The new approach of determination of weight factors in the process of

certification a city as the favourable business environment

1Dragan Randjelovic*

The University of Criminalistic and Police Studies, Cara Dusana 196,11080 Belgrade Serbia;

2Jelena Stankovic

University of Nis, Faculty of Economics, Trg kralja Aleksandra Ujedinitelja 11,18000 Nis Serbia;

3Milan Randjelovic

City of Ni, Local Economic Development Office, 7 jula 2, 18000 Nis, Serbia;

4Milos Randjelovic

HELP Nis, 18000 Nis, Serbia;

Abstract

One of the key problems in the application of multi-criteria analysis methods is to determine the importance

of the criteria in the model. The relevance and validity of decisions are directly conditioned by the relevance

of a given set of criteria for evaluating alternatives, as well as the correctly determination of weights of these

criteria. This is the reason why there are a number of methodologies developed with the aim of calculating

the importance of each of the criteria for the given problem. All methodologies are classified into two main

groups: subjective and objectively. This paper presents a new procedure of integration by two recognized

methods for determining weight of factors - Analytic Hierarchy Process (AHP) method, as a subjective

method and entropy as an objective method. The procedure of the application is shown on the real,

contemporary local economic problem in Serbia - the process of cities and municipalities certification on the

favourable business environment.

Keywords

Determination of Weight Criteria, Friendly Bussines Certification, Multi-criteria decision making

* Author to whom all correspondence should be addressed: email dragan.randjelovic@kpa.edu.rs, Phone +381648925012,

Fax +381113162152

mailto:dragan.randjelovic@kpa.edu.rs

1. Introduction

The modern problem of the Serbian economy is, above all, much expressed uneven economic

development. This problem itself is not rare, as it is not realistic to expect that the development of

all municipalities in the country is completely equal, but it is important to take measures to reduce

the gap between highly developed and underdeveloped communities. One way involves the

initiative to create a friendly business environment in municipalities. This can be achieved by

identifying and then presenting the comparative advantages of individual cities and municipalities.

This task can be realized through the certification of cities and municipalities with a favourable

business environment and this is a practice that is carried out in Serbia last few years.

Program of certification cities and municipalities in Serbia was introduced in 2007 by the National

Alliance for Local Economic Development - NALED. NALED is an independent association of

companies, local governments and NGOs working together to create a favourable business

environment in Serbia. Since its establishment (2006) to date, NALED has been joined over 140

members and 20 institutional partners. Currently, the certification program encompasses 48 cities

and municipalities in Serbia. Immediate support NALED obtained by the U.S. Agency for

International Development (United States Agency for International Development - USAID).

Certification Program is supported by all relevant state institutions, including the Ministry of

Economy and Regional Development, Ministry of Human and Minority Rights, Public

Administration and Local Government, the Executive Council and the National Agency for

Regional Development. Direct, immediate effects of the certification process are reflected in the

growth of investments, and indirect in the decrease of unemployment and increase of living

standards.

The authors intend to determine the significance criteria identified as the most relevant for

certification, on the basis of data that have been reached in the certification process, provided by

local governments and NALED. One way to determine the importance of the criteria is based on the

use of subjective assessments and the preference of authorities responsible for conducting

certification. However, the significance of criteria may be defined objective approach as well, based

on the application of quantitative methods. By the application of mathematical and statistical

methods in determining the importance of the criteria, it has increased the reliability of

conclusions. The idea is to perform the integration of these two approaches and determine weights

that include the subjective perception of the decision makers about the importance of the observed

criterion, but also objectively quantified the importance of meeting the criteria for achieving the

greatest possible amount of investments in the city or municipality.

2. Material and methods

The problem of relative weight determination has existed since the formulation of the first multi-

criteria analysis methods. During that period several approaches have been proposed to determine

weights, (Hwang & Yoon, 1981) and (Saaty,1980). Most of them can be classified, depending on

the information provided for their calculation, in two mayor groups: subjective and objective

approaches. Subjective approaches determine weights that reflect subjective judgment, while

objective approaches determine weights by making use of mathematical models, and they do not

consider subjective judgment (Liu,2003).

The most popular subjective approaches are the Analytic Hierarchy Process (Saaty, 1977), least

squares comparison (Chu, Kalaba & Spingarn, 1979) , Delphi method (Hwang & Lin,1987), etc.

The objective approaches include methods such are LINMAP - Linear Programming Techniques for

Multidimensional Analysis of Privileged (Srinivasan, Shocker, 1973), various computer-aided

mathematical models (Srinivasan & Shocker,1973), Data Envelopment Analysis (Charnes, Cooper

& Rhodes,1978), the entropy method (Hwang & Yoon, 1981), principal component analysis and

multi-attribute programming methods (Fan, Ma & Tian, 1999), etc.

Two proposed methods for integration in order to determine relative weights in multi-criteria

models, chosen by authors are AHP method and entropy. There are many different applications of

those methods, as well as many different manners of their aggregation. The application in supply

chain management is proposed by Bindu, R. S. and B. B. Ahuja and it deals with multiple attribute

nature of vendor selection problem to which AHP method is applied using verbal assessments for

relative measurements. The technique used for assigning weights is the entropy method (Bindu &

Ahuja, 2010). Research conducted by Hamidi, Naser , Pouya Majd Pezeshki and Abolfazl

Moradian in aim to determine important criteria which have effects on selecting the best brands in

beverage industries evaluate the weight of each criterion for selecting the best brand in the

beverage market (Hamidi, Pezeshki & Moradian, 2010). Then the major criteria weights are

analysed using the AHP method and entropy. Finally, weights are then determined using the

compromised weighting method. Fuzzy AHP method is proposed to determine the rank in logistic

centre location scheme evaluation by Chen, Yan and Lili Qu, (Chen & Qu, 2006). In order to

include the domain expertise in the decision process and improve evaluation performance, it is

developed a fuzzy MCDM (multi-criteria decision making) model to modify the fuzzy AHP

weights based on the entropy technique, by making use of the decision matrix information through

Delphi method. Ma, Jian, Zhi-Ping Fan and Li-Hua Huang proposed an integrated approach to

determine attribute weights in the multiple attribute decision making problems (Ma,Fan &

Huang,1999). The approach makes use of the subjective information provided by a decision maker

and the objective information to form a two-objective programming model. Thus the resulting

attribute weights and rankings of alternatives reflect both the subjective considerations of a decision

maker and the objective information. An example is used to illustrate the applicability of the

proposed approach. Xuan Zhou, Fengming Zhang, Xiaobin Hui and Kewu Li proposed an expert

evaluation of information in group decision making by determining experts' weights based on the

new aggregation method of cluster analysis and entropy (Zhou, Zhang,Hui & Li,2011).

Inspired by the above research results, the authors have conducted research in order to create an

algorithm for the integration of results obtained using the AHP method and entropy. The

significance of this research is the possibility of its concrete application to solve the current

problems in the field of local economic development, such as improving the methodology which is

applied in the business friendly certification process of municipalities in Serbia.

3. Case - study

Information basis for the analysis are the data provided by NALED about six cities that fulfilled

criteria for certification on a favourable business environment and have the status of the sample in

this study. According to the NALED criteria for evaluating the business environment of

municipalities in Serbia are the following:

C1: Strategic planning of local economic development in partnership with businesses

C2: Special department in charge of local economic development (LED), FDI promotion and

business support - existence of LED Office

C3: Business council for economic issues advisory body with the mayor and local

governments

C4: Efficient and transparent system for acquiring construction permits

C5: Economic data and information relevant for starting and developing a business

C6: Multilingual marketing materials and website

C7: Balanced structure of budget revenues / debt management

C8: Investing in the development of the local workforce

C9: Cooperation and joint projects with local business on fostering LED

C10: Adequate infrastructure and reliable communal services

C11: Transparent policies on local taxes and incentives for doing business

C12: Electronic communication and on-line services

To set up an appropriate model is necessary to specify the characteristics of municipalities in the

certification process. For receiving the title "business friendly", it is necessary that municipality

meets above 75% of the criteria. However, a significant lack of understanding of such methodology

is that these 75% is the average fulfillment percentage of all presented twelve criteria, which means

that one or two criteria can even be unfulfilled, even when the average score of all criteria is above

75%. Thus, the importance of the criteria is not included in the process of determining the level of

compliance criteria and that is the basic drawback of this process. Hence, it arises the idea that by

using subjective and objective methods can be determined the appropriate weights for the business

friendly certification model. The level fulfillment of criteria of municipalities in the sample is given

in Table 1.

Table 1. Level of fulfillment for all criteria in sample

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 Average

Criterion

Type max max max max Max max max max max max max max max

1

Municipality

1 0.800 1.059 1.000 0.732 0.875 1.000 1.000 0.733 0.636 0.829 1.000 1.250 0.910

2

Municipality

2 1.000 0.824 0.750 1.000 0.925 1.000 1.000 0.933 1.000 0.878 1.000 1.000 0.943

3

Municipality

3 0.625 0.947 0.800 0.941 0.857 1.182 0.900 0.750 0.667 0.940 0.929 1.100 0.887

4

Municipality

4 0.900 0.824 0.875 1.000 0.950 1.000 1.000 0.700 0.682 0.756 1.000 0.750 0.870

5

Municipality

5 1.000 0.618 1.000 0.780 0.600 0.667 1.000 0.600 0.591 0.976 0.833 1.250 0.826

6

Municipality

6 1.000 1.059 0.750 0.939 0.900 0.944 1.000 0.867 0.909 0.793 1.000 1.250 0.951

Average level of

fulfillment per

criterion

0.888 0.889 0.863 0.899 0.851 0.966 0.983 0.764 0.748 0.862 0.960 1.100 0.898

Regardless the fact that of the importance of the criteria is not taken into account, NALED gave

their preference on the importance of each criteria through evaluation of sub-criteria by which these

criteria are defined. Specifically, each of the criteria has a certain number of sub-criteria (some as

many as 18 sub-criteria). These sub-criteria are divided according to the importance to three groups:

eliminating sub-criteria, very influential sub-criteria and important sub-criteria. Thereby,

eliminating sub-criteria are the most significant factors because their fulfillment is the first

condition in the evaluation of the business environment by the verification commission. Therefore,

the rate of this group of sub-criteria is 2, the rate of very influential sub-criteria group is 1, and the

rate of the group of important criteria is 0.5. Presence of eliminating, very influential and important

criteria is the basis of determining the weights of each of the twelve relevant criteria in the model.

The evaluation of importance, which is goven in Table 2, is nothing else but the average rating of

importance of sub-criteria which is defined significance criteria.

Table 2. Importance of criteria according to NALED

Criterion C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12

Criterion

rate 1.250 1.050 0.950 0.900 0.660 1.000 0.800 1.100 1.250 0.850 0.750 1.150

This methodology for determining the significance of the relevant criteria in the model was the

starting point for authors research. In order to apply a scientific approach based on determination

of subjective and objective weights, as well as formulation of new integrated approach that the

authors are presented in this paper, it is necessary to define some assumptions. The assumptions for

determining the weight problem described as follows:

Assumption 1: Subjective preferences of the decision maker about the importance of the criteria

expressed through weights determined by subjective methods are approximately equal to the

value of weights obtained by objective approach, if the decision maker preference is based on

absolutely correct and rational perception of the problem.

Assumption 2: Ratio between objective and subjective weights may be considered as a relevant

coefficient in the integration of these approaches in order to determine the weights that contain

both these components.

In order to determine the weights that include subjective and objective components, it is necessary

to implement the following methodological procedures:

quantify the subjective preferences using adequate scale;

determine the weights on the basis of subjective preferences using the AHP method;

analyse the importance of the particular criterion fulfillment in the observed municipality of

objective and quantitative technique such as entropy;

determine the weights based on objective indicators provided by entropy results;

propose a procedure for the integration of certain subjective and objective weights.

3.1. AHP-Subjective approach for weight determination

Analytic Hierarchy Process (AHP) belongs to the group of subjective methods and is one of the

most popular method of multi-criteria analysis and a tool for decision making on the selection of

optimal alternative(s), especially in cases where there is a possibility of a hierarchical structuring of

relevant criteria. AHP method is the kind of quantitative technique that can incorporate in the model

both qualitative and quantitative criteria, (Saaty, 1977) and (Saaty,2001).

Multi-criteria decision making problems are those where it is implied that a decision maker

supposed to identify the optimal course of action, considering a set of conflict criteria. Complexity

in decision making situations involves quantitative and qualitative criteria, different measurement

scales, and multiple comparisons. The ability to assign a preference rank for general decision

making situations is needed as well as simplicity of methods (Saaty,1986). The AHP is a suitable

method that provides a logical and scientific basis for such multi-criteria decision making problems

and has been widely applied to both individual and group decision making scenarios from the early

1980s, (Wind & Saaty,1980) and (Saaty,& Vargas,1994). AHP is a quantitative tool that has been

used in almost all problems related to multi-criteria decision making and its application includes

about 150 different kinds of problems (Vaidya & Kumar,2006). AHP method is a method for

formulating and analysing decisions that can successfully be used to measure the influence of many

factors relevant to the possible outcomes of decisions as well as for forecasting i.e. the performance

of relative probability distribution of outcomes.

According to Saaty (Saaty,1986), the AHP was founded on three design principles: (i)

decomposition of the goal-value structure where a hierarchy of criteria, sub-criteria, and alternatives

is developed, with the number of levels determined by the problem characteristics; (ii) comparative

judgments of the criteria on single pairwise comparisons of such criteria with respect to an upper

criteria; and (iii) linear-based synthesis of priorities where alternatives are evaluated in pairs with

respect to the criteria on the next level of the hierarchy, and criteria can be given a priority (e.g.

preference) expressed as a weight in the AHP matrix.

Let the problem is defined as a general problem of multi-criteria analysis, where it is necessary to

evaluate m of available alternatives, on the basis on n relevant criteria.

On the stage of decomposition, the problem is viewed as a hierarchical structure, where the goal is

on the top, while the criteria by which a decision is made are treated at the lower levels. At the

lowest hierarchical level is a range of alternatives, which comparisons are necessary to make.

The next phase involves, in addition to collecting data and its peer evaluation. There is, first of all,

makes pairwise comparison of criteria and alternatives at a given level of hierarchy, but also in

relation to the criteria of the directly higher level. Pairwise comparison of alternatives is done in

response to the question of which of the two observed attributes that characterize an alternative to

the given criteria, is better in terms of meeting the criteria and contribution to the certain objective.

Strength of preference is expressed by the ratio scale with increments of 1-9. The preferred level of

1 shows equality of observed attributes, while the level of 9 indicates absolute, the strongest

preference of one attribute over another (Ma, & Zhang,1991) and (Leskinen, 2000). Such a scale

was formed by Saaty (Saaty, 1977) and it is used in essentially the AHP method and for its entire

later advanced variant (revised AHP or ANP).

Thus, defined scale allows comparisons in a limited scope, while the perception is a sensitive

enough to make a difference in the alternatives importance. Based on pairwise comparison of

alternatives, the reciprocal matrix can be formed (dimension nn on the criteria level, or mm on

the alternatives level), where the elements aii = 1, while the elements aji are the reciprocal of the

elements aij, i.e. aji = 1/ aij, i j and i, j = 1, 2, ..., n.

Figure 1. Hierarchical structure of business friendly certification model

Assuming that the observed decision problem is the one which can be defined by the previously

described matrix form, these phases can be concretized as follows. In the first phase, the problem is

viewed as a hierarchy, where are on the top the goal of the observed problem, and the aim of the

problem is to determine the weights of criteria in the model. At the lower level are the criteria,

which comparison should be made based on the expressed preferences of the decision-maker. The

structure of the problem is given in Figure1. Following phase is the determination of reciprocal

matrix. Reciprocal matrix, on the level of criteria, of the business friendly certification model is

given in Table 3, according to the preferences provided by NALED.

Table 3. Reciprocal matrix for business friendly certification model

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12

C1 1 3 4 4 8 3 6 2 1 5 6 2

C2 1/3 1 2 3 6 1 4 1 1/3 3 4 1/2

C3 1/4 1/2 1 1 5 1 3 1/2 1/4 2 4 1/3

C4 1/4 1/3 1 1 4 1/2 2 1/3 1/4 1 3 1/4

C5 1/8 1/6 1/5 1/4 1 1/5 1/3 1/6 1/8 1/4 1/2 1/7

C6 1/3 1 1 2 5 1 3 1/2 1/3 3 4 1/2

C7 1/6 1/4 1/3 1/2 3 1/3 1 1/4 1/5 1 2 1/5

C8 1/2 1 2 3 6 2 4 1 1/2 4 5 1

C9 1 3 4 4 8 3 5 2 1 5 6 2

C10 1/5 1/3 1/2 1 4 1/3 1 1/4 0.2 1 2 1/4

C11 1/6 1/4 1/4 1/3 2 1/4 1/2 1/5 1/6 1/2 1 1/5

C12 1/2 2 3 4 7 2 5 1 1/2 4 5 1

Using the procedure of the AHP method, it determines priority vector for the criteria in the model.

The results are presented in Table 4.

Table 4. Criteria importance of business friendly certification model

Criteria Priority Vector

C1 0.191572435

C2 0.091015872

C3 0.060865513

C4 0.046027224

C5 0.015076309

C6 0.074900384

C7 0.030610045

C8 0.112190751

C9 0.189180090

C10 0.036087104

C11 0.022203512

C12 0.130270761

3.2. Shannons entropy objective approach for weight determination

Let us assume, following (Sanchez, & Soyer,1998), that Cj = (a1j, a2j,,amj ) denotes a priority

vector according to a certain criterion, after arithmetic normalization (so that the vector's co-

ordinates sum up to 1).

Entropy for this vector may be defined as:

1

( ) ln(a ), i=1,mn

j ij ij

j

H a

(1)

In information theory the entropy H (wj) can be defined as a measure of uncertainty of a discrete

random variable X, which can take a value from the finite set (x1, x2, ., xn) such that probability

that X is going to be equal to xj is wj and can be denoted as P (X =xj) = wj.

In the multi-criteria context, entropy can be used as well for determination of priority of alternative,

and then the priority pi (Uden & Kwiesielewicz, 2003), calculated according to analogous

procedure given for weights wj, can be interpreted as the probability that the i th alternative will be

preferred by the decision-maker.

One of the most important properties of entropy is that:

H(X ) 0 (2)

The entropy of a discrete distribution with finite support has always nonnegative value. It can be

equal to zero when all elements of the sum in equation (1) are equal to zero, simultaneously. Such a

case is possible only when one value of a discrete random variable has the probability equal to one

and all the other values have probabilities equal to zero. Described situation is the one that there is

no uncertainty about which value random variable will take, because probability equal to one means

certain event.

Entropy achieves the maximum value of the uniform distribution given by following equation:

H(1/ n,,1/ n) = ln n (3)

This characteristic of entropy is consistent with the definition of entropy as a measure of

uncertainty, i.e. the maximum is reached when all values of random variable X have equal

probability.

Based on previously described procedure authors of this paper are determined weights of criteria,

and this resulta are presented in Table 5.

Table 5. Relative importance of criteria determined by objective approach

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12

Entropy Results 0.139 0.127 0.063 0.038 0.011 0.101 0.038 0.076 0.139 0.038 0.025 0.101

Weights Based on

Entropy 0.155 0.142 0.070 0.042 0.012 0.113 0.042 0.085 0.155 0.042 0.028 0.113

4. Results and discussion

Integration procedure for weights determination in which are included AHP and entropy method

involves the following steps:

1. determine the ratio ratio between the objective and subjective weights determined using the

following formula:

, 0 2 and : 2, 2

obj

j

j jsub

j

(4)

If the subjective perception of decision maker is perfectly rational, or if an objective approach to

determining the importance of criteria to the greatest extent respects the personal opinion of the

decision maker, then the value of a ratio is equal to 1, or weights obtained by the these two

approaches are equivalent.

2. determine of an integrated solution that includes a subjective preference of the decision maker

but also an objective set of model parameters through the formula:

int

(2 )

2

sub obj

j j j

j

(5)

3. normalization of the integrated solution by formula:

int

int

1

j

j n

j

j

(6)

One block scheme for the described algorithm can be given in the for which authors are presented

in Figure 2.

Figure 2. Proposed algorithm's scheme

Based on the results obtained by subjective and objective approach presented in Table 6, and

according to Step 1 of proposed integration algorithm, values of ratio are given in Table 7.

Table 6. Weights determined by subjective and objective approach

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12

Subjective

Weights

( )

0.192 0.091 0.061 0.046 0.015 0.075 0.031 0.112 0.189 0.036 0.022 0.130

Objective

Weights

( )

0.155 0.142 0.070 0.042 0.012 0.113 0.042 0.085 0.155 0.042 0.028 0.113

Table 7.

Values of ratio

1 2 3 4 5 6 7 8 9 10 11 12

0.8098 1.5573 1.1552 0.9214 0.8143 1.5050 1.3855 0.7560 0.8200 1.1752 1.2566 0.8653

Results according to Step 2 and Step 3 are presented in Table 8.

Table 8. Weights determined by new integrated approach

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12

Results of

Integration

0.339

8

0.204

5

0.129

7

0.088

2

0.026

8

0.168

5

0.068

5

0.190

3

0.338

2

0.077

4

0.048

6

0.240

6

Integrated

Weights

( )

0.176

9

0.106

4

0.067

5

0.045

9

0.014

0

0.087

7

0.035

6

0.099

1

0.176

0

0.040

3

0.025

3

0.125

3

5. Conclusions

The basis of research starts from the need to determine the relative importance of criteria in the

problems of multi-criteria decision analysis. Namely, for making timely and correct decisions, it is

crucial to determine the weights of the criteria relevant for the given problem. For this purpose has

been developed a range of methodologies for determining the weight coefficients, which represent

support for the formation of multiple criteria analysis model that realistically represents the

relationship between the criteria in the model.

All these methodologies can be classified into two main groups - the subjective and objective. Both

approaches have their advantages and disadvantages, but what is most important is that only the

integration of both approaches can get weights that take into account both components and

therefore, the resulting weights can be considered more realistic.

This paper presents the new algorithm for the integration of subjective and objective approach to

determining the weights.

Also, the algorithm is applied in solving real, contemporary problem of the Serbian economy.

Current engagement of authors is focused on the implementation of this procedure in a model that

includes all certified municipalities in Serbia, not only the sample as shown in this paper.

Acknowledgement

This work was supported by the Ministry of Education, Science and Technological Development of

Republic of Serbia, Project No III44007. As well, authors would like to thank to the National

Alliance for Local Economic Development, Republic of Serbia for provided assistance and

information necessary for this research.

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