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

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

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