A rough set approach for evaluating vague customer requirement of industrial product-service system_Wenyan Songa

International Journal of Production Research, 2013
Vol. 51, No. 22, 6681–6701, http://dx.doi.org/10.1080/00207543.2013.832435
A rough set approach for evaluating vague customer requirement of industrial
product-service system
Wenyan Song a *, Xinguo Ming a , Yi Han b and Zhenyong Wu a
a State Key Laboratory of Mechanical System and Vibration, Institute of Computer Integrated Manufacturing, School of Mechanical
Engineering, Shanghai Jiao Tong University, Shanghai, China; b Department of Organization Management, Guanghua School of
Management, Peking University, Beijing, China
(Received 1 April 2013; accepted 30 July 2013)
This research mainly focuses on the customer requirements’ evaluation in the early development of industrial productservice
system (IPS 2 ). IPS 2 can maintain and enhance manufacturer’s competitiveness by integrating tangible product
and intangible service. Accurately capturing and understanding customer requirement are critical for successfully developing
the right IPS 2 for the right customer. However, there are few researches on requirement evaluation in the early
planning phase of IPS 2 development. And IPS 2 requirement evaluation often involves much subjectivity and vagueness.
To solve these problems, a systematic evaluation approach for eliciting and assessing IPS 2 requirement under vagueness
is proposed. The proposed model of industrial customer activity cycle can efficiently support requirement elicitation from
the lifecycle perspective. Besides, the integrated rough group analytic hierarchy process method can effectively deal with
subjectivity and vagueness in the IPS 2 requirement evaluation process. To demonstrate the potential of the approach, an
application in an air compressors system is also illustrated.
Keywords: requirement evaluation; industrial product-service system (IPS 2 ); industrial customer activity cycle (I-CAC);
rough group analytic hierarchy process (AHP)
1. Introduction
With intensified competitions in manufacturing industry, companies have to keep close relationship with customers and
offer high value-added solutions (Chen and Sackett 2007; Gebauer 2008). Customer requirements determine what companies
supply in today’s demand-driven market (Galbraith 2002; van Halen, Vezzoli, and Wimmer 2005). Nowadays,
customers tend to require more comprehensive solutions, not just products or services; accordingly, manufacturers
should shift to more systematic thinking and aim at offering integrated bundles of products and services, which is also
known as product-service systems (PSS) or hybrid products (Mont 2002). In this context, the industrial product-service
systems (IPS 2 ) (Meier, Roy, and Seliger 2010), characterised by the integration of tangible product and intangible service,
is regarded as the key to increase competitiveness of a manufacturer. Industrial solutions integrating products and
services are now a common practice in many business-to-businesses (B2B) applications, which can maintain or enhance
functionality of a product or a service if properly integrated (Müller, Schulz, and Stark 2010).
To offer integrated industrial solutions, requirement elicitation and prioritisation have decisive roles in the
development of IPS 2 through considering the requirements of the stakeholders systematically. Although many researchers
provide some generic guidelines for the product requirements’ generation and prioritisation, there are few such
approaches formally introduced for IPS 2 development. Many researchers mentioned customer requirements without
offering methodological supports to handle them at a more detailed level (Ericson et al. 2009). In literature and in
practice, a methodology for requirement elicitation and prioritisation with regard to IPS 2 is missing. One of the major
challenges is to successfully elicit different expectations of different stakeholders due to lack of effective requirement
generation tools for IPS 2 . The other challenge is to prioritise the requirement list, i.e. requirement prioritisation.
However, this is difficult due to the qualitative, arbitrary and ambiguous linguistic judgements and preferences. Different
experts have different knowledge and experiences and each expert judges the importance of customer requirements from
his/her own subjective perceptions and feelings, which would lead to subjectivity. The vagueness exists in the
*Corresponding author. Email: 198212swy@163.com
Ó 2013 Taylor & Francis

6682 W. Song et al.
judgement scales that are often defined fuzzily and not known precisely, such as ‘low’, ‘moderate’ and ‘high’. The
objective of this study is to provide a systematic support for the elicitation and prioritisation of customer requirements
during the planning and early development phase of an IPS 2 .
There are still no methods to effectively elicit requirement of IPS 2 and manipulate the subjectivity and vagueness in
them until now. The main contributions of this research are as follows:
• The research firstly introduces industrial customer activity cycle (I-CAC) to provide a structural way for the
IPS 2 requirements elicitation, which enables all requirements to be concretised based on the stakeholders’ interaction
around customer activity.
•
Based on the elicited requirements, the rough group analytic hierarchy process (AHP) method is used to effectively
manipulate subjectivity and vagueness of IPS 2 requirement judgements with rough logic under vague
environment.
•
The proposed approach provides a more rational requirement evaluation framework without demanding much
prior information.
The rest of this paper is organised as follows: literature review which serves as basis of the proposed method are
reviewed in Section 2. The research method is described in Section 3. The proposed rough set group requirement evaluation
approach is explained in Section 4. The proposed method is illustrated with a case study of the air compressor in
Section 5. Also, the authors make a comparison between fuzzy AHP approach (Kwong and Bai 2002) and the proposed
approach to show advantages of proposed method in manipulating the subjectivity and vagueness in this section. The
conclusions and recommendation are offered in Section 6.
2. Literature review
2.1 Industrial product-service system (IPS 2 )
Although there have been some researches about IPS 2 , a systematic review of the IPS 2 requirement research domain is
still missing. However, requirement elicitation and prioritisation are important inputs for designing effective and innovative
IPS 2 . The manufacturer may be failed in development of IPS 2 if it cannot capture key requirements of customers.
The high complexity in manufacturing systems and the fast changing customer needs have altered the perception of
product engineering. New innovative solutions are necessary to ensure business success. The concept of IPS 2 (Aurich,
Schweitzer, and Fuchs 2007) originates from technical PSS (Aurich, Fuchs, and Wagenknecht 2006), i.e. the application
of PSS in specific industrial context. Meier and Krug (2006) later label industrial product-service systems as IPS 2 . IPS 2
initially aims at integrating products and services in the phase of development and delivery. It is characterised by the
integrated and mutually determined planning, development, provision and use of product and service shares including
its immanent software components in B2B applications and it represents a knowledge-intensive socio-technical system
(Meier, Roy, and Seliger 2010). Customising an IPS 2 is primarily based on partially substituting product and service
components to meet customer requirements. The objective of IPS 2 is to add value to satisfy customer needs during the
whole lifecycle of a PSS (Müller et al. 2009). The basic idea of IPS 2 is not to separately provide products and services
but to offer a defined result, a system’s availability or even functionality. It is mainly driven by a systematic blending of
goods with industrial services, such as maintenance, adoption to changing needs, reconfiguration and upgrading, etc.
Those service shares of IPS 2 are provided over the whole life cycle to enhance customer value (Matzen, Tan, and
Andreasen 2005; Tan and McAloone 2006).
Tukker (2004) proposes that the IPS 2 could be classified into three categories, i.e. product-oriented, use-oriented and
result-oriented. In the product-oriented IPS 2 , the provider offers the sale of products and also opens service channels for
additional service shares such as upgrades, maintenance and consultancy. In the use-oriented IPS 2 , the provider maintains
the rights to a product and makes the product available for use in a service environment via service shares such as
product leasing and renting. In the result-oriented IPS 2 , the provider delivers service content independent of product
choice, such as activity management, pay per service unit and functional result. IPS² strategy must adapt to the specific
IPS² business model (function-oriented, availability-oriented and result-oriented) to the certain market segments (Meier,
Völker, and Funke 2011). Yang et al. (2009) propose an engineering methodology utilising product life cycle data for
realising product-oriented PSS and use-oriented PSS for consumer products. Each IPS² has a general lifecycle of
planning, development, implementation, operation and closure, which is determined by the phases of the established
product/service phases (Meier and Uhlmann 2012).
IPS 2 is also customer lifecycle-oriented integrations of products and services, realised in an extended value creation
network (Aurich, Fuchs, and Wagenknecht 2006; Mont 2002). In fact, every IPS 2 has a specific network organisation

International Journal of Production Research 6683
with autonomous network participants. Each of the network participants is responsible for a provision of IPS 2 specific
services. Network participants in an IPS 2 can be categorised as: IPS 2 customer, IPS 2 provider, IPS 2 supplier and IPS 2
operator (Meier et al. 2009). Co-creation networks including solution providers, end users, suppliers and other partners
are critical to achieving the goals of IPS 2 , because they facilitate interactions among IPS 2 partners and act as mechanisms
for creating value and exchanging information among stakeholders (Durugbo et al. 2010; Durugbo and Riedel
2013; Krucken and Meroni 2006). Industrial partners in the IPS 2 co-creation networks could also leverage knowledge of
network structures and behaviour in searching for potential partners (Krucken and Meroni 2006). Meier (2013) provides
a generic IPS 2 development process model which structures the methods and tools to create an integrated IPS 2 model
for the further IPS 2 operation. The model is expected to be used for marketing, requirements engineering, concept development
and design, etc. Meier, Roy, and Seliger (2010) propose an approach for knowledge-based support of the IPS 2
concept development methodology by deducing concepts for IPS 2 from given requirements. Sakao and Lindahl (2012)
provide a customer value-based evaluation of PSS with design information. Erkoyuncu et al. (2011) focus on the cost
estimation for IPS 2 . Rese, Karger, and Strotmann (2009) determine quantified value of an IPS 2 for an individual
customer over its lifecycle based on net present value approach and the real options approach.
Some themes, such as IPS 2 delivery, processes, value creation networks, knowledge management and business
models, can be seen in the literature (Cedergren et al. 2012), others often focus on the PSS/IPS 2 concept, origin,
features, benefits and barriers to adoption, available methods, organisation and operational resource planning (Baines
et al. 2007; Beuren, Ferreira, and Miguel 2013; Boehm and Thomas 2013; Meier, Völker, and Funke 2011). However,
how to develop specific IPS 2 is still scarce in the past research. Therefore, it is urgent to develop the PSS approach
theoretically, methodologically and operationally (Mont 2003).
Although some researches have focused on the definition, classification and organisation of IPS 2 , there are few studies
on the IPS 2 requirements’ elicitation and evaluation, which are the most important input of the early planning of
IPS 2 . Since the IPS 2 is totally different with solely product, service or simply combination of the product and service,
the past requirement elicitation and evaluation from product and service domain is not suitable for the IPS 2 designing.
Therefore, it is necessary to design new tools and models to generate and evaluate the requirement for IPS 2 .
2.2 Requirement elicitation and evaluation
2.2.1 Requirement elicitation
In the domain of engineering design, requirement is believed to be success factor of product development projects (Ulrich
and Eppinger 2008). The satisfaction of the customer and stakeholders are key factors for the successful solutions
(Nuseibeh and Easterbrook 2000). Requirement has been recognised as a critical factor influencing delivered quality of
solution. Bailetti and Litva (1995) highlight the importance of integrating customer requirements into product design.
Requirement vagueness could influence the following design activities, such as product family design (Perlman 2013).
Requirements’ elicitation is a basic process in the planning and development of product, service or system. Regarding the
tools and the methods for needs identification and requirements’ definition, a number of approaches have been proposed in
the literature (see Table 1).
Although many researches on the requirement exist in the product or service development domain, there are few studies
focused on service requirements’ elicitation and even fewer on the IPS 2 requirements’ elicitation. Most of the
researches fail to consider the interaction of stakeholder’s requirements. IPS 2 is in fact a co-design and user activity-centred
system, which has to consider much about the requirement at the beginning of the design project. However, the requirements
generation and evaluation is not addressed properly in IPS 2 planning and development research so far. Therefore, to
exploit the full solution space of product-service integration, a clear understanding of customer requirements is critical in
IPS 2 planning and development (Ericson et al. 2009).
2.2.2 Requirement evaluation models
Requirements’ prioritisation is recognised as an important activity in product development. Company has to establish
the relative priorities of the requirements due to resource limitations. Prioritisation could help managers make the necessary
trade-off decisions. Prioritisation decisions are made by stakeholders, including users, managers, developers or their
representatives. Various evaluation models have been applied to determine the importance of customer requirement (see
Table 2).
Customers’ opinions are often vague and contain ambiguity and multiple meanings (Fung, Popplewell, and Xie
1998). The crisp method could not manipulate this. Some researchers adopt fuzzy methods (see Table 2). However,
fuzzy set theory-based requirement evaluation approaches has the limitations stemming from the pre-set fuzzy

6684 W. Song et al.
Table 1. Requirement elicitation in the past research.
Literature
Pahl, Wallace, and Blessing (2007)
Ehrlenspiel (1995)
Yan, Chen, and Khoo (2001), Hauge and Stauffer
(1993), Tseng and Jiao (1998)
Wang and Zeng (2009)
Jiao and Chen (2006)
Miaskiewicz and Kozar (2011)
Van Husen (2007)
Steinbach (2005)
Durugbo and Erkoyuncu (2013)
Hosono et al. (2010)
Akasaka et al. (2010)
Berkovich et al. (2009)
Focus of research
Provide a guideline to elicit product requirements which refers to customers,
designers, lifecycle phases, cost and time as sources for requirements
Provides a hierarchical requirement model with two categories, i.e. technicaleconomical
and organisational requirements
Use hierarchical or tree structure for the elicitation of customer requirements, e.g.
the customer property hierarchy, the requirement taxonomy, and the FR topology
Support requirements elicitation with a computer system based on dialogue.
Review of customer requirement management in the domain of product
engineering
Utilise personas for representing and communicating customer requirements
Proposes a checklist to discover stakeholders and influencing factors, such as
economic, legislative, and social factors to analyse requirements for productrelated
services
Proposes a comprehensive list of service attributes including responsiveness,
patience, and reliability, etc
Explore the role of information systems for facilitating the engineering of service
requirements.
Focus on nonfunctional requirements (NFRs) for service development
Define specific service requirements that should be focus of improvement
Focus on the process and tools of the requirements engineering for product,
service, and software engineering
Table 2. Different evaluation models of customer requirement.
Literature
Model/method
Subjectivity
manipulation
Vagueness
manipulation
Flexible
evaluation
structure
Less priori
information
(e.g. pre-set
membership
function)
Bhattacharya, Sarkar, and Mukherjee
(2005),
De Felice and Petrillo (2011),
Fung, Ren, and Xie (1996), Bhattacharya,
Geraghty,
and Young (2010), Raharjo, Xie, and
Brombacher (2011)
Integrating AHP with
QFD
√ √
AHP √ √
Sahney, Banwet, and Karunes (2004) Empirical study
Zhai, Khoo, and Zhong (2009)
Dominance-based rough √ √
set approach
Wu, Liao, and Wang (2005) Grey theory and QFD √
Wang (2012) Non-linear programming Partially √
Ho, Lai, and Chang (1999) and Lai, Ho, Group decision-making √ √ √
and Chang (1998)
technique
Kwong and Bai (2002, 2003) Fuzzy AHP Partially √
Kahraman, Ertay, and Büyüközkan (2006) Fuzzy ANP Partially √
Karsak (2004) Fuzzy Delphi method Partially
Wang (1999) Fuzzy QFD Partially
Notes: ‘√’ denotes that consideration is included in the model. ‘’ denotes that consideration is not included in the model.
membership function that relies much on the subjective and heuristic judgements of experts. Thus, the priority would be
affected. Besides, the fuzzy interval indicating the degree of subjectivity is fixed in relation to the types of membership
functions. This is not true in reality, because the boundary interval that denotes estimation range in real world varies
across experts with different knowledge and experience.

International Journal of Production Research 6685
Although many researches focus on the qualitative description of IPS 2 (e.g. definition, classification and organisation,
etc) and elicitation and evaluation of product/service requirement, there are still few studies on the customer
requirement generation and evaluation for IPS 2 . Therefore, it will be of value to propose a systematic IPS 2 requirement
management approach including requirement elicitation and requirement prioritisation. In this respect, this paper tries to
explore the following topics:
• Develop an effective tool for eliciting IPS2 requirements considering different stakeholders interaction and their
interests.
Build a structured and flexible framework for IPS2 requirements’ evaluation to identify the priority.
• Develop a mechanism to effectively manipulate the subjectivity and vagueness in the requirement evaluation
process under the circumstance of less priori information.
3. Research method
The case study method is adopted to test and verify the proposed requirement evaluation method of rough group AHP
based on I-CAC. Specifically, two research points are to be verified: (1) whether the model of I-CAC could be used
as an effective approach to elicit and generate the IPS 2 requirement and (2) whether the rough group AHP method
could well manipulate the subjectivity and vagueness in the requirement evaluation. All the data were gathered
through air compressor company visits made from October 2012 to December 2012. The data of IPS 2 requirements
are mainly collected from the design documentation, in-depth structured interviews and archival records of the company,
while the judgements of the importance of IPS 2 requirement are collected from the focus group and Delphi
method. With the collected data, the proposed IPS 2 requirements’ evaluation approach is validated. Further evaluation
by in-depth interviews in selected company and comparisons with fuzzy method are also conducted to reveal the
features of the method.
4. IPS 2 requirement evaluation based on the I-CAC and rough group AHP
From the review and analysis in Section 2, it is necessary to develop a more effective approach to systematically elicit
and evaluate uncertain IPS 2 requirement. The uncertainty mainly has four types of source, i.e. fuzziness, heterogeneity,
incompleteness and fluctuation. Fuzziness refers to the vague nature of the decision maker’s understanding of the relative
importance among the IPS 2 requirements. Heterogeneity derives from the different tastes of customers. Fluctuation
is associated with the change of customer requirements over time. Incompleteness arises from lack of information in
IPS 2 requirements. In our research, we mainly deal with the first type of uncertainty; namely, fuzziness (vagueness). In
this work, the authors propose a rough group AHP method to evaluate the IPS 2 requirement elicited from I-CAC analysis.
The method combines the advantage of AHP in requirement evaluation structure and strength of rough set theory in
manipulating vagueness and subjectivity. With the aid of the proposed method, it is expected that IPS 2 can easily find
the critical customer requirements for further design of IPS 2 . In sum, this study aimed at providing a systematic method
for requirements’ elicitation and prioritisation under vague environment. In the proposed approach, the whole requirement
assessment process is separate into two main functional parts as shown in Figure 1. Below, each functional part is
analysed in detail.
4.1 IPS 2 requirement elicitation based on the I-CAC analysis
Requirement elicitation is the beginning of IPS 2 development project. The first functional part is to obtain an understanding
of the problem that IPS 2 is to solve. In this functional part, I-CAC is reviewed, stakeholders are identified and
customer value and requirement are elicited. This process is typically performed by a requirement engineer team with
enough expertise and experience in implementing elicitation techniques.
4.1.1 Construct model of I-CAC
Contrary to the conventional product thinking, value is not embedded in the industrial product but is generated by
supporting the industrial customer’s activities related to the use of the product. To facilitate the use of industrial product,
both pre-use activities (e.g. installation, training) and post-use activities (e.g. disposal) should also be concerned.

6686 W. Song et al.
Figure 1. Framework of the IPS 2 requirement elicitation and evaluation.
Therefore, to obtain industrial customer’s requirement systematically and effectively, a new tool named I-CAC analysis
is proposed in this section. An I-CAC consists of three kinds of activities, pre-what goes on before the industrial customer
obtains the expected result, during-what happens while they derives the core benefit and post-what happens after
long use of the product. Each category consists of several key activities. As is shown in the middle ring of Figure 2, in
the phase of pre-use, customers firstly conduct product selection and matching to choose the most appropriate products
to satisfy their production need. This activity would be significant to the overall function and operation efficiency. The
procurement includes activities such as bargaining, delivery, inspection and payment. After procurement, installation,
debugging and commissioning of the product is necessary to ensure the quick and reliable equipment starting and running.
In the phase of during use, operation of industrial product mainly focuses on the efficient use and collecting relevant
information of the product. To improving equipment operation efficiency and reduce equipment lifecycle costs,
MRO (maintenance, repair and overhaul) is adopted, which includes activities such as disassembly, diagnosis, spare part
supply, etc. In the final phase of post-use, upgrading and scrapping are related activities equipment dismantling, assessment,
refurbishment and recycling.
It is only when a product interacts with customer in an activity that designers can actually determine the benefit,
costs or even, the environmental effects. The I-CAC model could be tailored for the actual context of different types of
industrial products. A key concept here is the life time perspective, which takes a broader, holistic and longer term perspective,
which often reveals the business potential of the whole value chain.
4.1.2 Stakeholder identification and relationship mapping in the I-CAC model
In the first step, different stakeholders (direct or indirect) throughout the lifecycle are identified so that designers can
acquire common value from them later. A stakeholder could either be from the external or internal organisational
environment. There are various stakeholders around the I-CAC, each with different types of stakes in the decisions made
during the development of an IPS 2 . The stakeholders include end users/customers, spare part suppliers, laws and
regulations, procurement engineer, operator, and IPS 2 providers (see outer ring in Figure 2). Those stakeholders play

International Journal of Production Research 6687
Figure 2. I-CAC and stakeholders.
different roles in different phase of customer activity cycle. For example, end users in the activity of product selection
and matching mainly presents their requirements of the product, while in the activity of operation, they use the result or
function of the product.
In the second step, it is necessary to identify the relations among the stakeholders around the customer activity,
because the value and requirement embed in those relationships. Interactions between stakeholders include: exchanging
information and knowledge, operating products, executing instructions and providing supporting tasks or spare parts. An
illustration of stakeholders’ interactions in activity of installation, debugging and commission is shown in the middle of
Figure 3. The IPS 2 provider installs, debugs and trials the industrial product on request the end user’s demands. Meanwhile,
the end user obtains the function of the product from the operator’s work (operation of the equipment). To ensure
the operator to provide reliable results with the product, IPS 2 provider also offers training and maintenance. Other stakeholders’
interactions can be obtained in the same way.
Figure 3. An illustration of requirement elicitation in the phase of installation, debugging, and commission.

6688 W. Song et al.
4.1.3 Customer value identification and requirement elicitation
The customer value is the benefit obtained by customers when their requirements are fulfilled. It is also the common
vision of stakeholders for the IPS 2 . The expression of customer value can be a sentence clearly describing the added
value provided by the new IPS 2 in different activities; for example, the customer value is ‘quick start of the system’
once the procurement contracts is signed. When the common value of customer has been identified, relevant
stakeholders’ requirement related with the value could be determined. To support this process, a number of methods for
gathering and collecting the information from the different stakeholders exist. Those methods include, for example,
interviews, focus groups, brainstorming, use cases, checklists and questionnaires. For example, IPS 2 is often complex
and automated system; professional installation, debugging and commission are valuable for customers, which would
increase the customer’s satisfaction. Industrial customer needs the IPS 2 provider to guide the installation and adjust the
key parameters of the equipment at the starting period. Therefore, the value of ‘Quick start of the system’ can be
converted into the requirement of ‘Professional installation, debugging, and commission’ (see Figure 3).
4.1.4 Construction of hierarchical structure for IPS 2 requirement
Owing to the diverse, imprecise and linguistic characteristic of customer requirements, it is necessary to grouping them
into meaningful hierarchies or categories for easy understanding and analysis. Affinity Diagram (Cohen 1995) can be
utilised to structure customer requirements, because it is a method of arranging random data into natural and logical
groups. The IPS 2 requirement management team firstly interprets the elicited customer requirements into simple and representative
expressions. Then, these phrases would be combined into many affinity groups, and the phrase that could
capture the primary theme and key points of the group would be selected as the header while its group members could
be stratified into a tree structure. With this effort spent, customer requirements can be organised as a tree-like structure
with an increasing number of items moving from left to right. Figure 4 shows a sample IPS 2 requirement hierarchy.
4.2 IPS 2 requirement prioritisation based on rough group AHP
Designers also need to prioritise requirements so that they can make decisions on which requirements to fulfil when
different requirements cannot be fulfilled at the same time. The conventional prioritisation methods always ignore the
Figure 4. Hierarchical structure for IPS 2 requirement.

International Journal of Production Research 6689
vagueness and subjectivity of decision information in uncertain innovation situations. Therefore, in this section, in order
to cope with vague and subjective information in IPS 2 requirement prioritisation, the authors introduce rough number
concept based on the rough set theory in group AHP. The rough set theory can enable stakeholders to well express their
true perception and evaluation without any priori information.
4.2.1 Construction of pair comparison matrix and consistency test
Invite expert team to make pair-wise comparisons of IPS 2 requirement to obtain crisp evaluation matrix. The kth expert
pair-wise comparison matrix M k is as follows:
2
3
1 r12 k ... r1n
k r21 k 1 r2n
k M k ¼ . . . . . . 6
7
4
5
rn1 k rn2 k 1
k ¼ 1; 2; ...m (1)
where rij k is the kth expert’s judgement for the ith IPS 2 requirement’s importance compared with the jth requirement, m
is the number of experts and n is the number of IPS 2 requirement. It is necessary for testing consistency of pair-wise
comparison matrix. Consistency test can be conducted as follows.
CI ¼ k max n
(2)
n 1
CR ¼
CI
; (3)
RI(n)
CI is consistency index, k max is the largest eigenvalue of matrix M k , n is the dimension of the matrix M k ; CR is
consistency ratio and RI(n) is random index that depends on the dimension of the matrix (Saaty 1977) (see Table 3).
When CR < 0.1, pair-wise comparison matrix pass the consistency test, experts’ evaluations on the IPS 2 requirement
are in consistency and acceptable. While CR > 0.1, experts need to adjust their judgements until pass the consistency test.
After consistency test, IPS 2 requirement management team could then build group requirement evaluation matrix ~R
as follows:
2
3
1 ~r 12 ... ~r 1n
~r 21 1 ~r 2n
~R ¼ 6 . . .
. . .
. 7
(4)
4
. . 5
~r n1 ~r n2 1
n
o
where ~r ij ¼ rij 1; r2 ij ; ...; rk ij ; ...; rm ij .
4.2.2 Determination of the rough group requirement evaluation matrixn
o
Assume that there is a set of m classes of human judgements, J ¼ rij 1; r2 ij ; ...; rk ij ; ...; rm ij ordered in the manner of
rij 1 \ r2 ij \ ... \ rk ij \ ... \ rm ij .U is the universe including all the objects and Y is an arbitrary object of U, and then
the lower approximation of rij k and the upper approximation of rij k can be defined as:
Lower approximation: Apr(r k ij ) ¼[fY 2 U=J(Y ) rk ij g (5)
Upper approximation: Apr(r k ij ) ¼[fY 2 U=J(Y ) rk ij g (6)
Table 3. Random index RI(n).
Dimension 1 2 3 4 5 6 7 8 9
RI 0 0 0.58 0.9 1.12 1.24 1.32 1.41 1.45

6690 W. Song et al.
Convert the crisp judgement sequence ~r ij in matrix ~R into rough number form to obtain rough group evaluation matrix
R. The geometric mean is adopted to synthesise individual judgements, because it preserves the reciprocal property of
pair-wise comparison matrixes without violation of the Pareto principle (Forman and Peniwati 1998).
Thus, the judgement, rij k, can be represented with a rough number defined by its lower limit Lim(rk ij ) and upper limit
Lim(r k ij ) as follows: Lim(r k ij ) ¼ YN ijL
m¼1
x ij
! 1=NijL
(7)
Lim(r k ij ) ¼
YN ijU
m¼1
y ij
! 1=NijU
(8)
x ij and y ij are the elements of lower and upper approximation for r k ij . N ijL and N ijU are the number of objects included in
the lower approximation and upper approximation of r k ij , respectively.
Then, the rough number form RN(r k ij ) of ~r ij can be obtained using Equations (5)–(8),
where r kL
ij
and r kU
ij
The interval of boundary region (i.e. r kU
ij
h
i
RN(r k ij ) ¼ Lim(rk ij ); Lim(rk ij )
h i
¼ r kL
ij
; r kU
ij
; (9)
are the lower limit and upper limit of rough number RN(rij k ) in the kth pair-wise comparison matrix.
rij kL ) indicates the degree of vagueness. A rough number with a smaller
interval of boundary region is interpreted as more precise one.
Thus, the rough sequence RN(~r ij ) can be obtained as follows,
nh
RN(~r ij ) ¼ r 1L
ij
; r 1U
ij
i h
; r 2L
ij
; r 2U
ij
i
h
; ; r mL
ij
The average rough interval RN(~r ij ) can be obtained by using rough computation principles (8)–(10):
h i
RN(~r ij ) ¼ r L ij ; rU ij
; r mU
ij
io
(10)
(11)
r L ij
¼
Ym
k¼1
r kL
ij
! 1=m
(12)
r U ij
¼ Ym
k¼1
r kU
ij
! 1=m
(13)
rij L and rij
U are lower limit and upper limit of rough number ½rij L; rU ij Š, respectively. m is the number of experts.
Then, the rough group decision matrix R can be obtained as follows:
2
½1; 1Š ½r12 L ; rU 12 Š ... ½rL 1n ; rU 1n Š 3
R ¼ ½r21 L ; rU 21 Š ½1; 1Š ½rL 2n ; rU 2n Š
6
.
.
. . . .
. 7
4
5
½rn1 L ; rU n1 Š ½rL n2 ; rU n2Š ½1; 1Š
(14)

International Journal of Production Research 6691
4.2.3 Calculate rough weights of IPS 2 requirement
Calculate rough weights of each IPS 2 requirement gRW i in different hierarchy with the following equation.
gRW i ¼½RW L
i
; RW U
i
Š (15)
RW L
i
¼ n
sffiffiffiffiffiffiffiffiffiffiffiffi
Y n
i¼1
r L ij;
RW U
i
¼ n
sffiffiffiffiffiffiffiffiffiffiffiffi
Y n
i¼1
r U ij
(16)
i =1, 2, …, n.
In the same way, rough weights of IPS 2 requirement can be got in any other hierarchies.
Finally, each requirement’s overall priority is calculated using multiplication synthesis method from top level to
bottom level.
4.2.4 IPS 2 requirement prioritisation
To covert the rough IPS 2 requirement weight into crisp value, here the authors introduce the optimistic indicator λ
(0 6 λ 6 1); to transform the rough weight gRW i into crisp value RW i . If decision-makers are more optimistic about their
judgements, then λ can select a bigger value (λ > 0.5). If decision-makers are more pessimistic about their evaluations, λ
should select a smaller value (λ < 0.5). If decision-makers keep a moderate attitude, in other words, neither more
optimistic nor more pessimistic, λ selects a certain value 0.5. The transformation calculation is as follows:
RW i ¼ (1
k)RW L
i
þ kRW U
i
(17)
According to the weights from the above steps, all the requirements of IPS 2 can be prioritised, and the important
value-based requirements can also be focused.
5. Case study
In this section, IPS 2 requirement evaluation of a rotary oil-free air compressor is taken as an example to demonstrate
the application of the proposed approach in the real world. In this case, the rotary oil-free air compressor is mainly
designed and sold to pharmaceutical plants that need clean compressed air for washing bottles and starting pneumatic
valves. Company H is a Fortune 500 manufacturer who is specialised in providing different air compressors and related
services for industry: pharmaceutical industry, metallurgical industry, shipbuilding, and mining. The company H now is
more and more concerned with the selling industrial services associated to their air compressors throughout the customer
activity lifecycle, such as air compressor selection consulting, installation and debugging, MRO, and energy saving solutions,
etc. The objective of the IPS 2 requirement evaluation in this case study is to identify key points that the customer
(pharmaceutical plant) is concerned for further IPS 2 design, and therefore, enhance the customer satisfaction and loyalty.
To reveal the advantages of the rough requirement evaluation method, the authors also make comparisons between the
proposed approach and the fuzzy group evaluation method.
5.1 Implementation of the proposed requirement evaluation method
5.1.1 IPS 2 requirement elicitation
First, a survey based on I-CAC is used to analyse main activities of the customer. The activities are pre-sales consulting,
procurement, installation, debugging and commissioning of air compressor, operation and use, MRO, etc. The disposal
of air compressor is not considered here as the pharmaceutical plant has its own special channel to recycle the scrapped
compressor.
Second, the related stakeholders around customer activities are identified. Interactions between stakeholders and the
nature of their relationships such as exchanging information, products or instructions are also identified. For example,
the stakeholders and their relationships in the MRO activity are captured in the Figure 5. There are three main stakeholders,
i.e. air user, IPS 2 provider and operator. The air user proposes the air demand, the operator meet this demand
with the air compressor operation and the IPS 2 provider is mainly responsible for reliable air supply with professional
MRO and spare parts supply in this phase. Similarly, the stakeholders and their relationships in other customer activities
can be acquired, which are not listed here due to the limited space.

6692 W. Song et al.
Figure 5. The value and requirement around the customer activity of MRO.
Third, the customer value, which is the common focus of stakeholders for the IPS 2 , is identified in this step by
using the interviews and focus groups. Value here is actually the definition of the IPS 2 in terms of the requirement
the industrial service is going to meet. For instance, to achieve the value of ‘High reliability, and long service life
of air compressor’, the requirement ‘Efficient, and reliable MRO with accurate operation information of air compressor’
has to be fulfilled. That is, the requirement is the cost of achieving the value. Similarly, the value in the
delivery of air compressor is mainly ‘Using immediately without time consuming for the starting period’. This
value is related with the requirement ‘Filed guidance and training at the starting period’. Thus, in this way, the rest
of requirements can be acquired.
Fourth, Affinity Diagram is used to structure customer requirements. The elicited customer requirements are firstly
interpreted into simple and representative expressions. For example, ambiguous requirement in the Figure 5 (Efficient,
and reliable MRO with accurate operation information of air compressor) is represented by three concrete sub-requirements,
i.e. ‘Disassembly and reassembly easily’, ‘24-h service (Feedback in 30 min, and on-site with spare parts in 3 h)’
and ‘Remote monitoring, early warning and failure diagnosis’. Similarly, other requirements could be also interpreted.
Then, all the phrases would be bundled into many affinity groups, and the header with its group members could be
obtained in Figure 6.
5.1.2 IPS 2 requirement prioritisation
Step 1 Construct pair comparison matrix and test consistency
An expert team is built for the evaluation IPS 2 requirement which consists of five experienced team members. They are
procurement engineer, operator, end user, MRO engineer and IPS 2 designer. The work experience of experts ranged
from 4 to 10 years in their own domains. Pair-wise comparisons between IPS 2 requirements are conducted in each
hierarchy until each comparison matrix can get through the consistency test.
Take the R 4 (Guarantee and optimisation of normal operation), for example (R 41 : Compressor flow P 7m 3 /min,
discharge pressure P 0.8 Mpa; R 42 : Integrated structure; R 43 : no vibration and air flow pulse, noise < 75 dB; R 44 : Simple
and comfortable manipulation; and R 45 : Energy saving rate: 18–35%), to illustrate computation process. The five
experts’ comparison matrixes of requirement importance for R 4 are as follows:

International Journal of Production Research 6693
Figure 6. Hierarchical structure for IPS 2 requirement of rotary oil-free air compressor.
According to formula (10) and (11), consistency ratio CR 1 = 0.010 < 0.1, CR 2 = 0.017 < 0.1, CR 3 = 0.029 < 0.1,
CR 4 = 0.004 < 0.1 and CR 5 = 0.002 < 0.1, so the consistency of each pair-wise comparison matrix of the requirement R 4
(Guarantee and optimisation of normal operation) is acceptable.
Then, the group evaluation matrix of requirement ~R 4 can be obtained by combining the above five pair-wise
matrixes together.
2
~R 4 ¼
6
4
1; 1; 1; 1; 1 5; 7; 5; 3; 5 3; 3; 1=2; 1=3; 3 3; 5; 2; 2; 3 5; 3; 3; 1; 1=2
1=5; 1=7; 1=5; 1=3; 1=5 1; 1; 1; 1; 1 1=2; 1=3; 1=8; 1=8; 1=2 1=2; 1=2; 1=2; 1; 1=2 1; 1=3; 1=2; 1=3; 1=8
1=3; 1=3; 2; 3; 1=3 2; 3; 8; 8; 2 1; 1; 1; 1; 1 1; 3; 5; 7; 1 3; 1; 5; 3; 1=5
1=3; 1=5; 1=2; 1=2; 1=3 2; 2; 2; 1; 2 1; 1=3; 1=5; 1=7; 1 1; 1; 1; 1; 1 3; 1=3; 3; 1=2; 1=5
1=5; 1=3; 1=3; 1; 2 1; 3; 2; 3; 8 1=3; 1; 1=5; 1=3; 5 1=3; 3; 1=3; 2; 5 1; 1; 1; 1; 1
3
7
5

6694 W. Song et al.
The same procedure can be conducted to other IPS 2 requirements and sub- requirements to get their comparison
matrixes. Other group requirement evaluation matrixes are not listed here due to space limitation.
Step 2 Determination of the rough group requirement evaluation matrix
Get the rough group comparison matrix R with the original group comparison matrix from the step 1. To get the rough
form of group comparison matrix, it is necessary to transform the elements ~r ij in group IPS 2 requirement evaluation
matrix ~R 4 into the rough number form according to formula (5)–(9).
Take the element in ~r 42 ¼f5; 7; 5; 3; 5g in ~R 4 to illustrate the rough number conversion process,
Lim(3) ¼ 3
p
Lim(5) ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
4 5 5 5 3 ¼ 4:401
p
Lim(3) ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
5 3 5 5 5 7 ¼ 4:829
p
Lim(7) ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
5 3 5 5 5 7 ¼ 4:829
p
Lim(5) ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
4 5 5 5 7 ¼ 5:439
Thus, r k 42 can be represented in the rough number form RN(rk 12 ),
RN(r 1 12 ) ¼ RN(r3 12 ) ¼ RN(r5 12
) ¼ RN(5) ¼½4:401; 5:439Š;
RN(r 2 12
) ¼ RN(7) ¼½4:829; 7Š;
RN(r 4 12
) ¼ RN(3) ¼½3; 4:829Š:
According to the Equations (10)–(13), the average rough interval of RN(~r 42 ) ¼½4:152; 5:586Š. Similarly,the rough
number form and average rough interval for other elements in the group decision matrix ~R 4 can be acquired.
Therefore, the rough group comparison matrix R 4 can be obtained,
2
3
½1:000; 1:000Š ½4:152; 5:586Š ½0:804; 2:338Š ½2:324; 3:473Š ½1:069; 3:140Š
½0:179; 0:241Š ½1:000; 1:000Š ½0:180; 0:377Š ½0:514; 0:642Š ½0:238; 0:573Š
R 4 ¼
½0:428; 1:244Š ½2:650; 5:550Š ½1:000; 1:000Š ½1:484; 4:167Š ½0:715; 3:027Š
6
7
4 ½0:288; 3:473Š ½1:558; 1:945Š ½0:240; 0:674Š ½1:000; 1:000Š ½0:400; 1:668Š 5
½0:318; 0:935Š ½1:746; 4:193Š ½0:330; 1:400Š ½0:599; 2:499Š ½1:000; 1:000Š
In the same way, the other IPS 2 requirements’ group comparison matrixes in rough number form can also be
obtained. Other group comparison matrixes in rough number form are not listed here due to space limitation.
Step 3 Calculate rough weights of IPS 2 requirement
Calculate rough weights of IPS 2 requirement and sub-requirement (see Table 4) in the light of formulae (15) and (16).
Similarly, the rough weights for the first hierarchy of IPS 2 requirements can be obtained as follows.
RW R0 ¼fw R1 ; w R2 ; w R3 ; w R4 ; w R5 g¼f½0:788; 1:454Š; ½0:360; 0:743Š; ½0:237; 0:287Š; ½2:495; 3:575Š; ½1:745; 3:081Šg
The final overall weight is calculated using multiplication synthesis method from top level to bottom level.
The results are also listed in Table 4. Normalised weights for other IPS 2 requirements are also calculated similarly in
Table 4.

Table 4. Rough weight of IPS 2 requirement.
IPS 2 requirement Sub-requirement Rough weight Normalised rough weight
R 1 (easy and accurate decision-making of
R 11 [1.000, 1.000] [0.788, 1.454] [0.082, 0.151]
air compressor selection), [0.788, 1.454]
R 2 (procurement process support), [0.360, 0.743] R 21 [0.329, 0.427] [0.118, 0.318] [0.012, 0.033]
R 22 [1.296, 1.968] [0.466, 1.463] [0.048, 0.152]
R 23 [1.355, 2.057] [0.488, 1.529] [0.051, 0.159]
R 3 (quick start using of the air
R 31 [0.680, 1.278] [0.161, 0.367] [0.017, 0.038]
compressor system), [0.237, 0.287]
R 32 [0.418, 0.925] [0.099, 0.266] [0.010, 0.028]
R 4 (guarantee and optimisation of
normal operation), [2.495, 3.575]
R 5 (efficient, and reliable MRO with
accurate operation information of
air compressor), [1.745, 3.081]
International Journal of Production Research 6695
R 33 [1.230, 2.420] [0.292, 0.695] [0.030, 0.072]
R 41 [1.527, 2.696] [3.809, 9.639] [0.395 ,1.000]
R 42 [0.331, 0.507] [0.825, 1.812] [0.086, 0.188]
R 43 [1.037, 2.443] [2.588, 8.736] [0.269, 0.906]
R 44 [0.533, 1.500] [1.330, 5.363] [0.138, 0.556]
R 45 [0.643, 1.688] [1.605, 6.035] [0.167, 0.626]
R 51 [0.373, 0.775] [0.650, 2.387] [0.067, 0.248]
R 52 [1.024, 1.788] [1.786, 5.510] [0.185, 0.572]
R 53 [0.986, 1.920] [1.720, 5.915] [0.178, 0.614]
Table 5. Crisp requirement weight and rank of IPS 2 requirement under different vagueness.
IPS 2 requirement
λ =0 λ = 0.5 λ =1
Crisp weight Rank Crisp weight Rank Crisp weight Rank
R 11 0.082 8 0.116 9 0.151 11
R 21 0.012 14 0.023 14 0.033 14
R 22 0.048 11 0.100 11 0.152 10
R 23 0.051 10 0.105 10 0.159 9
R 31 0.017 13 0.027 13 0.038 13
R 32 0.010 15 0.019 15 0.028 15
R 33 0.030 12 0.051 12 0.072 12
R 41 0.395 1 0.698 1 1.000 1
R 42 0.086 7 0.137 8 0.188 8
R 43 0.269 2 0.587 2 0.906 2
R 44 0.138 6 0.347 6 0.556 6
R 45 0.167 5 0.396 3 0.626 3
R 51 0.067 9 0.158 7 0.248 7
R 52 0.185 3 0.378 5 0.572 5
R 53 0.178 4 0.396 4 0.614 4
Step 4 IPS 2 requirement prioritisation
Then, IPS 2 requirement management team introduces the optimistic indicator λ = 0, 0.5 and 1, respectively, transforming
the normalised rough weight of requirement into crisp value with formula (17) (see Table 5).
The weight of IPS 2 requirement can be seen in Table 5. When experts are more cautious (λ = 0), the priority of IPS 2
requirement is as follows:
R 41 > R 43 > R 52 > R 53 > R 45 > R 44 > R 42 > R 11 > R 51 > R 23 > R 22 > R 33 > R 31 > R 21 > R 32 :
When experts have a moderate propensity (λ = 0.5), the priority of IPS 2 requirement is as follows:
R 41 > R 43 > R 45 > R 53 > R 52 > R 44 > R 51 > R 42 > R 11 > R 23 > R 22 > R 33 > R 31 > R 21 > R 32 :
When experts have much optimistic propensity (λ = 1), the priority of IPS 2 requirement is as follows:
R 41 > R 43 > R 45 > R 53 > R 52 > R 44 > R 51 > R 42 > R 23 > R 22 > R 11 > R 33 > R 31 > R 21 > R 32 :

6696 W. Song et al.
Table 6. Comparison between the I-CAC method and the method Company H used before.
System perspective Lifecycle consideration Stakeholders interaction Value focus
I-CAC model
Company H’s
method used
previously
Consider product and
service requirement
systematically
Fragmented and fixed
requirement template
Focus on full customer activity
cycle (i.e. pre-use, during use,
and post use)
Focus on the static requirements
before selling product to
customer
Consider different
stakeholders interaction
around customer activity
Mainly focus on end user,
and often ignores other
stakeholders
Core benefit of
customer, e.g. clean
compressed air
The product function,
e.g. flow and pressure
We invite the designers and lead customers to evaluate the prioritising results from the rough group AHP method,
and the interview results show the prioritisation are more accurate than that of the past. Both the lead customers and
designers confirm that the results reflect their real judgements and evaluations.
If the manager takes different risk-bearing attitude, i.e. adopt different indicator λ, the crisp weight of IPS 2 requirement
would be different. For example, for the requirement R 11, the weigh is, respectively, 0.082 (λ = 0), 0.116 (λ = 0.5)
and 0.151 (λ = 1). This difference would lead to their different design priority and resource allocation.
The results indicate that R 41 (function: compressor flow P 7m 3 /min; discharge pressure P 0.8 Mpa), R 43 (Safe and
smooth operation), R 45 (Energy saving rate: 18% to 35%), R 53 (remote monitoring, early warning and failure diagnosis)
and R 52 (24-h service: feedback in 30 min, and on-site with spare parts in 3 h) are top five requirements which should
be given much priority. The weight rankings of some IPS 2 requirements such as R 51 (disassembly and reassembly
easily) and R 11 (professional consulting and report of air compressor selection and matching) are dependent on the
propensity of experts.
R 41 and R 43 are considered to be the top two important requirements because they are the compressed air user’s core
value. In this respect, importance of R 41 and R 43 would influence the selection of IPS 2 business model in the later
design phase, i.e. product-orientated, availability-orientated or result-orientated. Besides, according to the field survey,
power consumption of compressed air systems accounts for about 20% of the total power consumption in the customer
company. Energy consuming costs of an air compressor account for about 70% of it lifecycle cost. Therefore, R 45 is also
given higher priority, and it is necessary to consider using variable frequency adjusting technology, heat recovery and
pipeline optimisation to save energy in the following design phase. The experts highlight the R 53 , because it is necessary
to know exactly where the problem is located when or even before a problem occurs. With fulfilment of R 53 , the maintenance
of air compressor would be easier and cost effective for the IPS 2 provider.
5.2 Comparison and discussion
In order to reveal the effect of the I-CAC method in supporting elicitation of IPS 2 requirements in the Company H, we
compare this method with that Company H used previously. The company mainly uses collection template of requirement
which contains some fixed items such as product function, reliability and warranty. Table 6 presents the comparison
between the I-CAC method and the method Company H used before.
Requirement manager and engineers considered that the method provided a logical, understandable and step-by-step
to analyse IPS 2 requirements. They also said they often checked whether some requirements has been covered or not
with the I-CAC method. Besides, requirement manager and customer representatives regarded that the final priority was
reasonable and acceptable because it reflected well the true perception of customer’s expectation. The requirement
manager also proposed that it was necessary to develop a computer system to support the requirement elicitation and
evaluation.
The customer requirement evaluation with fuzzy group AHP using symmetrical triangular fuzzy number (Kwong
and Bai 2002) has also been applied in the case study for further comparison. The comparison results of rough and
fuzzy approach are shown in Figure 7.
The customer requirements’ weights from rough group AHP and fuzzy group AHP are almost different with each
other (see Figure 7). For example, the rough approach considers the R 41 as the most important customer requirement
(w 41 = 0.395, when λ =0; w 41 = 0.698, when λ = 0.5; w 41 = 1.000, when λ = 1). However, in the fuzzy approach, the
requirement R 53 is considered as the most important customer requirement (w 53 = 0.420, when λ =0; w 53 = 0.710, when
λ = 0.5; w 53 = 1.000, when λ = 1). The other IPS 2 requirements also have different ranks, such as R 43 , R 45 and R 52 . The
weight differences in the two methods are derived from the different subjectivity and vagueness manipulation
mechanisms.

International Journal of Production Research 6697
Figure 7. Comparison between rough and fuzzy customer requirement evaluation approach.
In fact, the fuzzy interval that denotes the degree of subjectivity and vagueness is fixed in relation to the types of
membership functions. For example, in the fuzzy comparison process of R 4 , the five selected experts rate ‘R 41 ’ relative
to ‘R 42 ’ are 5, 7, 5, 3 and 5, which are represented in form of fixed fuzzy interval [4,6], [6,8], [4,6], [2,4] and [4,6],
respectively (see Figure 8). The geometric mean of the five experts’ judgements is [3.776, 5.860] in the fuzzy approach.
However, this average fuzzy interval does not truly reflect the actual situation of the judgements, because the boundary
interval that denotes estimation range in customer requirement evaluation process varies across experts who have different
knowledge, experience and expertise. On the contrary, in rough group AHP approach, the ratings of 5,7,5, 3 and 5
are converted into the flexible interval form [4.401, 5.439], [4.829, 7], [4.401, 5.439], [3, 4.829] and [4.401, 5.439],
respectively (see also in Figure 8). This rough conversion brings a general description of experts’ opinion, and presents
a more holistic judgement. The group average interval from the rough method is [4.152, 5.586] which not only reflects
the size of weight but also the actual estimation range. Thus, the rough AHP provides a more accurate approach to
describe the status of customer requirement of IPS 2 . The same results can be also found in other customer requirements’
Figure 8. Different vagueness manipulations for judgements on requirement R 41 relative to R 42 .

6698 W. Song et al.
evaluation process. Besides, it is not necessary for the rough group AHP method to subjectively pre-set the fuzzy
membership function for interval number conversion, which is common in fuzzy methods.
The degree of vagueness measured by the interval of the boundary region influences the final weights of IPS 2
requirements. For example, in the rough method, the degree of vagueness for requirement R 11 is 0.069 (rough weight of
R 11 is [0.082, 0.151]), and its weight is 0.116 (λ = 0.5). However, in the fuzzy method, the degree of vagueness for
requirement R 11 is 0.087, and its weight is 0.222 (λ = 0.5). This is because of the fuzzy method’s overestimation of
vagueness degree (the boundary region) for requirement R 11 (0.087 > 0.069). The same can be found in the other
requirements’ weights.
Furthermore, the rough group AHP method can identify the small change of expert group’s preference and inconsistency,
because it can flexibly adjust its boundary according to consensus of experts’ preferences. For example, value of
judgements 5, 5, 5, 5 and 7 can be converted into fuzzy interval [4, 6], [4, 6], [4, 6], [4, 6] and [6, 8], and rough interval
[5, 5.348], [5, 5.348], [5, 5.348], [5, 5.348] and [5.348, 7]. When experts readjust their judgements as 5,7,5, 3 and
5, the fuzzy intervals are transformed into [4,6], [6,8], [4,6], [2,4] and [4,6] and rough intervals are converted into
[4.401, 5.439], [4.829, 7], [4.401, 5.439], [3, 4.829] and [4.401, 5.439]. Apparently, the newly transformed fuzzy
interval still has a fixed boundary two, which is not realistic in the practice because it cannot distinguish the change and
inconsistency of experts’ judgements. In the fuzzy approaches, all the cognitive differences are assumed to be
equidistant. This would ultimately influence the quality of decision-making in IPS 2 requirement evaluation.
6. Conclusions and recommendation
IPS 2 requirement elicitation and requirement prioritisation are two major challenges in the early development of IPS 2 .
This is because few effective requirement generation tools for IPS 2 are available. Besides, prioritising the requirement
always involves qualitative, arbitrary and ambiguous linguistic judgements and preferences. This research explores to
design a systematic IPS 2 requirement evaluation approach based on Group AHP and rough set theory. The proposed
approach utilises the I-CAC to elicit the customer requirement of IPS 2 . It integrates strength of both group-AHP and
rough set theory to handle subjective customer requirement assessments. The validation of the proposed approach in the
case of air compressor shows that this approach can be used as an effective requirement evaluation tool for IPS 2 .In
sum, the rough set approach reveals the following features:
First, the I-CAC considering the interaction of different stakeholders provides a systematic process for IPS 2 requirement
elicitation. It also helps to generate the IPS 2 requirement from the perspective of lifecycle and customer value.
Second, IPS 2 requirement evaluation using rough group AHP has a flexible boundary that well reflects expert’s subjective
and vague judgements. Third, the proposed IPS 2 requirement evaluation method can avoid relying much on priori
information (e.g. pre-set membership functions in fuzzy methods). Fourth, the rough group method can discern the
change of decision makers’ preferences, and manipulates the inconsistency of experts’ judgements in requirement evaluation
process.
Although the approach provides a simple and effective mechanism for IPS 2 requirement elicitation and evaluation
involving subjective judgement in group decision environment, it has limitations. When the pair-wise comparison matrix
does not pass the consistency test, experts have to adjust their judgements to pass the consistency test which is time
consuming. Besides, industrial practitioners’ lack of rough logic domain knowledge may affect efficient use of the
method. In future research, it is necessary to computerise the rough group AHP model to reduce the burden of the
judgements’ adjustment and facilitate the use of the method. Rough group Analytic Network Process (ANP) approach
will be used to take into consideration the interdependencies among customer requirements of IPS 2 . Also, to
obtain innovative design concept of IPS 2 , the integration of the proposed requirement evaluation approach with other
tools (e.g. QFD and TRIZ) could be considered in further research. In addition, more implementation tests are needed
to gain external validity.
Acknowledgement
The authors would like to thank all the anonymous reviewers for their helpful comments and suggestions on this manuscript.
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