A novel way of transforming the scales

1. 242 Int. J. Society Systems Science, Vol. 9, No. 3, 2017
Copyright © 2017 Inderscience Enterprises Ltd.
Scale transformation of analytical hierarchy process
to Likert weighted measurement method: an analysis
on environmental consciousness and brand equity
Siddharth Misra* and Rajeev Kumar Panda
School of Management,
National Institute of Technology, Rourkela,
Odisha, India
Email: sid.misra1983@gmail.com
Email: panda.rajeevkumar@gmail.com
*Corresponding author
Abstract: The interdisciplinary research has found relevance in every field of
data analysis, interpretation and decision making applications. The choice of
important variables along with the criteria gives rise to the immense reliance of
the researchers on quantitative data. The flexibility of choosing between scales
for decision making, give rise to a new era of translation of scales. It also aids
the researcher to reduce their efforts put in the data collection process. It needs
more expertise to select the appropriate tool and scales for measuring the
variables and their impact. For this purpose this piece of work is an attempt to
convert Saaty’s 9 point scale used for analytical hierarchy process (AHP) to a
generalised Likert scale for ranking. Analytical hierarchy process (AHP) is an
appropriate multicriteria decision making model, which suits the prioritising of
variables for decision making process. But AHP is a much complex technique
and involves the high computational ability. This research article attempts to
reduce the computational ability, and adopts a novel model known as a Likert
weight measurement method (LWMM), this lightweight model is widely
accepted. In psychometric feedback LWMM is universally established scaling
technique and in this case has been used to prioritise environmental conscious
attributes and activities for improving brand equity.
Keywords: Likert weight measurement model; LWMM; exploratory data
analysis; analytical hierarchy process; AHP; environmental consciousness;
brand equity; BE.
Reference to this paper should be made as follows: Misra, S. and Panda, R.K.
(2017) ‘Scale transformation of analytical hierarchy process to Likert weighted
measurement method: an analysis on environmental consciousness and brand
equity’, Int. J. Society Systems Science, Vol. 9, No. 3, pp.242–255.
Biographical notes: Siddharth Misra is a PhD student and Teaching Assistant
in the School of Management at the National Institute of Technology,
Rourkela. His research interests focus on the study of environmental
consciousness, brand equity and modern tools. He has served in two major
projects in the field of finance and human resource management and currently
working on his PhD research in marketing. He has earned a fellowship from
ICSSR, Delhi for one year and has published two papers.

2. Scale transformation of AHP to LWMM 243
Rajeev Kumar Panda is an Assistant Professor of Marketing in School of
Management, National Institute of Technology, Rourkela and heads two
innovation and entrepreneurship centred sponsored projects in the Institute
Innovation and Entrepreneurship Development Centre and Support for
Entrepreneurial and Managerial Development of SMEs through incubators. He
has co-authored this paper and is the research supervisor of Mr. Siddharth
Misra. His perception of the environment for innovation at NITR stems from
his experience as part of the above project. At the institute of national
importance focused on science and technology, which is going through rapid
waves of both entrepreneurship and technological innovation, he plays a pivotal
role in bridging the gaps between both.
1 Introduction
Exploration is often explained in terms of searching latent information in a dataset.
Exploratory data analysis (Tukey, 1962; Gutiérrez, et al., 2011) includes many techniques
like box plot (McGill et al., 1978), histogram (Pearson, 1895), multidimensional scaling
(Borg and Groenen, 2005), analytical hierarchy process (AHP) (Saaty, 1980) and many
more. From among the different techniques, AHP can alternatively be addressed as data
mining (Agrawal et al., 1993), and detective learning (Tukey, 1977), in modern days. The
technique of exploration of potentially useful information and discovery of the novelty of
a large amount of data is the essence of modern research. The interdisciplinary research
has found application in every field of data analysis, interpretation and decision making
applications (Sudha and Baboo, 2011). In past years, the major findings are adopted in
AHP. The technique has found its application in various domains, e.g., marketing
(Sivakumar et al., 2015), banking (Ishizaka and Nguyen, 2013; Ahmad et al., 2011),
investment (Kiliç and Kaya, 2015; Chen and Lee, 2010) and resource allocation (Ho,
2008). The objective behind adopting techniques is to make the existing business
profitability, offer higher quality services and quicker decision making easier than even
before. This also helps in reducing human efforts and cut cost. With these sorts of desires
and requirements, exploratory data analysis turns into a major innovation, empowering
business to a more precise anticipation of opportunities and threats produced by their
resources.
The choice of decision alternatives for appropriate decision making has become a key
to success for all brands. The choice regarding the resource allocation towards the
different environment attributes and activities of a brand has become critical procedure
which needs more aptitude to rank and choose the best possible alternative for near
perfect decision (Siringi, 2012). The innovation intricacy of prioritisation and choice
making skills has expanded for better decisions. In a dynamic scenario where the
markets’ needs and wants are changing (Rajan and Xavier, 2016), the brands need to look
into their environmental claims frequently and work towards the efficient allocation of
resources for better brand equity (BE). For any brand the expense that is made on the
environmental resources (Wheeler et al., 2013) is essential to choose from the alternatives
after prioritising the criteria. The pursuit of the best choice is a constant procedure for
brands keeping in mind the end goal to redesign the assortment of item range according
to the environmental needs of customers. There might be other alternatives for

3. 244 S. Misra and R.K. Panda
environmental consciousness for any item, but in this matter ranking the best activities
and attributes is more vital.
The various aspects to select an environmental attribute and activity might be first,
considering the number of environmental attributes and activities and the relationships
between them and choose the best environmental attribute and activity among the various
existing alternatives. Environmental attributes and activities choice decisions are
complicated because of various conditions ought to be regarded as in making a decision.
Customer needs and demands have grown to be a major issue in business management,
particularly in branding and environmental technique (Motwani and Youssef, 1999). The
main purpose of environmental attribute and activity choice process is to optimise risk,
value to the customers, develop proximity and analyse the impact of environmental
consciousness, which is effective in attaining BE (Li and Fun, 1997). In addition, the
frequent use of environmentally friendly products and BE centric principles by a variety
of brands, the environmental attribute and the activity choice question is now extremely
relevant (Petroni, 2000). Selecting the best method for decision making effectively brings
about the lessening of purchase risk and optimise the resource allocation, thereby
increasing the environmental consciousness and improved BE. Environmental attributes
and activity choice can be performed by a multi criteria decision science process and
these are influenced by many contradictory factors (Hu, 2009). Thus, the decision makers
ought to assess the swap between the different criteria. Multi criteria decision making
supports the decision makers in examining and select a single option out of a collection
of alternatives (Amid and Ghodsypour, 2006). Choosing appropriate environmental
attribute and activity has become a major issue in establishing BE.
2 Research background
According to the literature we can find different choice methods for ranking the
environmental attribute and activity. The linear weighting model proposed by the authors
is rated on several criteria for prioritising and choosing environmental attribute and
activities. This leads to a categorical model where the ratings are converted into a single
score. This model is not only easiest and quickest but is quite economical which makes it
simple and easy to adopt. But recent events and the need for subjectivity have forced the
model to become imprecise (Petroni, 2000).
The performance evaluation of the environmental attribute and activity on BE can
easily be done by fuzzy logic (Chen et al., 2006). Decision makers were supported by this
approach to allocate resources to each environmental attribute and activity. In the same
line another robust method allows the decision makers to prioritise alternatives when
multi criteria complex problem decisions are involved. This method is called as the AHP,
which includes hierarchical arrangements of variables and their prioritisation (Lin and
Lee, 2009).
AHP is quite easy to understand and use. This technique has the beauty to incorporate
both quantitative and qualitative data. It is seen that AHP is the most commonly used
methods for decision making and has been easily adopted for selection of alternatives in
prioritising environmental attribute and activity for BE. When in a model hierarchy is
incorporated and criteria are present AHP becomes the most favoured methods of
decision making. Saaty (1980) has proposed this model of AHP. The theoretical validity
and empirical effectiveness have often been discussed in the world forum. In this method

4. Scale transformation of AHP to LWMM 245
complicated problems were first structured in the form of hierarchical decision by the
decision makers. There are three levels of hierarchy involved in this method the lowest
being the alternative, middle being the criteria and the top level is the goal. This method
has its own limitation one being the complexity, so its implementation gets difficult. A
second limitation is that if two or more decision makers are working on it, then a
difference in opinion due to the varied weights can make the matter more cumbersome
(Hawley et al., 2012). AHP is more subjective to expertise based on knowledge,
experience and judgements of the decision maker (Brungardt, 2011; Sarabando and Dias,
2012). It also lacks the assessment of uncertainties and risks involved in the selection of
environmental attribute and activity’s performances (Yusuff and Poh Yee, 2001).
Additionally, it requires the high computational ability to prioritise and rank the
variables.
Recently, brands have resorted to applications based on business intelligence to
gather more information regarding the impact of environmental consciousness on BE.
The business intelligence includes information regarding an array of decisions made on
environmental attributes and activities from the recent history of environmental
consciousness. In order to meet the requirements of data mining, mitigating the
complexity of computational ability of AHP and increase the reusability of data collected
from the AHP scale, a real need for transformation of scale becomes indispensable. This
transformation not only helps in making computational ability easier, but also
incorporates psychometric method. Therefore, we adopted a novel method of solution
called Likert weight measurement method (LWMM), where the weights of different
values are given to attributes of different significance (Guo et al., 2010). This process is a
part of LWMM and is known as weighted association rule mining (WARM).
3 Allied portions
Liu and Hai (2005) considered the choice of alternatives by integrating collaborative BE
and used Saaty’s (1980) Analytical hierarchy method to come up with a novel approach.
In this technique the weighted summation of the rating of votes and the chosen votes are
compared. This method is known as voting AHP (VAHP). It enables the decision makers
to use simpler methods as compared to AHP without losing the hierarchical property of
prioritising performance of environmental attributes and activities by assigning weights
to it. The managers applied VAHP in generating superior purchasing alternatives and
analysed systematically the relevant criteria with respect to the inbuilt trade–offs
(Pencina et al., 2011). This method finds its scope in performance assessment, business
strategy and policy making in the recent decades to come (Liu and Hai, 2005). AHP
method was also used by Yahya and Kingsman (1999) to prioritise and selecting the best
option available for vendor selection. This leads to a clue that this method can become an
important tool in choosing environmental attribute and activity for deciding business
allocation for strategising improvement of BE. A glaring example of the application of
this tool is the program sponsored by government for entrepreneurial development in a
country like Malaysia.
Tam and Tummala (2001) in their empirical research found the application of the
AHP method in a company called telecommunication system. This company was
dependent on multi criteria and multi person complex decision making process for its

5. 246 S. Misra and R.K. Panda
selection of vendors and has invested a huge amount of money on it. So the author
employed AHP to help the choice makers to test the impact of strength and weakness of
supplier systems by comparing the suitable alternatives and criteria. By implementing
AHP decision making becomes easier and faster. The data can be transferred to the excel
sheet for easy computation and analysis. Similarly, Yu and Jing (2004) worked upon a
novel judgment model to choose the most favourable decision solution on vendor and
environment related attributes based on unique brands. By using linear programming
(LP) and AHP it was found that the previous research of Tam and Tummala (2001)
proposes that the trust factor between customer and brand fetch best criteria for cost
reduction (Yu and Jing, 2004). The results concluded that trust is the important attribute
to be established in Tian Jin Electric Construction Company. So LP and AHP can be
adopted for considering the tangible and intangible factors leading to the environmental
attribute and activity choice, influencing of interpersonal and inter-firm trust (Pencina
et al., 2012). From the research we can derive that the quality criteria play a vital role
over quantity in influencing the environmental attribute and activity choice. The above is
tested against other criteria like loyalty, image and satisfaction, but focused trust has
succeeded over all other environmental attribute and activity choice methodology.
An efficient mining methodology was proposed by Wang et al. (2000) for weighted
association rule. This carried the philosophy that in a specific weight domain numerical
weights can be assigned to items for a meaningful judgement of ranks. For example, if
compared ratings for items are [9, 1] in the Saaty’s 9 point scale can be interpreted as
[5, 1] for 5 point Likert scale. This is a classic example of an accurate weighted
association rule. This signifies that if a customer rates a paired attribute like
environmental performance (EP) over environmental communication (EC) and gives nine
for the former and one to the later attribute than the same customer will prefer EP five
times as compared to EC if taken alone. WARM is done in two folds first by following a
certain algorithm which follows standard association rules for generating item sets rather
than weights. And then implements the same set during rule generation to achieve highest
weights. There is no change in the process of item set generation in WARM (Garrido et
al., 2013). Rather, it targets the generation of weighting factors after examining the
appropriate weighted association rules. So by doing this we are maintaining association
rule as an outcome of post processing of WARM method.
Granular concepts came into existence in the past decade where proposition was
made for the use of multilevel association rules along with conceptual hierarchy are
integrated together (Han and Fuin, 2002). This was a derivative work from the idea of
Liu (1999) and inspires to extend the work of the association rule mining model to derive
multi threshold supports. The threshold of the model is set to a maximum threshold of
five and a minimum of one and if 0 occurs, then it is set to minimum threshold of one
after the transformation from 9 to 5 and 1 to 0 and 1. This minimum item support (MIS)
rule appears as a key rule for the association. Here the customer can assign a changed
threshold of the item which is comparable to the normal allocation of weights of the item.
It is a method by which we can detect the rare item rules without generating unnecessary
rules. So it can be used for the best sorting purpose.
So, looking into the above criteria and essence of scales there is a necessity of
reusability of the data which was collected with much of hardship. And for contributing
to a new research by using the existing tools had encouraged the scale transformation
from AHP scale to Likert weight measurement method (LWMM).

6. Scale transformation of AHP to LWMM 247
4 Likert weight measurement method (LWMM)
The rating scale which is generally used in questionnaires and the broadly accepted scale
for the investigation is the Likert scale. This is from a psychometric scale where
respondents reply to specific statements by the level of their agreements. Psychologist,
Rensis Likert was the inventor of this scale and the scale is coined after his name. In this
the respondents are allowed to respond to statements depending upon the objectives and
subjective criteria according to their agreement levels. These statements along with
option of answers are called the Likert items (Chatterjee and Hadi, 2012). According to
the psychometric researchers five point scales is most favoured rating scale, but Likert 7
and 9 point scale are also preferred in some cases. But according to the recent empirical
research the mean attained by using 5 or 7 levels is relatively higher than the outcome of
the highest attainable score of 10 point scale and the stretch is statistically significant. It
is also seen that apart from the mean other characteristic like kurtosis, skewness and
spread across the mean are mostly unchanged. The typical format of a 5 point Likert is
measured by nominating numeric from 1 to 5 which is as follows (Table 1):
Table 1 Likert scale and corresponding responses
1 One: strongly disagree/highly dissatisfied
2 Two: disagree/dissatisfied
3 Three: neither agree nor disagree/neutral
4 Four: agree/satisfied
5 Five: strongly agree/highly satisfied
The rule to describe the implied relationships among the large number of transactions
between items is called the association rule. Given in our AHP example, we have three
levels of hierarchy. The goal, i.e., BE is the item space, in which the attributes like EP,
EC and environmental positioning (EPo) are the criteria and environmental activities like
eco literacy (EC), interpersonal influence (II) and value orientation are alternatives. The
criteria are the subset of goal and the responses can be collected in a set of 9 points as a
comparable response. Similarly, the sub criteria or the alternatives are the subset of
criteria. So, their responses are also taken in pairs in accordance with the criteria. The
responses are tabulated in the excel sheet according to their 9 point Saaty’s scale
response. This can be denoted as dataset D of transactions. Let A be a non-empty subset
of goal. The maximum of the itemset A in D is denoted as maxD(A). Then, a Likert 5
point itemset LikertD(A) is derived from the formula round (maxD(A)/9*5). The
association is created by Likert function which will return the absolute value of the
relation [A, max, round]. The LikertD(A) is larger than 0 and has to lie between 1 and 5.
If a user’s AHP response returns a zero after transformation, then it is set to the threshold
of one as in 5 point Likert scale since there is no provision for 0. It is assumed that if a
researcher gets a 0 while conversions, then the response means strong disagreement
which is scaled back to one. This association rules have been an active research topic
because of its uniqueness and ease of use (Agrawal and Srikant, 1994; Agrawal et al.,
1993).

7. 248 S. Misra and R.K. Panda
The different techniques adapted for acceptance of weight in mining have given rise
to new concepts. Association rule mining requires supports to establish relations. The
item scales are not considered as they appear, but are read in a transformed scale in the
WARM. This transformation needs a weighted support over traditional support for
counting purpose (Ploeg et al., 2014). The purpose behind using weighted support and
not using frequency alone is to prioritise the choice of the alternative in the order of their
significance in the dataset. If the minimum support threshold is below the weighted
support then the item set is considered as large and is significant for our observation. The
user specified threshold values are represented by the cost and the margin of significance.
The relative arbitrary allocation of support threshold makes the method more meaningful.
5 Theoretical framework
The theoretical framework about Likert weight measurement method (LWMM) has been
discussed in this piece of work. This is specifically designed using multi criteria decision
making process for environmental attribute and activity choice. The complex decisions
deal with structured technique of analytical hierarchy process (AHP). The evaluation of
alternative solutions, quantification of elements, representation and structuring a rational
and comprehensive framework is made easy by the use of AHP. The representation of the
sample scenario for environmental attribute and activity relationship is depicted in 33
records in the following Table 2. It contains three environmental attribute and three
activities along with the Saaty’s 9 point responses.
The Table 3 represents the transformed responses from Saaty’s scale to Likert
weighted measurement method scale (LWMM) using the Table 2. Table 2 incorporates
the 33 item sets and there are three criteria and nine alternatives has been considered with
a Saatys’ 9 points scale for each item set where nine is the most important response and
one being neutral and 2, 3, 4, 5, 6, 7 and 8 are relative importance level in an ascending
order from low to high. Table 3 contains the transformed scale where the 9 points of
Saaty are transformed to 5 point Likert weights. The algorithm converts the user’s
responses to the respective Likert equivalent by incorporating assumptions into it. In this
transformed scale five is the highest response and one is the lowest response traversing
through 2, 3 and 4. This transformation is done because in general calculation the AHP
feedback is not suitable for implementation and generalisation. Hence, the introduction of
the Likert weighted measurement method has become inevitable, after the transformation
Table 4 is introduced for the final rating and prioritising.
The frequencies of the respective weights are given by the notation Fq(1), Fq(2),
Fq(3), Fq(4) and Fq(5) and Σ LikertD(A) is the total sum of the responses for each
criteria. The calculation of the weight derived from frequency is known as Rating, which
is calculated as:
Rating = (Fq(1)*5+Fq(2)*4+Fq(3)*3+Fq(4)*2+Fq(5)*1)/ LikertD(A)∑
Table 4 shows the aggregate rating of each criterion and is computed by summing the
Likert scale responses for each criterion.

8. Scale transformation of AHP to LWMM 249
Table 2 Sample record contains AHP responses of environmental attribute and activities
Criteria(environmentalattribute)ELalternatives(environmentalactivities)
Respondents
EPECEPEPoECEPoELIIELVOIIVOELIIELVOIIVOELIIELVOIIVO
1818117711818711718711717
2417114711618156116161581
3435955655556655556463537
4785576877765877765768778
5618117811314811314611314
6717118611818611818711718
7715581717117717117181818
8645986959657959657867575
9555555111111111111111111
10161881716118716118171881
11817118611781611781811819
12171818817171817171818171
13919191818181818181919191
14718171918151918151918141
15676767656565656565656666

9. 250 S. Misra and R.K. Panda
Table 2 Sample record contains AHP responses of environmental attribute and activities
(continued)
Criteria(environmentalattribute)ELalternatives(environmentalactivities)Respondents
EPECEPEPoECEPoELIIELVOIIVOELIIELVOIIVOELIIELVOIIVO
16191818818151818151817171
17615114153141153141125151
18315116215113215113156121
19555555767676767676666676
20985555999999999999989898
21911781818181818181719181
22718181918151918151818151
23758665564766564766677677
24411412123112123112412131
25555555878878878878878878
26817181718161718161717161
27557655868667868667767969
28817121816171816171817171
29676767656565656565656666
30858555777676777676576788
31558655868767868767767969
32746557752166752166217758
33918191711551711551611771

10. Scale transformation of AHP to LWMM 251
Table 3 Transformed feedback for criteria
Saaty’s 9 point response maxD(A)
LikertD(A) =
round(maxD(A)/9*5)Respondents
EP EC EP EPo EC EPo EP EC EPo EP EC EPo
1 8 1 8 1 1 7 8 1 7 4 1 4
2 4 1 7 1 1 4 7 1 4 4 1 2
3 4 3 5 9 5 5 5 3 9 3 2 5
4 7 8 5 5 7 6 8 8 8 4 4 4
5 6 1 8 1 1 7 8 1 7 4 1 4
6 7 1 7 1 1 8 7 1 8 4 1 4
7 7 1 5 5 8 1 7 8 1 4 4 1
8 6 4 5 9 8 6 5 4 9 3 2 5
9 5 5 5 5 5 5 1 1 1 1 1 1
10 1 6 1 8 8 1 1 8 8 1 4 4
11 8 1 7 1 1 8 8 1 8 4 1 4
12 1 7 1 8 1 8 1 7 8 1 4 4
13 9 1 9 1 9 1 9 9 1 5 5 1
14 7 1 8 1 7 1 8 7 1 4 4 1
15 6 7 6 7 6 7 6 7 7 3 4 4
16 1 9 1 8 1 8 1 9 8 1 5 4
17 6 1 5 1 1 4 6 1 4 3 1 2
18 3 1 5 1 1 6 5 1 6 3 1 3
19 5 5 5 5 5 5 6 7 7 3 4 4
20 9 8 5 5 5 5 9 9 9 5 5 5
21 9 1 1 7 8 1 9 8 7 5 4 4
22 7 1 8 1 8 1 8 8 1 4 4 1
23 7 5 8 6 6 5 7 6 5 4 3 3
24 4 1 1 4 1 2 4 1 4 2 1 2
25 5 5 5 5 5 5 9 9 9 5 5 5
26 8 1 7 1 8 1 8 8 1 4 4 1
27 5 5 7 6 5 5 7 7 7 4 4 4
28 8 1 7 1 2 1 8 2 1 4 1 1
29 6 7 6 7 6 7 6 7 7 3 4 4
30 8 5 8 5 5 5 8 6 6 4 3 3
31 5 5 8 6 5 5 7 7 7 4 4 4
32 7 4 6 5 5 7 7 5 7 4 3 4
33 9 1 8 1 9 1 9 9 1 5 5 1

11. 252 S. Misra and R.K. Panda
Table 4 Shows the weight measurements, rating and the criteria ranking
Respondents LikertD(A) of EP LikertD(A) of EC LikertD(A) of EPo
1 4 1 4
2 4 1 2
3 3 2 5
4 4 4 4
5 4 1 4
6 4 1 4
7 4 4 1
8 3 2 5
9 1 1 1
10 1 4 4
11 4 1 4
12 1 4 4
13 5 5 1
14 4 4 1
15 3 4 4
16 1 5 4
17 3 1 2
18 3 1 3
19 3 4 4
20 5 5 5
21 5 4 4
22 4 4 1
23 4 3 3
24 2 1 2
25 5 5 5
26 4 4 1
27 4 4 4
28 4 1 1
29 3 4 4
30 4 3 3
31 4 4 4
32 4 3 4
33 5 5 1
Σ LikertD(A) 116 100 103
Fq(1) 4 10 8
Fq(2) 1 2 3
Fq(3) 7 3 3
Fq(4) 16 13 15
Fq(5) 5 5 4
Rating 0.7069 0.98 0.92233
Ranking 3 1 2

12. Scale transformation of AHP to LWMM 253
The choice of alternatives can also follow the same way as for criteria. The rating and
ranking of the environmental attribute and activity are done based on ratings, the criteria
which have higher weights or ratings will be selected first and then others will follow
descending. If there is a tie between the ratings, then the Likert scale may be varied from
5 points to another point scale and the same method can be used for breaking a tie and the
manager may utilise the previous history to make a decision. The pruning of invalidity
and inconsistency of data has made the computation easier as compared to AHP and
effective for decision making as it acts as an additional backbone of environmental
attribute and activity selection.
6 Conclusions
Environmental attributes and activities choice and evaluation of its effect on brand have
developed into one of the upcoming subjects in operations and brand supervision
narrative, particularly in sophisticated decision science. Our proposal of Likert weight
measurement method (LWMM) is a lightweight model for environmental attributes and
activity choice process and this requires a reduced amount of computational ability as
compared to AHP. This LWMM model is supported by weight association rule mining
model and is a key tool in exploratory data analysis. This lightweight model is not only
the easiest model for the choice of the environmental dimensions of BE, but also finds its
scope in various other fields of operation and is easy to implement and integrate.
References
Agrawal, R. and Srikant, R. (1994) ‘Fast algorithms for mining association rules in large
databases’, Proc. 20th Int. Conf. Very Large Data Bases, VLDB, Vol. 1215, pp.487–499.
Agrawal, R., Imielinski, R. and Swami, A. (1993) ‘Mining association rules between sets of items
in large data sets’, ACM Sigmod Record, Vol. 22, No. 2, pp.207–216.
Ahmad, K., Rustam, G. and Dent, M. (2011) ‘Brand preference in Islamic banking’, Journal of
Islamic Marketing, Vol. 2, No. 1, pp.74–82.
Amid, A. and Ghodsypour, S. (2006) ‘Fuzzy multi-objective linear model for environmental
attribute and activity choice a supply chain’, Production Economics, Vol. 104, No. 2,
pp.394–407.
Borg, I. and Groenen, P. (2005) Modern Multidimensional Scaling: Theory and Applications,
2nd ed., Springer-Verlag, New York.
Brungardt, C. (2011) ‘The intersection between soft skill development and leadership education’,
J. Leadership Educ., Vol. 10, No. 1, pp.1–22.
Chatterjee, S. and Hadi, A.S. (2012) Regression Analysis by Example, 5th ed., Wiley, New York.
Chen, S. and Lee, L. (2010) ‘Fuzzy multiple attributes group decision-making based on the interval
type-2TOPSIS method’, Expert System Application, Vol. 37, No. 4, pp.2790–2798.
Chen, T., Lin, C.T. and Huang, S.F. (2006) ‘A fuzzy approach for supplier evaluation and choice in
supply chain management’, International Journal of Production Economics, Vol. 102, No. 2,
pp.289–301.
Garrido, L.E., Abad, F.J. and Ponsoda, V. (2013) ‘A new look at Horn’s parallel analysis with
ordinal variables’, Psychol Methods, Vol. 18, No. 4, pp.454–474.
Guo, J., James, G., Levina, E., Michailidis, G. and Zhu, J. (2010) ‘Principal component analysis
with sparse fused loadings’, J. Comp Graph Stat., Vol. 19, No. 4, pp.930–946.

13. 254 S. Misra and R.K. Panda
Gutiérrez, E., Adenso-Díaz, B., Lozano, S. and Moreno, P. (2011) ‘An exploratory study of
Spanish households’ WEEE disposal behaviour’, Int. J. of Society Systems Science, Vol. 3,
No. 4, pp.385–398.
Han, J. and Fuin, Y. (2002) ‘Discovery of multiple-level association rules from large databases’,
VLDB, Vol. 95, pp.420–431.
Hawley, S.R. et al. (2012) ‘Generating social capital through public health leadership training: a
six-year assessment’, Health Educ. Res., Vol. 27, No. 4, pp.671–679.
Ho, W. (2008) ‘Integrated analytic hierarchy process and its applications – a literature review’,
European Journal of Operational Research, Vol. 186, No. 1, pp.211–228.
Hu, Y.C. (2009) ‘Fuzzy multiple-criteria decision making in the determination of critical criteria
for assessing service quality of travel websites’, Expert Systems with Application, Vol. 36,
No. 3, pp.6439–6445.
Ishizaka, A. and Nguyen, N.H. (2013) ‘Calibrated fuzzy AHP for current bank account selection’,
Expert Systems with Applications, Vol. 40, No. 9, pp.3775–3783.
Kiliç, M. and Kaya, İ. (2015) ‘Investment project evaluation by a decision making methodology
based on type-2 fuzzy sets’, Applied Soft. Computing, Vol. 27, No. 3, pp.399–410.
Li, C. and Fun, Y. (1997) ‘A new measure for environmental attribute and activity performance
evaluation’, IIE Transactions, Vol. 29, No. 1, pp.753–758.
Lin, L. and Lee, H.M. (2009) ‘Fuzzy assessment method on sampling survey analysis’, Expert
Systems with Applications, Vol. 36, No. 16, pp.5955–5961.
Liu, B., Hsu, W. and Ma, Y. (1999) ‘Mining association rules with multiple supports’, The 1999
International Conference on Knowledge Discovery and Data Mining, pp.337–341.
Liu, F. and Hai, H. (2005) ‘The voting analytic hierarchy process method for selecting supplier’,
Int. J. Prod. Econ., Vol. 97, No. 3, pp.308–317.
McGill, R., Tukey, J.W. and Larsen, W.A. (1978) ‘Variations of box plots’, The American
Statistician, Vol. 32, No. 1, pp.12–16.
Motwani, J. and Youssef, M. (1999) ‘Supplier selection in developing countries: a model
development’, Emerald, Vol. 10, No. 13, pp.154–162.
Pearson, K. (1895) ‘Contributions to the mathematical theory of evolution, II, skew variation in
homogeneous material’, Philosophical Transactions of the Royal Society A: Mathematical,
Physical and Engineering Sciences, Vol. 186, pp.343–414.
Pencina, M.J., D’Agostino, R.B. and Demler, O.V. (2012) ‘Novel metrics for evaluating
improvement in discrimination: net reclassification and integrated discrimination improvement
for normal variables and nested models’, Stat. Med., Vol. 32, No. 2, pp.101–113.
Pencina, M.J., D’Agostino, R.B. and Steyerberg, E.W. (2011) ‘Extensions of net reclassification
improvement calculations to measure usefulness of new biomarkers’, Stat. Med., Vol. 30,
No. 1, pp.11–21.
Petroni, A. (2000) ‘Vendor selection using principal component analysis’, The JSCM, Vol. 1,
No. 13, pp.63–69.
Ploeg, T.V.D., Austin, P.C. and Steyerberg, E.W. (2014) ‘Modern modelling techniques are data
hungry: a simulation study for predicting dichotomous endpoints’, BMC Medical Research
Methodology, December, Vol. 14, No. 1, p.137.
Rajan, C.R. and Xavier, M.J. (2016) ‘Dynamics of ecosystems – lessons from Indian case studies’,
Int. J. of Society Systems Science, Vol. 8, No. 3, pp.226–239.
Saaty, T.L. (1980) The Analytic Hierarchy Process, McGraw-Hill, NY.
Sarabando, P. and Dias, L.C. (2012) ‘Comparison of decision rules to mediate negotiations with
incomplete information’, Int. J. of Society Systems Science, Vol. 4, No. 4, pp.381–404.
Siringi, R. (2012) ‘Determinants of green consumer behaviour of post graduate teachers’, Journal
of Business and Management, Vol. 6, No. 3, pp.19–25.

14. Scale transformation of AHP to LWMM 255
Sivakumar, R., Kannan, D. and Murugesan, P. (2015) ‘Green vendor evaluation and selection using
AHP and Taguchi loss functions in production outsourcing in mining industry’, Resources
Policy, Vol. 46, No. 1, pp.64–75.
Sudha, N. and Baboo, S. (2011) ‘Evolution of new WARM using Likert weight measures (LWM)’,
IJCSNS International Journal of Computer Science and Network Security, Vol. 11, No. 5,
pp.70–75.
Tam, M. and Tummala, V. (2001) ‘An application of the AHP in vendor choiceof a
telecommunications system’, Omega, Vol. 29, No. 2, pp.171–182.
Tukey, J.W. (1962) ‘The future of data analysis’, The Annals of Mathematical Statistics, Vol. 33,
No. 1, pp.1–67.
Tukey, J.W. (1977) Exploratory Data Analysis, Reading, Addison-Wesley, MA.
Wang, W., Yang, J. and Yu, P. (2000) ‘Efficient mining of weighted association rule(WAR)’,
Proceedings of the ACM SIGKDD Conference on Knowledge Discovery and Data Mining,
pp.270–274.
Wheeler, M., Sharp, A. and Thiel, M.N. (2013) ‘The effect of ‘green’ messages on brand purchase
and brand rejection’, Australian Marketing Journal, March, Vol. 21, No. 2, pp.105–110.
Yahya, S. and Kingsman, B. (1999) ‘Vendor 208 a review of supplier selection methods in
manufacturing industries rating for an entrepreneur development programme: a case study
using the analytic hierarchy process method’, JORS, Vol. 50, No. 9, pp.916–930.
Yu, X. and Jing, S. (2004) ‘A decision model for supplier selection considering trust’, Chinese
Business Review, Vol. 3, No. 6, pp.15–20.
Yusuff, R. and Poh Yee, K. (2001) ‘A preliminary study on the potential use of the analytical
hierarchical process (AHP) to predict advanced manufacturing technology (AMT)
implementation’, Robotics and Computer Integrated Manufacturing, Vol. 17, No. 5,
pp.421–427.