Framework for qualitative risks analysis using Fuzzy AHP

This research paper proposes a new method for qualitative risks analysis using Fuzzy AHP theory in the construction industry. The paper provides a detailed literature review on the concept of Fuzzy AHP in risks assessment, contribution of different authors, and a summary. The research methodology includes a qualitative and descriptive approach. The proposed framework for risks assessment through Fuzzy AHP model is presented in the findings section. The paper concludes with a discussion on the future scope of the project, research limitations, and recommendations.

Research paper
Framework for qualitative risks analysis using Fuzzy AHP

Contents
1. Introduction.........................................................................................................................2
Background.............................................................................................................................2
Problem Statement..................................................................................................................3
Research Questions................................................................................................................3
Research aims and Objectives................................................................................................4
Research Methodology...........................................................................................................4
2. Literature Review...............................................................................................................5
i. Concept of Fuzzy AHP in risks assessment................................................................5
ii. Contribution of different Authors................................................................................8
iii. Summary:..................................................................................................................10
3. Research Methodology.....................................................................................................11
Introduction..........................................................................................................................11
Research Method..................................................................................................................11
Data Collection.....................................................................................................................11
Data analysis.........................................................................................................................12
Summary...............................................................................................................................14
4. Findings............................................................................................................................14
Proposal of Risks Assessment through Fuzzy AHP model:.................................................18
5. Discussion.........................................................................................................................19
6. Conclusion........................................................................................................................21
Introduction..........................................................................................................................21
Future scope of the project...................................................................................................21
Research Limitation..............................................................................................................21
Recommendation..................................................................................................................21
7. References.........................................................................................................................22

1. Introduction
Background
The failure of the construction project is because of two major reason one is the delay in
completing the project in the scheduled time and other is to manage the resources for the
process undertaken within the approved cost of the project (Alrashed, Alrashad, Taj, Phillips,
and Kantamaneni, 2014). The qualitative analysis of the risks associated with the project
helps in developing effective project strategy and setting priority to the risks associated with
the project so that it can effectively completed within the given duration of time. The
outcome of the project will not be retrieved in relation to the project objectives, goal, mission,
and vision due to the occurrence of uncertainty and risks associated with the deployment of
every stage of the project (Azevedo, Ensslin, and Jungles,2014). The project goal and
objectives cannot be achieved due to the occurrence of the risk. The frequency and the
probability of the risks define its impact on the working program of construction project. The
likelihood of the risks explore the barriers associated in the project success. The uncertainty
of the risks results in the delay of project completion, difficulties in completing the scheduled
task and in-scope activities, and others. The study of the literature review helps in finding the
different methds proposed by the different authors in their research work for analysing the
occurrence of the risks associated with the project. The systematic deployment of the project
management methodology and principles works in the direction of minimizing the risks
occurrence. The use of project methodology helps in analysing the presence of risks in four
step process which are named as identification of risks, assessment of the risks, generating
response to the risks, and emphasis on monitoring and reviewing process of the risks. The
systematic arrangement of the risks increases the level of satisfaction in the customers by
completing the construction program within the given period of time. The analysis of the
literature review provides a direction and guidelines to propose a method which can be
utilized for the assessment of risks. The need and requirement of the managing the risks
arises due to the increasing failure of the construction project. The innovative methodology
should be proposed for identifying and evaluating the presence of risks and its mitigation plan
at an early stage of the project. The quality of the construction project depends upon the time
and cost required in completing the project (Carbonara, Costantino, and Gunnigan, 2012).
There are different parameters of risks and uncertainty which increases the dedicated time

and cost. It ends with the consequences of project failure. The purpose of this paper is to
present new method which is capable of identifying and assessing the risks associated with
the project. The management of risks in the project initialization phase helps in completing
the project successfully.
Problem Statement
Traditionally, it is difficult to evaluate the risks and uncertainties at an early stage of the
project. This increases the level of complexities associated with the project. The management
of resources depends on the availability of funds for completing the program. After
identification of such a gap that exist in the industry of building construction, this research
now comes in. it aims to help contractors know the risks to pay more attention too (Chan,
Yeung, Calvin, Wang, and Ke, 2014). This will introduce a technique that will rank the risk
according to their respective weights. The development of the new proposal based on Fuzzy
AHP theory helps in finishing the given task within the specified time and cost.
Research Questions
The following are the questions that the project will be seeking to answer on the topic of the
qualitative risk that are facing the building and construction industry.
 What are some of the risks that the building and the construction industry is
Vulnerable to?
 How the risks can be analysed qualitatively using fuzzy-AHP?
 How the probability and impact of risks can be assessed by linguistic terms and using
Fuzzy AHP?
 What is the procedure used for implementing the Fuzzy AHP in analysing the risks
associated with the construction program?
 How Fuzzy AHP is used in the proposed model for analysing the presence of risks?
 How the allocation of risks helps in improving the quality of the construction project
program
 What methodology should be undertaken to analyse the implication of Fuzzy AHP in
analysing the presence of risks in the project?
 What are the advantages of using the Fuzzy AHP in identifying the project risks?

Research aims and Objectives
Aim
The aim of the research paper is to review the literature for proposing the new method for
risks assessment and evaluation by making use of Fuzzy AHP theory.
Objectives
The development of the construction is equipped with various risks and uncertainties
associated with the project. The objectives of the research paper are highlighted below:
 Identification of the major risks associated with the construction project
 Analysis of the literature review to provide innovative program of Fuzzy AHP to
resolve the complexities associated with the project
 Proposing the new framework for Fuzzy AHP for risks assessment in the construction
world
 Use of Fuzzy AHP in identifying the risks in the construction program
 Identifying the probability of risks occurrence
 Process and procedure followed in implementing the Fuzzy AHP model for analysing
and assessing the presence of risks associated with the project
 Analyse the impact of risks using Fuzzy AHP technique converting linguistic terms
by introducing Fuzzy numbers.
 Classify the different identified risk according to the order of their risk factor by AHP
process.
(Introduction part is systematically divided into required section and with longer background
section, more no. of required RQ, detailed Research Objectives, and research approach in the
methodlogical section of the same)
Research Methodology
The qualitative and descriptive research methodology should be followed for analysing the
risks associated with the construction project and implication of Fuzzy AHP procedures to
minimize the impact of risks and uncertainties at early stages. The analysis of the literary
sources helps me to get a direction to identify risks associated with the construction industry
through the use of Fuzzy AHP theory. The development of the fuzzy AHP model gives the
clear precise view of managing the risks and uncertainties which are in correlation with the
construction projects. The study of literature review is the main source of data collection of

my research in providing the direction to propose a new model based on Fuzzy AHP system
for the assessment of risks and uncertainties amalgamated with the construction program
(Elkan, 2016).
(The information regarding interviews and questionnaire is totally removed)
2. Literature Review
(Specifies problem domain and fuzy solution provided by the researchers in the their paper and also
the literature review is divided into two segments as asked with the detailed structure and format
asked for literary sources)
The construction industry is facing problem in managing the risks associated with every step
of project cycle program. Every organization makes use of different risks monitoring
program to minimize the uncertainty of the construction project (Eriksson, and Furuskold,
2014). The literature review helps in analysing the risks associated with the construction
project and the implication of Fuzzy AHP in managing the risks associated with the project.
The authors focus on identifying the risks in the development program of constructing the
building. The magnitude of the risks should be measured by analysing the risks severity and
risks likelihood related with the construction program. The measure of the risks impact
defines the priority of the risks to be resolved to lower down the project risks (Firmanzyah,
Veronika, and Trigunarsyah, 2016). The process of identifying the qualitative risks analysis
helps in evaluating the probability of risks and its impact on the development process of
construction project. The generation of the risks matrix helps in identifying the probability of
the risks. The mitigation strategies are composed of sequence of processes which are
classified as risks avoidance program, risk transfer process, risks management, and
acceptance of risks (Halil, Nasir, Hassan, Shukur, 2016).
The analysis of the different perspective of the authors helps in evaluating the factors
responsible for delaying the construction work of the undertaken building. The major project
fails due to the incapability of the project manager in taking effective decision for the
completion of the project without any complexity. They are having limited skills of creative
thinking in managing the issues and flaws of the organization (Hyari, and Kandil, 2009). The
problem of decision making can be resolved by managing the multi-criteria aspect of solving
the given problem. The deployment of analytical hierarchical process helps in providing the
multi-criteria environment to take applicable decision in solving the given scenario of

complexity in construction project. The collection of qualitative and quantitative data helps in
managing the uncertainty and complexity exist with the underlying construction program.
i. Concept of Fuzzy AHP in risks assessment
The evaluation of risks is calculated by developing the decision tree to identify the linguistic
terms used in the existing projects. The precision should be given to the preparation of the
fuzzy set for managing the ideas, opinions, thoughts, and decision to resolve the scenario of
problems and risks. The AHP principles help in influencing the decision of the project
manager which is based on the selection procedures from multi-criteria decision making
environment (Halil, Nasir, Hassan, Shukur, 2016). The implication of fuzzy analytical
hierarchy process (FAHP) helps in presenting the Fuzzy AHP to diagnose the parameters of
risks and uncertainty associated with the project (Ibrahim, 2014).
The member functions are developed for identifying the fuzzy set of the given problem. The
member function which is used for defining the fuzzy subset is described as
The value of m1, m2, and m3 are in the form of continuous improvement function. The
critical activities of the project can be identified by evaluating the linguistic variables of the
fuzzy set which are obtained by designing the member function and consistency matrix of the
construction process undertaken (Rajput, 2017). The identification of the critical activities
can be done by evaluating the weights and priority associated with the management of the
identified risks and uncertainty of the project (Kharaiweish, 2013). The member function
which is used for defining the critical activities is given by:
The estimation of the risks and uncertainty depends upon the input given to the Fuzzy AHP
for measuring the parameters of the ambiguity identified in the construction management
program (Jethwa, Bhavsar, and Malek, 2017). The values of the linguistic variables satisfy
the following condition:

There are different fuzzy analytical hierarchy process methods which can be used for
managing and evaluating the risks occurred with the construction program (Kolodiziev,
Tyschenko, Azizova, 2017). The authors in their research work have provided the list of
FAHP different methods to solve the complexity of the construction project with their
associated advantages and disadvantages (Raz, Shenhar, and Dvir, 2011). The deployment of
the FAHP methodology helps in providing multi-criteria view to the problem discovered in
the construction project.
There are different methods used for analysing the presence of risks associated with the
project such as development of the Fault tree analysis (FTA) program, development of event
tree analysis, development of the probability grid, and analysis of the risks sensitivity
(Laufer, Takacs, Rudas, 2018). The innovative program of Fuzzy AHP proposal helps in
minimizing the calculation work performed in evaluating the risks assessment by developing
the linguistic variables for identifying the presence of risks associated with the construction
program (Lee, Han, Quising, and Villaruel, 2012). The linguistic variables of the Fuzzy AHP
helps in finding the risks severity and risks likelihood of the project to provides weightage to

the risks which results in analysing its impact on the construction program. The linguistic
terms which are used for defining the Fuzzy AHP are represented as L for likelihood, V for
severity, and E for risks factors (Reddy, 2015). The priority and weightage can be provided to
the risks by developing a risks matrix which is composed of three parameters risks severity,
risks likelihood, and risks index (Li, Hussein, Lei, and Ajweh, 2014). The Analytical
hierarchical process is used for defining the relationship between the parameters to calculate
the probability and impact of risks occurrence in the different steps of project management
program (Li, and Zou, 2014). The magnitude of the risks can be measured by developing the
relationship between the linguistic variables of the construction program. The author focuses
on developing the Fuzzy AHP model for the analysis and identification of risks associated
with the construction project. The Fuzzy AHP model is composed of five process which are
classified in the table below:
Process Description
Classification of risks The risks breakdown structure should be
developed for the identification and analysis
of risks associated with the project.
Representation of risks in natural language The probability, severity, and likelihood of
the risks should be determined by analysing
the complexity of risks uncertainty
Aggregation of the Fuzzy AHP assessment
process
Development of member function and
consistency matrix with the fuzzy
aggregation of the Fuzzy AHP program for
the assessment of the risks
Computation of Weighted average for the
Fuzzy AHP
The Fuzzy AHP algorithm and member
functions are used for allowing weightage to
the risks identified
Approximation of Linguistic variables The development of fuzzy set with the use of
linguistic variables
The risks analysis through the Fuzzy AHP model helps in completing the project successfully
by minimizing the complexities through the allocation of risks weightage to the identified
risks with the application of member functions for the linguistic variables of the fuzzy set.

ii. Contribution of different Authors
(Research work of different authors is given in the table below as asked by the student)
On summarising the literature review, the emphasis can be given to the work of different
authors in the field of creation of Fuzzy AHP for evaluating the risks associated with the
construction project. The table below summarises the quality work done by the researchers in
their paper:
Authors Contribution
Morote, A., Vila, F. (2011). A fuzzy
approach to construction project risks
assessment.
The authors focus on identifying the risks in
the development program of constructing the
building.
Tusuz, F., and Kahraman, C. (2014). Project
risk evaluation in using a fuzzy analytic
hierarchy process: An application of
information technology projects
The authors focuses on developing the risks
matrix associated with the construction
program. The emphasis is also given on the
risks factors identified in managing the flow
of working process in the construction field
(Laufer, Takacs, Rudas, 2018)
Taroun, A., Yang, B., and Lowe, D. (2014).
Construction risks modelling and assessment:
Insights from the literature review.
The author come up with the newer
technology of Fuzzy AHP and theory for
identifying the linguistic variables associated
with the project which can be the major
reason for the failure of the project
Majumder, D., Debnath, J., and Biswas, A.
(2013). Risks analysis in construction sites
using fuzzy reasoning and fuzzy analytic
hierarchy process.
The AHP principles help in influencing the
decision of the project manager which is
based on the selection procedures from multi-
criteria decision making environment.
Li, H., Hussein, M., Lei, Z., and Ajweh, Z.
(2014). Risk identification and assessment of
modular construction utilizing the fuzzy
analytic hierarchy process and simulation.
The author works on applying the Fuzzy
AHP for identifying the critical activities
associated with the project which can be
major reason for the failure of the project by
adding weightage to the risks existed with the
project (Lee, Han, Quising, and Villaruel,
2012).
Sadhna, C., and Shanmungapriya, S. (2017). The author focuses on constructing the

Assessment of risks in construction project
by modified fuzzy analytic hierarchy process.
member function of the Fuzzy AHP to
analyse and evaluate the impact of risks on
the construction process undertaken for the
completion of the project.
Azevedo, R., Ensslin, L., and Jungles, A.
(2014). A review of risks management in
construction: Opportunities for improvement.
The identification of risks in the project
initiation phase helps in completing the
project within time and cost. The level of
satisfaction of the internal and external
customer can be improved by managing the
risks at glance for synchronising the project
activities according to the project
requirement.
Alrashed, I., Alrashad, A., Taj, S., Phillips,
M., and Kantamaneni, K. (2014). Risk
assessment for construction project in Saudi
Arabia.
The assessment of the risks depends upon the
evaluation of risks, identification of the risks
probability, identification of risks severity,
analysis of fuzzy numbers in terms of
linguistic variables, and others. The linguistic
terms helps in analysing the fuzzy number in
the management of risks severity and
likelihood.
Reddy, A. (2015). Risks management in
construction industry- A Case study.
The researcher focuses on developing the
risks matrix and their associated management
plan to resolve the complexity of the given
case study
Ogunbayo, O. (2014). Contractor and project
managers assessment of risk identification
exercises in the Nigerian construction
industry.
The research carry over their research in
construction industry of Nigeria for analysing
the severity of risks and their impact on the
construction process.
iii. Summary:
The innovative program of Fuzzy AHP proposal helps in minimizing the calculation work
performed in evaluating the risks assessment by developing the linguistic variables for
identifying the presence of risks associated with the construction program. The identification

of the critical activities can be done by evaluating the weights and priority associated with the
management of the identified risks and uncertainty of the project. The Analytical hierarchical
process is used for defining the relationship between the parameters to calculate the
probability and impact of risks occurrence in the different steps of project management
program (Summary of 100 words as required)
(The risks tables and other details of the risks are completely removed from the paper as
asked by the student)
3. Research Methodology
Introduction
The research methodology is applied for collecting data and information required for the
project from online and offline sources to provide an effective direction to the research
program. The organization of surveys, interviews, and questionnaire helps in analysing the
problems faced by the top executives in completing the construction project. The major data
is collected from reviewing the literary sources. The research works of the different authors
have been taken under consideration for analysing the efficiency of FAHP methods in
resolving the risks allocated with the project.
Research Method
The qualitative and descriptive analysis of the risks associated with the construction project
helps in measuring the impact and consequences of the uncertainty in completing the given
task for the completion of construction project (LLveskoski, 2014). The identification of risks
and their associated sources helps in analysing the risks severity, risks likelihood, and their
aggregation is used to calculate the risk priority and risks ranking for analysing the impact of
it on the development process of the construction program. The detailed study of the
literature review helps in providing the path and motivation to provide innovate method to
resolve the complexities of the project (Sadhna, and Shanmungapriya, 2017). The Fuzzy
AHP analytic hierarchy process framework can be effectively developed for managing the
risks. The research work of the different authors helps in guiding the research to propose an

efficient Fuzzy AHP model for the successful assessment of the risks in the construction
industry.
Data Collection
The data is collected from online and offline sources for analysing the efficiency of the
FAHP principles in managing the risks existed with the construction project. Some of the
methods which are used for collecting the data are discussed below:
Analysis of the Interview session organized by the researcher in their research work: The
evaluation of the interview with the high professionals of the construction world by the
researchers in their research work helps in identifying the limitation of the construction
project which can become the reason of project failure. The experts focus on the
methodology they use in their existing work to take effective decision in solving the
complexities of the project. The sharing of experience, knowledge, and observations of the
top executives and manager helps in analysing the flaws and limitation of the construction
project in solving and determining the uncertainties (LLveskoski,2014). It helps in giving
direction to adopt the principle of Fuzzy AHP in determining the risks by developing multi-
criteria decision making environment.
Study of the Literature Surveys: The study of the on-site survey report of the construction site
done by the previous researchers helps in observing the working process undertaken by the
experts to complete their given task within the allocated time. It helps in identifying the cause
and reason for the project failure.
Literature review: The analysis of the research work done by the different authors in the field
implying Fuzzy AHP for resolving the complexities of the construction program. The
descriptive analysis of the risks helps in analysing their impact and priority in completing the
critical activities of the project. The literature review helps in analysing the risks associated
with the construction project and the implication of Fuzzy AHP in managing the risks
associated with the project.
(Data collection methodology is completely changed and it is the data collected from the
literary sources and the methodology undertaken by the other researchers as asked by the
student)

Data analysis
During the study of the research work I have prepared the risks evaluation matrix for
analysing the efficiency of the proposed project. The systematic synchronization of the data
collected from different sources helps in analysing the problem domain which exist with the
construction world and identifying the risks priority associated with the identified risks. The
framework should be developed for managing the risks and uncertainty existed with the
project plan and schedule (Shastri, 2012). The data is collected in the following format:
Risks Impact Traditional
Methods used
for Resolving
Advantages and
Disadvantages
Limitation of the
method
(Data analysis is also modified)
The table below shows the analysis matrix developed for analysing the risks parameters
associated with the construction project. It helps in analysing the efficiency of the proposed
model of FAHP in assessing the risks associated with the project. The table below shows the
sources of the risks in construction project:
Risk Sources
Lack of work safety and health parameters
Natural Disaster
Changes in the climatic condition
Delay in project approval
Lack of coordination in sharing of resources
Lack of partnership
Lack of agreement with the contractor company (Singh, 2017)
Lack of managing supply and demand of resources
Lack of managing resources on the site location
Lack of sharing of information
Lack of coordination and cooperation among team
Wrong selection of the project methodologies
Failure of project schedule

Wrong estimation of project cost
Wrong distribution of resources
Wrong distribution of roles and responsibilities
Lack of continuous improvement plan and change management plan (Salah, and
Moselhi,2018)
Wrong selection of the contractor company
No clarification of rules and regulation on the agreement
Misunderstanding
Wrong selection of the team members
Lack of skills and expertise
Lack of training and development program
Lack of proper distribution of resources
Lack of proper scheduling of project activities (Tusuz, and Kahraman, 2014)
Adoption of new technology
Lack of skills and expertise of project team
Unavailability of trainer
Technical complexities
Change in the organisation structure
Installation of new hardware and software
The construction of the Fuzzy AHP framework helps in evaluating the probability, priority,
and impact of the risks identified. The analysis of the critical activities at an early stage helps
in completing the project by taking effective mitigation plan before their existence (Prasad,
Reddy, Kumar, Reddy, 2012). It helps in minimizing the risks occurrence which in turn helps
in resolving the complexities associated with the project and completed the project without
any hindrance and from internal and external resources. The fuzzy approach can be applied to
the construction program for identifying the risks by analysing the different parameters which
can affect the working of the construction program (Majumder, Debnath, and Biswas, 2013).
Summary
The data collected from the literature review and deployment of interview, questionnaire, and
survey helps in identifying the major risks associated with the construction project. The
identification of the risks at an early stage of the project helps in completing the given

program without any complexities (Merrit, and Ricketts, 2012). The development of FAHP
model helps in settle down the risks before their occurrence. The multi-criteria environment
helps in improving the decision making capability of the project manager to take effective
decision in solving the risks.
4. Findings
(Findings included the new Fuzzy AHP framework to analyse the risks in the construction industry)
The major findings of this research are identification of the risks associated with the
construction project, classification of risks parameters in completing the construction
program, application of Fuzzy AHP for evaluating the risks occurrence, and development of
Fuzzy AHP framework for solving the risks associated with the project. The major
parameters which help in proposing the methods of Fuzzy AHP in assessing the risks are the
study of event tree analysis and fault tree analysis (Monnappa, 2017). The methodology of
the Fuzzy AHP helps in analysing the risks due to the technology failure or presence of
human error. The mathematic logics are created based on the undertaken fuzzy set for
assessing the uncertainty of the construction program (Morote, Vila, 2011). After the analysis
of the literature review, I propose a Fuzzy AHP model for evaluating the risks occurrence
existed with the construction project.
The proposal of Fuzzy AHP helps in the process of risks identification and risks assessment.
The evaluation and assessment of the risks is done in three steps in the proposed model of
Fuzzy AHP (Mouraveiv, 2012). The three phases are categorised as preliminary phase, Fuzzy
inference phase, and risk index and its corresponding ranking. The ranking of the risks helps
in identifying the risks impact on the undertaken construction process (Ngoma, Mundia,
Kaliba, 2014)). In the preliminary phase, the classification of the risks and its associated
factors takes place. The qualitative approach is laid down for collecting details of data and
information required for analysing the uncertainty of the construction projects. In the fuzzy
inference phase, the linguistic variables are defined for the construction of fuzzy sets. The
scaling of the fuzzy sets helps in defining the member function for the evaluation of the risks
to prepare the consistency matrix of the risks identified (Ogunbayo, 2014). The risks index
and ranking phase depends upon the analysis of risks severity and risks likelihood. The
following diagram is the proposed model of Fuzzy AHPs used for evaluating the risks existed
with the construction project.

The deployment of the proposed Fuzzy AHP model is effective in identifying the risks
associated with the project along with risks severity, risks likelihood, risk index and ranks,
and risks impact.
The process and procedure used for fuzzy risks assessment is given below in the following
table:
Process Description
Measuring the risks parameters The assessment of the risks depends upon the evaluation
of risks, identification of the risks probability,
identification of risks severity, analysis of fuzzy numbers
in terms of linguistic variables, and others (Otieno, 2014).
The linguistic terms helps in analysing the fuzzy number
in the management of risks severity and likelihood.
Management of Fuzzy inference The application of Fuzzy AHP helps in estimating
parameters of risks by using Fuzzy AHP operators. The
measure of Fuzzy AHP output program depends upon the
input parameters used to develop the fuzzy set.
Process of De-fuzzification The process of fuzzification helps in calculating the
numerical value of the risks in the development of the
construction program. The initialization of the comparison
matrix helps in resolving the inconsistency problems.

The development of the fuzzy set depends upon the following parameters:
 Mapping of risks in the construction program between the interval of 0 and 1
 Identification of constant value
 Relationship between [a,b] a and b parameters
 Relationship between [c,d] c and d parameters
The member function can be effectively developed for the given fuzzy set of linguistic
variables for measuring the impact of risks associated with the construction project. The
development of trapezoidal function helps in analysing the member function of the Fuzzy
AHP program. The member function which is used for assessing the risks is given below
The above function is used for assessing the risks is based on triangular Fuzzy AHP
approach. The capability of risks assessment by the proposed framework of Fuzzy AHP
framework can be improved by extending the triangular parameter to trapezoidal approach of
fuzzy framework. The extension is done in the following fuzzy function in estimating the
risks:
Addition of fuzzy numbers:
The function extended for the addition of the fuzzy number is given by
A1 + A2 = (a1 add a2, b1 add b2, c1 add c2, d1 add d2)
Subtraction of Fuzzy numbers
The function extended for the subtraction of the fuzzy number is given by
A1 - A2 = (a1 sub a2, b1 sub b2, c1 sub c2, d1 sub d2)
Multiplication of fuzzy numbers
The function extended for the multiplication of the fuzzy number is given by

A1 * A2 = (a1 mul a2, b1 mul b2, c1 mul c2, d1 mul d2)
Division of fuzzy numbers
The function extended for the division of the fuzzy number is given by
A1 / A2 = (a1 div a2, b1 div b2, c1 div c2, d1 div d2)
The scalability of the risks can be optimized by multiplying the set the fuzzy numbers with
the scalar quantity which can be given as:
When the value of K is greater than zero
K * A = (k * a, k*b, k*c, k*d)
When the value of K is less than zero
K*A = (k * d, k*c, k*b, k*a)
Proposal of Risks Assessment through Fuzzy AHP model:
The following flowchart is the proposed model for initiating and assessing the risks
associated with the construction project.
Development of the risks assessment team groups
Identification of the parameters, factors, and sources for risks analysis
Development of the risks hierarchical structure
Development of risks preliminary research
Development of risks factor and construction of member function
Defining of the linguistic variables
Identifying the scaling factor used for managing the fuzzy number

The proposed model helps in setting priority to the risks identified by analysing the risks
severity and risks likelihood associated with the construction program. The assessment of the
risks can be effectively drawn by calculating the aggregation of risk severity and risks
likelihood to calculated the risk priority and impact.
5. Discussion
(Discussion section focuses on answering the research question undertaken for the study)
Defining risks probability and risks index
Measuring parameters of risks identification
Aggregating the fuzzy number to allocate weightage to identify the risks
priority
Comparing the pair wise risks assessment of the given fuzzy numbers
Aggregating the fuzzy numbers for setting priority and risk index for ranking
Development of risk hierarchical structure based on the associated weightage
Defining the Fuzzy inferences
Development of consistency Index matrix
Initialization of Defuzzification
Assessment of the risks as output

The research study helps in developing the Fuzzy AHP model for minimizing the risks
associated with the construction project. The designing of the FAHP model is based on the
analysis of linguistic variables used for preparing the fuzzy sets for the construction project.
The facts collected from the literature review helps in analysing the benefits of Fuzzy AHP in
evaluating the risks associated with the project (Pribadi, and Pageran, 2013). The
identification of risks in the project initiation phase helps in completing the project within
time and cost. The level of satisfaction of the internal and external customer can be improved
by managing the risks at glance for synchronising the project activities according to the
project requirement. The value for money can be earned by minimizing the risks associated
with the project. The effective utilization of resources can be done by managing the risks
among the participating members on the basis of risks priority. The linear programming
method is used for setting weights to the risks for calculating the risks ranking of the
undertaken construction project. The precision should be given to the preparation of the fuzzy
set for managing the ideas, opinions, thoughts, and decision to resolve the scenario of
problems and risks. The AHP principles help in influencing the decision of the project
manager which is based on the selection procedures from multi-criteria decision making
environment. The crticical activities of the project can be identified by evaluating the
linguistic variables of the fuzzy set which are obtained by designing the member function and
consistency matrix of the construction process undertaken (Bao, Chan, Chen, and Darko,
2018). The deployment of analytical hierarchical process helps in providing the multi-criteria
environment to take applicable decision in solving the given scenario of complexity in
construction project. The analysis of the risk impact and ranking of the project activities
result in successfully completing the project within the given period of time and cost by
applying the principle of Fuzzy AHP analytical hierarchy process model.
SIGNIFICANCE AND THE SCOPE OF THE RESEARCH. This research will be very
resourceful to the whole industry as it aims to answer some of the questions that they face on
each day. It also comes to a place of been well understood as it is dealing with a project that
can be related to. In the building of house, the research starts its study from the conception of
the project, the designing of the project and finally to the actual activity which is the
construction. All factors are given attention too since they all have an effect to the actual
results. The research positions every project manager to be in a position of avoiding the major
risks that faces a project. One of the major impacts of the various risks in the building process
would be delaying in the completion of the project (Islam and Nepal 2016). This is a major

problem that is faced by many contractors in most cases in India. Consequently the results of
this delay are no pleasing. It at time makes the owner to incur additional cost which had not
been budgeted for. The contractor can decide to rush the project and this can affect the
project quality and other more problems. Another impact of these risks is the cost of the
project overrunning the budgeted cost (Roghanian and Mojibian 2015). This is very
dangerous as it is the reason that this is the major reason why many project starts and never
comes to end. This research will however explore over this whole issue and leave the project
manager at a better position of making decisions. Building is also encountered by the risk of a
poor quality of the end results. Sometimes the contractors can fail to follow the right direction
leading to a poorly built structure. This is dangerous as such houses are unfit for occupation
which at the end of the day turns to be a waste of money (Cerić, Marčić and Kovačević,
2013). Lastly, injuring of the workers is another major effect that a building project can face.
Building usually involves some dangerous activities such as excavating deep trenches and
much more. Even at times worker may fall from high places or even be injured by some of
the machinery used there in. this kind of project cannot continue without human resource and
therefore when one faces an accident, the whole project is affected in one way or the other
(Basahel and Taylan 2016). All this impacts tends to be liability in the project progress. This
research therefore gather all risks so as to help them in the analysing of the different risks that
exists
6. Conclusion
(The conclusion is divided into four section introduction, future scope of the research, research
limitation, and recommendation)
Introduction
The analysis of the literature review and findings of the project can be concluded with the
successful analysis of the risk identification and assessment with the implication of the
proposed FAHP model. The evaluation and assessment of the risks is done in three steps in
the proposed model of Fuzzy AHP. The three phases are categorised as preliminary phase,
Fuzzy inference phase, and risk index and its corresponding ranking. The ranking of the risks
helps in identifying the risks impact on the undertaken construction process.

Future scope of the project
The future scope of the project is to prepare a research program for implementing the
quantitative approach for risks assessment in the construction project with the use of Fuzzy
AHP operation.
Research Limitation
The limitation of the proposed project is that the data used for analysing the requirement of
the construction industry in identifying the risks is based on the observation, thoughts,
research work of the authors, and other qualitative sources. No real facts and figures are used
in the development of the FAHP model.
Recommendation
It is recommended to deploy the Fuzzy AHP in assessing the risks through the use of
quantitative research methodology. It helps in finding out the facts and figures associated
with the analysis of the risks in the construction program. The focus should be given on
collecting the details about the different sources of risks occurrence.
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