In today’s economy and society, performance analyses in the services industries attract more and more attention. The
traditional data envelopment analysis (DEA) approach requires a consistent operating environment. However, in reality,
there is a need to evaluate the units belonging to different environment. This reality challenges the traditional methods of
applying DEA theory to real-world cases where benchmarking across region can be a very important undertaking. This
paper introduces the fuzzy logic into DEA formulation to deal with the environmental variables so that the performance
of bank branches from different regions can be assessed. The inner-province and inter-province comparison are given based
on the fuzzy DEA results. These results are also compared with the results from traditional DEA analysis.
The banking industry is of great importance to every one of us. With the availability of new technology and
the Internet, more and more organizations are entering some aspect of the banking business and this results in
intense competition in the financial services markets. Major domestic banks continue to pursue all the opportunities available to enhance their competitiveness. Consequently, performance analysis in the banking industry has become part of their management practices. Top bank management wants to identify and eliminate the
underlying causes of inefficiencies, thus helping their firms to gain competitive advantage, or, at least, meet the
challenges from others.
Traditionally, banks have focused on various profitability measures to evaluate their performance. Usually
multiple ratios are selected to focus on the different aspects of the operations. However, ratio analysis provides relatively insignificant amount of information when considering the effects of economies of scale, the
identification of benchmarking policies, and the estimation of overall performance measures of firms. Asalternatives to traditional bank management tools, frontier efficiency analyses allow management to objectively
identify best practices in complex operational environments. Five different approaches, namely, data envelopment analysis (DEA) as[1–4] etc., free disposal hull (FDH) as in [5,6], stochastic frontier approach (SFA), also
called econometric frontier approach (EFA) as in [7–9], thick frontier approach (TFA) as in [10–12], and distribution free approach (DFA) as in [13–15], have been reported in the literature as methods to evaluate bank
efficiency. These approaches primarily differ in how much restriction is imposed on the specification of the best
practice frontier and the assumption on random error and inefficiency. Compared to other approaches, DEA is
a better way to organize and analyze data since it allows efficiency to change over time and requires no prior
assumption on the specification of the best practice frontier. Thus, DEA is a leading approach for the performance analysis in banking industry in literature. However, the traditional DEA analysis requires a consistent
infrastructure and operating environment in which the entities, appropriately called decision making units
(DMUs), operate. In reality there is a need to compare DMUs where some units may have a different environment which the others cannot adopt; hence, the comparisons are not always fair. This reality challenges the traditional methods of applying DEA theory to real-world cases. Banker and Morey [16] introduced categorical
inputs and outputs and their development rests on the assumption that there is a natural nesting or hierarchy of
categories. The same authors [17] had also dealt with the relative technical and scale efficiencies of decision
making units when some of the inputs or outputs are exogenously fixed and beyond the discretionary control
of the DMU managers. Cooper et al. [18] introduced a method to do the cross-system comparison. They make
use of mixed integer LP (linear programming) problem with binary variables to evaluate DMUs in different
systems. The proposed mixed integer LP is solved by an algorithm where the units of one subsystem are evaluated relative to frontier based on the other subsystem. This is related to the super-efficiency proposed by
Andersen and Petersen [19]. Similar to the hurdle of super-efficiency DEA, the infeasible problem often occurs
when using BCC model to do cross-system comparison. As a result, the treatment offered by Cooper et al.’s
cannot be applied if we need to estimate the production frontier using a variable returns to scale (VRS) technology and separate the scale effect from productivity changes [20]. Furthermore, Lozano-Vivas et al. [21]
incorporate the environmental variables directly into the ‘‘basic’’ DEA model since adding variables to the
DEA model raises the efficiency scores. Their method of adding each environmental factor guarantees that only
the efficiency scores of DMUs with bad environmental conditions can change. This approach has a pre-requisite: they must know in advance the type of influence of each environmental variable on the efficiency scores. In
other words, each uncontrolled factor must have an influence of know orientation.
This paper introduces the fuzzy logic into DEA formulation to deal with the environmental variables so
that the performance of bank branches from different regions can be assessed. This approach can deal with
both quantitative and qualitative or linguistic environmental variables. In our formulation the environmental
variables serve as linking measures across different subsystems so that cross-region comparison can be done.
To deal with evaluation among different systems, our methodology provides an alternative to build BCC
model, which is a hurdle of Cooper et al. [18]. Our proposed fuzzy models are based upon the formulations
of Lertworasirikul et al. [22]. However, it differs from theirs by incorporating both crisp and fuzzy variables in
the models. Our fuzzy CCR model shows the powerful discriminating power, which is the main concern in
Lertworasirikul et al. [22].
The rest of the paper is organized as follows. Section 2 presents the fuzzy data envelopment analysis (DEA)
as well as the conceptual models. Section 3 gives the fuzzy DEA results and further discussion. Finally, our
conclusions and future work are presented in Section 4.
The main objective of this paper is to apply the fuzzy DEA models to deal with the environmental variables
so that the cross-region comparison is possible. In our formulation the environmental variables serve as linking measures across different subsystems in order to perform a cross-region comparison. To deal with evaluation among different systems, our methodology provides an alternative to build BCC model, which is a
hurdle of previous work by Cooper et al. [18]. Although our proposed fuzzy models are built upon the formulations of Lertworasirikul et al. [22], it differs by incorporating both crisp and fuzzy variables in the models.
Our fuzzy CCR model shows the powerful discriminating power, the main concern in [22]. Further consideration could be done by incorporating DEA and data mining techniques
