Which of the following is not one of the suggested modifications of the paired comparison technique?

Pairwise comparison methods

The first pairwise comparison method used for camouflage evaluation is the Law of Comparative Judgment (LCJ). LCJ is a psychophysical tool for performance evaluation, developed by Thurstone and described by Torgerson (1958). It is a forced-choice pairwise comparison method, where in this case different patterns are evaluated two at a time by a panel of observers, and through a statistical method the different patterns are ranked in terms of perceptible effectiveness. McManamey (1999) describes in detail how the method is used. In another publication he compares the POD techniques mentioned above with the LCJ (McManamey, 2003). He finds good correlation between the methods. The use of LCJ for camouflage evaluation is also described by Baumbach (2008). Hepfinger et al. (2010) describe a pairwise comparison method (in a simulation environment) where the perceptible effectiveness is rated in terms of the number of times it is selected by the observers. Although this method (LCJ) indicates the most effective pattern, it does not have a metric on how much better one design is in comparison with another one.

The second forced-choice pairwise comparison method is the Analytical Hierarchy Process (AHP). During a LCJ evaluation the observers only need to state which pattern they perceive as better, while with AHP they also need to state by how much the one design is better than the other. Baumbach has found the AHP to be a more meaningful method to evaluate camouflage patterns (Baumbach, 2008; 2010). The first reason for it to be a more effective method is that the result for AHP is expressed on a scale from 0 to 100. The result for LCJ is expressed as values on an open-ended scale, which makes comparison between different test setups very difficult. The second reason is that the AHP allows the user to calculate a consistency ratio, and any inconsistent data could be filtered out and not included in further analyses. A graph showing comparative results for an AHP as well as an LCJ evaluation (four different patterns) is shown in Fig. 5.9. Note how close the LCJ ranking is for Pattern2, Pattern3 and Pattern4 (right-hand scale). With an AHP analysis of the data a clear separation of the preferences is observed, while the ranking of these three patterns changes as well.

The advantage of using the psychophysical methods LCJ and AHP is that a large number of observers is not a prerequisite for accurate and statistically significant results, as is the case with a POD evaluation. It is also possible to perform a relatively quick evaluation in order to determine the effectiveness of certain designs. The overall effectiveness of a design, however, cannot completely be determined by AHP and LCJ, and can only be fully described by a POD evaluation.

2.2 Fuzzy AHP Method for Scoring the Soft Criteria

There are usually two ways for determining the relative priorities of the alternatives with respect to the soft criteria: the scaling system method (Manzardo et al., 2012; Othman et al., 2010) and the pairwise comparison method (Ren et al., 2014; Saaty, 1980). The scaling method scores the alternatives by using numbers (crisp numbers or gray numbers), while the pairwise comparison method determines the relative priorities of the alternatives via the pairwise comparison. The scaling method is simple and easy to be operated; however, it cannot assure the overall consistency among all the relative priorities of the alternatives with respect to each of the soft criteria. AHP is a widely used pairwise comparison method for determining the relative priorities of the alternatives with respect to the soft criteria (Ren et al., 2014; Saaty, 1980). However, the conventional AHP method uses nice scales (1, 2, …, 9) and their reciprocals to determine the comparison matrix and the relative priorities of the criteria, which requires the users to describe their opinions using crisp numbers. As human’s judgments are usually subjective, vague, and ambiguous, this limitation could result in the inconvenience of the users and inaccuracy of the results (Ren and Sovacool, 2014). Accordingly, this study adopted a fuzzy AHP method by combining the thoughts of the conventional AHP with the fuzzy set theory to quantify the relative priorities of the soft criteria. The fuzzy AHP method allows the stakeholders/decision-makers to describe their preferences by using linguistic variables, i.e., words or sentences in a natural or artificial languages, which is more suitable than the crisp numbers for depicting human’s judgments. The linguistic variables are in turn connected to fuzzy numbers through the membership functions (Afgan et al., 2008; Ren et al., 2015).

For a universe set, X, the fuzzy set A in X is characterized by a membership function μA˜(x)→[0,1], which quantifies the grade of membership of the element X to A (Amindoust et al., 2012; Mazloumzadeh et al., 2008; Zadeh, 1965). The membership functions can be of different formulation, but in practice, triangular and trapezoidal membership functions are most frequently used in the fuzzy logic as showed in Eqs. (9.1) and (9.2) (Mazloumzadeh et al., 2008), in which a, b, c, and d are parameters. For those unfamiliar to the fuzzy set theory, it also has been extensive used in some other literatures (Amindoust et al., 2012; Mazloumzadeh et al., 2008; Zadeh, 1965).

(9.1)μA˜(x)={ 0x≤ax−ab− aa<x≤bx−cb−c b<x≤c0x>c

(9.2)μA˜(x)={0x≤aorx≥dx−ab−aa<x≤b1b<x≤cx−dc−dx>c

In the fuzzy AHP method, the comparison matrix is first determined by using the linguistic terms, which are then transformed into fuzzy numbers (Table 9.2) (Tseng et al., 2009). Assuming X={ x1,x2,…,xn} is an object set, and U={g1,g2,…,gm} is a goal set, then, the performance of each object regarding each goal can be analyzed; the m-extent analysis values for each object can be obtained as the following equation:

Table 9.2. The Linguistic Terms and Corresponding Fuzzy Numbers for the Pairwise Comparison (Tseng et al., 2009)

(9.3)Mgi1,Mgi2,…,Mgim,i=1,2,…,n

where Mgij(j=1,2,…,m )=(lgij,mgij ,ugij) are the triangular fuzzy numbers.

Subsequently, the fuzzy AHP method is conducted according to the followed four steps as developed by Chang (1996) (Choudhary and Shankar, 2012; Heo et al., 2010; Tseng et al., 2009).

Step 1: The value of the fuzzy synthetic extent with respect to the ith object is defined as the following equation:

(9.4)Si=∑j=1 mMgij⊗[∑i=1n ∑j=1mMgij]−1

where ∑j=1mMgij and [∑i=1n∑j=1mMgij]−1 can be determined according to Eqs. (9.5) and (9.6), respectively.

(9.5)∑j= 1mMgij=(∑j=1m lgij,∑j=1mmg ij,∑j=1mugij),i=1,2,…,n

(9.6)[∑ i=1n∑j=1mMgi j]−1=(1∑i=1n∑j=1mugij ,1∑i=1n∑j=1m mgij,1∑i=1n ∑j=1mlgij)

Step 2: The degree of possibility of S2=(l2,m2,u2)≥S1=(l 1,m1,u1) is defined as the following equation:

(9.7)V(S2≥S1)= supy>x(min{μA˜( x),μB˜(y)})=height(S2∩S1)=μS2(d)={1 ifm2≥m10ifl1≥u2l1−u2(m2−u2)−(m1−l1)otherwise

where d is the ordinate of the highest intersection point between μM1 and μM2 as illustrated in Fig. 9.2. Both V(S2≥S1) and V(S1≥S2) are necessary for comparing S1 and S2 .

Step 3: The degree of possibility for a convex fuzzy number to be greater than the convex fuzzy number Si(i=1,2,…,k) is defined by the following equation:

(9.8)V(S≥S1, S2,…,Sk)=V(S≥S1)andV(S≥S2)and…and V(S≥Sk) =minV(S≥Si), i=1,2,…,k

Assuming that

(9.9)d′(Ai)=minV(Si≥Sk),k=1,2,…,nand k≠i

Then, the weight vector of the n elements Ai(i=1,2,…,n) can be determined by the following equation:

(9.10)W′=(d′(A1),d′(A2),…,d′(An) )T

where d′(Ai) is the weight of the ith element Ai, and W′ is the weight vector.

Step 4: The weight vector in Eq. (9.10) is normalized to obtain the weight of each element according to Eqs. (9.11) and (9.12), respectively. In Eq. (9.11), W is a nonfuzzy number.

(9.11)W=(d(A1),d(A2),…,d(An))T

(9.12)d(Ai)=d′(Ai)∑i=1nd ′(Ai)

After the normalization, the weights of the criteria satisfy the following equation:

(9.13)∑i=1nd(Ai)=1

where d(Ai) is the normalized weight of the ith element Ai, and W is the normalized weight vector.

3.4 Analytical Hierarchy Process

The AHP is a decision analysis method that considers both qualitative and quantitative information. The use of the AHP approach provided by Saaty (Saaty, 1980) to assess the criteria weightings in MCDM recently has become popular in different areas of system engineering (Su et al., 2010).

Suppose there are n criteria in some hierarchy, the pairwise comparison method proposed by Saaty (Saaty, 1980) can be used to establish the comparison matrix (denoted by matrix A), as shown in Eq. (8.22):

(8.22)A=[1a12⋯a1 na211⋯a2n ⋮⋯⋱⋮an1an2 ⋯1],

where aij denotes the relative importance of criteria i comparing with j.

The relative importance of criteria j comparing to i can calculated by Eq. (8.23):

(8.23)aji=1aij,aij>0,i,j=1,2,⋯,n.

As for different systems and different implementers, the result of comparison matrix A is not absolutely the same with each other. With the comparison matrix, the weighting coefficients of each indicator can be acquired by calculating the principal eigenvector of the comparison matrix, as shown in Eq. (8.24):

(8.24)[1a12⋯a1na21 1⋯a2n⋮⋯⋱⋮an1an2⋯1]|w1w1⋮wn|=λmax|w1w1⋮wn |,

where (w1,w2,⋯ ,wn)T is the maximal eigenvector of matrix A and λmax is the maximal eigenvalue of matrix A. The maximal eigenvector and maximal eigenvalue can be calculated in the form as shown in Eq. (8.25) by the tool box of MATLAB when the comparison matrix A have been determined.

(8.25)[Wmax,λmax]=eig(A),

where λmax and Wmax are the maximal eigenvalue and maximal eigenvector of the comparison matrix, respectively.

Then weighting coefficient vector can be calculated by normalization of the maximal eigenvector, as shown in Eq. (8.26):

(8.26)W=(w1 ∑i=1nwi,w 2∑i=1nwi,⋯,wn∑i=1nwi )T,

where W is the weight coefficient vector, wi represents the weight of indicator i, n represents the total number of the indicators.

If aik=aijajk,i,j,k=1,2,⋯,n, then the comparison matrix A can be recognized as consistent matrix. Theory proves that if n-dimensional comparison matrix is a consistent matrix, its maximal eigenvalue must be n. But, it is difficult to establish a comparison matrix which is consistent matrix absolutely. In actual cases, some comparison matrix that meets the condition of consistency check can be recognized as consistent matrix. Consistency ratio is the common method to judge whether a comparison matrix is consistent or not, as shown in Eq. (8.27):

(8.27)CR=CIR I,

where CR is consistency ratio, CI is consistency index, RI is the average random index with the same dimension with A.

The value of average random index can be acquired in Table 8.3, the consistency index can be computed in Eq. (8.28):

Table 8.3. The Value of the Average Random Consistency Index RI

(8.28)CI=λmax−nn−1,

where λmax represents the maximal eigenvalue of the comparison matrix A and n represents the dimension of the matrix.

When CR < 0.1, the matrix can be acceptable as consistent matrix, contrarily CR ≥ 0.1, the matrix should be modified until an acceptable one.

5 Conclusions

A sustainable supplier selection framework for SSCM has been proposed in this paper. After developing the sustainable supplier selection criteria based on a systematic status review, a novel integrated method based on pairwise comparison method, DEMATEL, and rough set theory has been proposed. Then it is validated in a case study of solar air-conditioner manufacturer. The new method not only reveals the structure of interactions among the supplier selection criteria, but also help to find the critical criteria affecting the performance of sustainable supplier selection.

Based on the weights of sustainability criteria obtained from the proposed method, the managers in company G do not necessarily to take much time and effort to determine the criteria importance and explore the interrelationships between criteria. They can focus more on providing supplier score regarding the various sustainability criteria. With the obtained criteria weights, these individual perceptions can be aggregated to identify proper sustainable suppliers or sustainability deficiencies of certain suppliers. The case study results also show that Quality, T & CD (Training and community development) and Delivery are the three most important criteria. They have great impact on the sustainable supplier selection in company G. To avoid the potential risk of sustainable supplier selection, managers should not only take into account the significance of evaluation criteria as in former supplier selection approaches, but also consider the causal-effect relationships between supplier selection criteria. Companies selecting their sustainable suppliers should observe which suppliers have features of better quality, sustainable training and community development, and better delivery performance.

In sum, the proposed methodology makes several contributions to the sustainable supplier selection:

A novel methodology for sustainable supplier selection considering both importance and interrelationships of criteria has been developed. Even though some methods consider the interactions among criteria, they consider that the indicators are equally important in dealing with the interrelationships of criteria. The proposed methodology integrates the merits of the pairwise comparison method, the DEMATEL and the rough number. To our knowledge, no previous studies have investigated the subject of supplier selection with this kind of integrated method.

Decision makers express their evaluations in linguistic term in supplier selection considering the increasing complexity of the environment and time pressure. Thus, the vagueness and subjectivity is kept and well manipulated based on the flexible rough number in the proposed methodology. The proposed methodology can manipulate the vagueness and subjectivity in the supplier selection without any prior information (e.g., pre-set membership function).

The proposed model is applied in selecting sustainable suppliers in SSCM. Very few studies take into account the sustainable issues in the supplier selection problem, thus the characteristic of the proposed method is distinct. The necessary information, such as the critical elements affecting sustainable supplier selection and the interactions among the criteria, can help companies and suppliers discern the potential areas for further improvement. Companies can focus on supplier development with the proposed method and help their suppliers improve sustainability in supply chain operations.

Even though the proposed methodology has some strengths in developing sustainable supplier selection criteria, there is still space to improve in the future. The outcome of the supplier selection model based on the integrated importance-influence analysis method is determined by managers in a solar air-conditioner manufacturer. It is beneficial to increase the number of involved companies in different industry to build a more generalized sustainable supplier selection model. In addition, application of other decision support methods (e.g., ANP, TOPSIS, and ELECTRE) will facilitate to extend the application with regard to the sustainable supplier selection. The proposed approach might be also applied to other SSCM problems in future research, such as sustainable supplier development and SSCM practice improvement.

8.1.3 Weighting methods

Criteria weighting was considered in most MCDM models because it directly influences the decision-making result. The criteria weighting methods in published papers have been listed and explained. Some researchers specified weights directly, while the majority of researchers thought that mathematical weighting methods were necessary. Compared with the latter, the former seems to be more applicable when the criteria number is small and their weights are easier to distinguish. Pairwise comparison method in the AHP has gained a very high degree of popularity due to its understandability in theory, simplicity in application and robustness of its outcomes. Some researchers have effectively improved traditional AHP by combining it with other techniques to address the shortcomings of AHP from the perspective of improving the reliability of expert opinions.

Single weighting technique is more common than integrated approach, while more and more researchers have begun to use hybrid methods to make up for the shortcomings of single method. Fuzzy theory is an important one of them. It has been widely used in combination with other weighting methods to deal with the imprecision and vagueness in human judgments and information. It is foreseeable the AHP method will still be the first choice for many researchers in the future because of its popularity and applicability. However, no single method can rank at best or worst because every method has its own strength and weakness depending upon its application in all the consequence and objectives of planning. Hybrid techniques are thereby developing to tackle such situations among more researches.

5 Discussion and conclusion

The aggregative risk degrees of “high-risk” grade, “medium-risk” grade and “low-risk” grade are always the-smaller-the-better whereas that of “no-risk” grade is always the-larger-the-better. According to the aggregative risk degrees, the no-risk and low-risk probability were 35% and 27.9%, respectively. According to the aggregative risk degrees, University A is in the risk grade “Low”. The results of this study are consistent with many studies. World Wide Web is ceaselessly penetrating all aspects of daily life and is thus guiding society to move forward. On the other hand, education system and schools have to adapt themselves However, education systems and schools must adapt to rapid social changes as they nurture manpower in the new era. Apparently, campus digitization is not only the latest trend in university education, but also a lofty ideal for campus information infrastructure. Taiwan has progressively constructed information infrastructure in all campuses and has thereby accumulated vast technical experience. This study attempted to assess the risks associated with campus digitization and to discuss the system structure and elements of campus information infrastructure together with RFID integration and applications in order to facilitate teachings. The RFID digital campus system implementation has several efficacies. (1) It simplifies the daily management of schools and greatly improves management efficiency. (2) It improves school infrastructure and appearance, and it interests students in science and technology. (3) It facilitates schools in achieving high quality and in realizing intelligent campus life.

In this work, risk management was defined as risk identification, risk analysis, response planning, monitoring and action planning tasks needed for interactive organization of people, resources, policies and procedures in order to minimize potential damage and losses. The proposed approach is based on the reciprocal additive consistent fuzzy preference relations rather than on conventional multiplicative preference relations. Specifically, this method considers only n − 1 judgments whereas traditional AHP considers n(n-1)2 judgments in a preference matrix with n elements. Clearly, the proposed approach can be executed faster and more efficiently compared to conventional pairwise comparison methods. In addition to helping organizations identify critical risk factors, the approach also provides decision makers with useful information about risk grade. The analysis results demonstrate that the six most important risk factors are Electronic wallet system management risk; Campus property system management risk; Library system management risk; Access system management risk; Attendance system management risk, Identity system risk. The analysis in this study also confirmed the applicability and feasibility of reciprocal additive consistent fuzzy preference relations for solving complex, hierarchical, multiple-attribute risk measurement problems.

The approach provides the key risk factors that administrators should consider before implementing a campus RFID system.

It provides educational officers and university administrators with improved understanding of risk factors for managing RFID digital campus systems.

It provides universities with an aggregative risk measure that can be used to identify critical risk factors affecting university management and to establish a risk management and campus control system.

It assists educational officers in facilitating and accelerating the decision-making process needed to implement the system and to improve campus competitiveness.

It confirms the applicability and feasibility of fuzzy preference relations for solving complex hierarchical multi-criteria aggregative risk measurement problems.

It contributes to the literature on measuring aggregative risk in school management.

It provides universities with an aggregative risk measurement mechanism that they can use to identify the critical risk factors affecting RFID digital campus system management and to establish a risk management and control system.

It proves the applicability and feasibility of fuzzy preference relation for solving complex hierarchical multi-criteria aggregative risk measuring problems.