ANETA BECKER
West Pomeranian University of Technology in Szczecin
Summary
In the article there has been characterised the application of information and communication technologies in Polish enterprises in 2008. With the use of ELECTRE TRI multi-criteria decision making method there have been classified Polish voivodeships in terms of application of ICT technology in enterprises. On the knowledge basis of relations of S outranking between objects and profiles, there has been assigned decision variants to categories according to the following procedures: optimistic and pessimistic.
Keywords: multi-criteria decision making methods, outranking relation, classification, information and communication technology
1. Introduction
During the past decade Information and Communication Technologies (ICTs) have become available, i.e. accessible and affordable, for the general public. IT, telecommunication, television and other media of electronic information transfer are more and more commonly used in process of products and services exchange in countries representing the high level of economic development [3]. However, a gap remains between users and non-users or between “haves” and “have nots”. There are several reasons for this “digital divide”: from missing infrastructure or access, to missing incentives to use ICTs, to a lack of computer literacy or skills necessary to take part in the Information Society [1].
A classic theory of decision making assumes that a decision maker has got defined preferences and that there is a priori utility function which allows defining a complete ordering over a set of analyzed variants. The solution of a decision problem relies on defining an analytical form of the utility function and next there is defined a variant for which the function adopts a maximum value. [Trzaskalik 2006, p. 43-44] Such an approach, which is based on the multi attribute utility theory, was criticised by researches focused on European (French) school of decision making whose precursor is believed to be professor Bernard Roy. Researchers conducted by scholars of this school led in last three decades to the study of a new decision making methodology and construction of a sequence of multi criteria methods (e.g. a group of ELECTRE method) which has wide application in various decision making problems. [Roy 1991, Roy and Bouyssou 1993]
B. Roy distinguishes three types of multi-criteria decision making issues in which the ELECTRE method can be applied:
• choice – choice of the best (distinguishing variants) what means A’ subset of A set from a point of view of F criteria set,
• ordering (ranking) – putting in order all variants of A set from the best one to the worst one, from a point of view of F criteria set,
• classification (sorting) – division of variants set into classes (categories), classification between them in terms of preferences.[Merad, Verder, Roy and Kouniali 2004, p.167; Trzaskalik 2006, s. 43]
One of the mentioned categories of decision making problems is the term of classification. According to a classic approach, the classification is a systematic division of objects (events) into: classes, sections, subsections, which is conducted according to a defined principle. [Encyklopedia 1974] The classification in a multi theory sense is a complete division of a particular set into a defined number of disjoint subsets. A subject of classification includes observation sets – objects usually defined by many features both measurable (quantitative) as well as non-measurable (qualitative). Such a division is conducted on the basis of probability relations and received subsets are called abstraction classes, probability classes or homogeneity classes.[Ostasiewicz 1998, p. 86]
Amongst a rich collection of multi criteria methods, the method which was specially designed to solve classification problems is called ELECTRE TRI and it is an example of a method based on the outranking relation.
The aim of the article is classification of Polish voivodeships in terms of application of information and communication technologies in enterprises in 2008. In classification researches there was used multi criteria decision making method ELECTRE TRI. It is necessary to add that the term of information and communication technologies is called information and communication techniques or information techniques. The Central Statistical Office refers to the family of technologies which process, gather and send information in an electronic form [GUS 2008, p.7]. 2. ELECTRE TRI classification method
The family of ELECTRA methods is based on S outranking relations and binary relations which say that a variant exceeds variant b when after taking into consideration available information connected with decision maker’s preferences, there are significant premises to claim that a variant is at least as good as variant b and that there are no important reasons to reject this statement. Roy 1991; La Gauffre, Haidar and Poinard 2007, p. 479; Roy and SłowiĔski 2008, p.185; Figueira, Salvatore and Roy 2009, p. 481]
In classification issues, in which ELECTRE TRI method was dedicated, the outranking relation is used to estimate a level of decision for variant a (objects) over profiles which separate classes from each other. [Doumpos, Zopounidis 2002, p. 568] The assignment of objects to classes is conducted according to two procedures: optimistic and pessimistic. Both procedures conduct classification on the basis of S outranking relations knowledge for every ordered pair (a,bk) where a (a1,a2,...,an) is a decision variant and b is a profile. k
The optimistic procedure relies on the comparison between variant a and in turn with bk
profiles (k=1,2,...,p−1,p), starting from the lowest profile ( 1
b ). If b is the first profile such as k
Pa
bk (b is widely preferred than a) then a is assigned to k C class. On the other hand, in the k
from the highest profile (b ). If p b is the first met profile such as k aSb then a is assigned to k Ck+1 class. La Gauffre, Haidar and Poinard 2007, p. 488; Doumpos, Zopounidis 2002, p. 571]
Input data in ELECTRE TRI method are criteria weights and thresholds: indifference, preference and veto. There should be also given a number of classes and defined their borders what means profiles separation. Every decision variant is described in terms of its values of criteria (variables). The initial functioning of calculation procedure, before the final object assignment to particular classes, is based on conducting a sequence of tests (compatibility and incompatibility). A detailed description of any indices that are used in constructing the whole classification procedures includes among others works of the following authors: Dias and Mousseau [2003]; La Gauffre, Haidar and Poinard [2007].
Checking the statement that aSb (or k bkSa) requires fulfilling two conditions. First, the
compatibility of outranking relations aSb (or k bkSa). Most criteria should support the thesis. The
overall concordance index ( , )∈[0,1]
k
b a
c is calculated with the use of partial concordance indices )
, ( k j ab
c and a set of criteria weights w which are defined by a decision maker. On the other j
hand, the construction of partial compatibility factors cj(a,bk) includes thresholds: indifference
j
q and preference p . The second condition which should be fulfilled is weak incompatibility or j
its lack. During the verification of this requirement none of criteria should be too strongly against the statement that aSb (or k bkSa). In calculation of discordance indices dj(a,bk)∈[0,1] there are
used thresholds: preference p and veto j v . j
Established indices c(a,bk) and dj(a,bk) can be encapsulated in one parameter
] 1 , 0 [ ) , ( ∈ k b a
σ that is called a credibility index and which reflects a level of statement reliability
that aSb (suitably k bkSa). The statement referring to aSb outranking is regarded as important if h
the reliability rate is σ( , )≥λ k
b
a where λ is a cut off point that was defined earlier and it adopts
values from the range [0,5;1].
The comparison of σ and λreveals the occurrence of four situations which take place
between decision variants and profiles which separate classes and namely they are: • k k k k k b a aSb bSa aIb b a, )≥ , ( , )≥ )( , ) ( (σ λσ λ ; a is indifferent with k b , • k k k k k b a aSb b Sa a b b a, )≥ , ( , )< )( ,¬ ) ( (σ λσ λ ; a is preferred to k b , • ab b a aSb bSa b a k k k k k)< , ( , )≥ )(¬ , ) , ( (σ λσ λ : k b is preferred to a , • k k k k k b a aSb bSa aRb b a, )< , ( , )< )(¬ ,¬ ) ( (σ λσ λ : a is incomparable to k b .
On the basis of knowledge of S outranking relations for every ordered pair (a,bk) there take places the assignment of variants to categories according to mentioned procedures: optimistic and pessimistic.
3. The characteristic of empirical material
In 2008 the Central Statistical Office conducted researches of ICT application in enterprises on a representative sample of 14 117 objects where the number of employees was equal at least to 10 workers and the run economic activity was classified according to the Polish Classification of Activities into the following sections: D (processing industry), F (construction), G (trade and repairs), H (hotels and restaurants), I (transport, storing and communication), K (real estate’s services, information technology, science), O (film, radio and television). [GUS 2008] The material was used to classify Polish voivodeships in terms of information and communication technology usage in enterprises.
Information obtained by the Central Statistical Office shows that in 95% of enterprises ,which took part in the research, computers are used at least once a week by 36% of their workers. Computers with access to the Internet were used by 93% of enterprises and by 28% of workers. 58% of enterprises were equipped with LAN computer network and every fifth enterprise had got wireless LAN. In 2008 every second examined enterprise used ERP systems (Enterprise Resource Planning – information technology system for planning enterprise resources). On the other hand, CRM software (Customer Relationship Management) that was used for collecting, connecting, processing and analysing information about clients and which may have an operational or analytical character, in the first approach was used by 19% of enterprises and in the second by 12% of economic entities. Almost every fifth enterprise used free software and almost 60% had broadband Internet. Issuing electronic invoice became popular (e-invoices). Among examined enterprises, 10% received electronic invoices and 5% issued them. According to the Central Statistical Office enterprises take advantage of using information technologies in such activity areas as: reorganization and dissemination of routine activities (20%), releasing resources (11%), increasing profits (10%), development of new products and services (10%).
The list of potential variable that were qualified to classification researches included several dozen features. According to the statement, that is an initial condition for acknowledgment various values to be diagnostic features, is their sufficient high variability Dziechciarz 2003, p. 30], From the initially defined set there were eliminated variables which were regarded as weakly diversified (variables without important information). There was adopted a critical value v* = 0,1. Next there was used numerical method of Z. Hellwig [Nowak 1990, p. 29] that is used in classification and collecting diagnostic features. The use of Hellewig’s method allowed revealing the following eight element set of variables (criteria) which includes a percentage of enterprises which:
• X1 – used the Internet to spread information connected with general policy and strategies of enterprise,
• X2 – had got application connected with human resources issues,
• X3 – had got own website that enables placing orders according to own specification, • X4 – had got own website that enables making on-line payments,
• X5 – had got own website that enables personalisation of website contents for regular users, • X6 – used automatic exchange of data with external entities in order to receive orders from
receivers,
• X7 – used automatic exchange of data with external entities in order to send or receive information about products,
Distinguished variables (criteria) were a base for fundamental researches on classifying Polish voivodeships in terms of enterprises engagement in information and communication technologies. 4. Researches results
In classification researches of Polish voivodeships in terms of ICT usage in enterprises there was used ELECTRE TRI 2.0a computer program. As the division of results there was taken classification into 3 concentrations. The numeration of groups was connected with the hierarchy of class importance what means concentration the first classified voivodeship in which the usage of information and communication technology was on the lowest level, the second – average voivodeships but the third class was represented by object of the highest level of the analyzed phenomenon. Because of the amount of classes (k=3), for the analysed decision problem, there were defined two profiles which defined class borders. For every of these profiles there were given threshold values: indiscernibility, preference and veto at every criterion. There were also assumed the following values of weights for particular criteria: w1=4, w2=2, w3=5, w4=7, w5=6, w6=6, w7=5,
w8=7. The lowest weight was assigned to the second criterion because of the application universality of human resources information system in enterprises. However, criteria which were highly technologically engaged in e-business were assigned the highest values. It was acknowledged that outranking is reliable when the reliability factor ı exceeds the cut off point
λ=0,75.
The assignment of a particular object to classes was obtained as a result of application of two procedures types: optimistic and pessimistic. The list of received concentration is included in table 1.
Table 1. Classification results according to ELECTRE TRI method
class 1 class 2 class 3 class 1 class 2 class 3
dolnoĞląskie kujawsko-pomorskie dolnoĞląskie kujawsko-pomorskie mazowieckie
lubelskie łódzkie lubelskie podkarpackie
lubuskie małopolskie lubuskie podlaskie
opolskie mazowieckie łódzkie pomorskie
podlaskie podkarpackie małopolskie Ğląskie
pomorskie zachodnipomorskie opolskie ĞwiĊtokrzyskie
Ğląskie warmiĔsko-mazurskie zachodnipomorskie
ĞwiĊtokrzyskie wielkopolskie
warmiĔsko-mazurskie wielkopolskie
Optimistic procedure Pessimistic procedure
Source: self-study
While analysing results received after optimistic procedure application, voivodeships were divided into two classes. However, most objects were assigned to the second group (average) but in the third group (the best one) there were six voivodeships. On the other hand, analyzing results received after pessimistic approach application, that is more strict approach, it can be noticed that a set of objects has been divided into three classes.
Fig. 1. Classification of Polish voivodeships in terms of ICT application in enterprises –
optimistic approach (source: self-study)
Fig. 2. Classification of Polish voivodeships in terms of ICT application in enterprises – pessimistic approach (source: self-study) Most voivodeships were assigned to the weakest group, what means the first one, seven objects were assigned to the second class, however, in the third class there was only one voivodeship. Comparing results received after application of two different procedures of objects assignment to groups, it can be claimed that a structure of particular procedure classes is definitely different. Optimistic approach proposed classification of voivodeship only to two better classes at the same time omitting the lowest one. However, the pessimistic approach put most objects in the first class what includes two voivodeships: Łódzkie and Małopolskie which according to the previous attitude were assigned to the third concentration. Both in the pessimistic and optimistic approach there are objects which can be called stable what means objects which definitely belong to their groups regardless of used method. Among them there are such voivodeships as: Mazowieckie (class 3), Podlaskie, Pomorskie, ĝląskie, ĝwiĊtokrzyskie (class2). A graphic presentation of results received with the use of ELECTRE TRI method is presented by figures 1 and 2.
5. Conclusions
Conducted researches were concentrated on the application of multi criteria method of decision making ELECTRE TRI in voivodeships classification in terms of the level of information and communication technologies application in enterprises.
ELECTRE TRI method is used for dividing a set of decision variants into subsets (classes) but there is assumed that classes are comparable in the sense of preferences what means that it is possible to compare any two classes and states that one class is better than the second one or vice versa. The application of ELECTRE TRI method requires from an analyst great knowledge about the examined decision problem. It is connected amongst others with: defining profiles that separate classes, assigning weights to criteria and establishing thresholds. This knowledge has influence on
DOLNOĝLĄSKIE ĝW IĉTOKRZY- SKIE WARMINSKO- POMORSKIE POMORSKIE ZACHODNIO- POMORSKIE MAZURSKIE ĝLĄSKIE OPOLSKIE MAŁOPOLSKIE PODKARPACKIE LUBELSKIE LUBUSKIE PODLASKIE MAZOWIECKIE ŁÓDZKIE WIELKOPOLSKIE KUJAWSKO- Group: first (8) second (7) third (1) DOLNOĝLĄSKIE ĝW IĉTOKRZY- SKIE WARMINSKO- POMORSKIE POMORSKIE ZACHODNIO- POMORSKIE MAZURSKIE ĝLĄSKIE OPOLSKIE MAŁOPOLSKIE PODKARPACKIE LUBELSKIE LUBUSKIE PODLASKIE MAZOWIECKIE ŁÓDZKIE WIELKOPOLSKIE KUJAWSKO- Group: first (0) second (10) third (6)
forming final classification results. ELECTRE TRI method may be used for a cognitive aims as a tool for examination a complex evaluation of social and economic reality that includes difficult analytical problems.
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Aneta Becker
West Pomeranian University of Technology in Szczecin 31, Janickiego st., 71-270 Szczecin, Poland
