Design life (C6) is another important dimension classified under the cause group.The maintenance activities for components and equipment should be guided by the design life stated in the design and specification, including instructions from equipment and component suppliers.
Maintenance information management (C5) is the other dimension included in the cause group, indicating the power of information and data in the decision-making process.The maturity of the maintenance management process can be determined by the degree to which information is available and used in the informed decision-making process.
Effect group indicators are influenced by other indicators.C11 (performance management) ranks first in the group of impact indicators.This shows that the performance of other indicators has a significant influence on C11, performance management.The other two impact indicators are C7 (maintenance budget/financial perspective) and C10 (risk management).Other indicators also have an impact on these criteria.
Overall, all indicators, the weighted average (6.48%-9.5%)and the centrality R+C (11.70-15.18),are in a narrow range.This shows that all criteria are more or less equivalent in terms of their importance for building maintenance performance measurement.Therefore, all criteria must be used as a basis for measuring the performance of maintenance management for public buildings.
A similar approach has been taken in calculating the weights for the individual indicators/KPIs/ under each criterion.Accordingly, the weights are presented in Table 14 where the normalised weights of the indicators for the twelve (12) maintenance maturity measures are calculated.The normalised weights of the criteria indicate the degree of importance of each dimension in measuring maintenance performance.Similarly, the normalised weights of the KPIs for each maintenance criterion are also calculated and presented.

Conclusion
The newly developed maturity model can be used to assess the current status and plan a change from the current stage to an advanced progression level based on 12 criteria/perspectives measured by indicators under each criterion.The weighting of each criterion and indicator is analysed and presented using Fuzzy DEMATEL-Multi-Criteria Decision-Making (MCDM).
Based on the (MCDM) analysis, the cause-effect diagram was created by mapping all the coordinate sets of Ri+Ci and Ri-Ci to visualise the complex relationships and assess the most important criterion of building maintenance and analyse how they influence each other.Accordingly, C8 (culture and leadership), C1 (maintenance policy and strategy), C6 (Design Life) and C5 (maintenance information management) are placed in the DEMATEL analysis cause group for building maintenance maturity criteria, indicating their importance.Here, C8 (culture and leadership) is the most important cause among all causes, followed by C1 (maintenance policy and strategy), which is consistent with the results of similar studies.All KPIs under Maintenance Policy and Strategy and Culture and Leadership are the most important perspectives where more efforts are needed to achieve a better level of progress, according to the result.According to DEMATEL MCDM, the cause group criteria (R-C, with positive value) are more important than the effect group criteria, C2, C3, C4, C7, C9, C10, C11 and C12 (with negative R-C value).
As mentioned earlier, C8 (culture and leadership) is the most important of the cause groups.This shows that the main reason for the lack of a maintenance policy in the institutions is that the leadership neglects the need for building maintenance.This is also firmly embedded in the culture.Finally, a building maturity assessment model based on weights calculated from DEMATEL and MCDM analysis for the criteria and indicators under each criterion is proposed and can be used as a selfassessment tool.Finally, Figure 6 presents a framework to guide the use of the self-assessment model.The ultimate self-assessment model to be used as a tool to measure the maturity of building maintenance practises has been developed in table format (Table 16).A reference example is also shown to demonstrate the correct application of the model (Table 17).Further studies are recommended to improve the accuracy of the weights for criteria and KPIs, as the DEMATEL method in the present study offers the possibility to weight two criteria or KPIs similarly.

Figure 1 .
Figure 1.The Five Levels of building maintenance maturity model.

Figure
Figure 5. Diagraph of Criteria/ Dimensions ranging from C1 to C12 since all notations are represented as C.
Figure 6.Hierarchy of Weighted Criteria and indicators

Table 2 . Performance measurement criteria description
Main objective for maintenance is to achieve the agreed building performance with minimum maintenance cost as defined by its KPS (C71 to C75) C 8 Culture and Leadership Awareness of People, Top Management Support, Attitude of Employees, Willingness of People to Learn New Methodologies & Training, and Values & Beliefs Towards Maintenance.(C81 to C83) C 9 Maintenance Materials and Spar part Management Considered as a main criterion since it is the second-highest cost of maintenance is the cost of maintenance spare part inventory.Companies save a significant amount of money through effective spare parts and materials management (C9 to C93) C 10 Risk Management A measures of risk management based on Risk Assessment Strategies & Objectives as risk is embedded in all activities to improve performance, (C101 to C104) C 11 Performance Management

Table 3 . Performance measurement KPIs with descriptions based on literatures Notation Indicators' (KPIs) Descriptions
An estimate of the asset's remaining useful or economic life in terms of its future potential to sustain the delivery of services or the costs of ownership and use not being viable.

Table 8 . Individual direct influencedirect-influence fuzzy matrix (aggregate for the two expert groups)
Culture and Leadership), C 1 (Maintenance Policy and Strategy), C 6 (Design Life), and C 5 (Maintenance Information Management) are the major cause groups of maintenance management.

Table 12 . Total-influence matrix T with (R+ C) and (R− C) values
*Values in bold Indicates higher than the threshold value.

Table 13 . Importance and relation values of criteria
* Values indicates the dimension is in the effect group.