Нечітка нейронна система для прийняття рішень у менеджменті
This paper introduces a systematic approach for intelligent decision support system design based on a class of neural fuzzy networks built upon a general neuron model. The neural fuzzy networks can formally represent and process both the qualitative (linguistic) and quantitative information, which u...
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| Дата: | 2019 |
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| Формат: | Стаття |
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The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute"
2019
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System research and information technologies| _version_ | 1867334386384371712 |
|---|---|
| author | Setlak, G. |
| author_facet | Setlak, G. |
| author_institution_txt_mv | [
{
"author": "G. Setlak",
"institution": null
}
] |
| author_sort | Setlak, G. |
| baseUrl_str | http://journal.iasa.kpi.ua/oai |
| collection | OJS |
| datestamp_date | 2019-08-07T15:26:01Z |
| description | This paper introduces a systematic approach for intelligent decision support system design based on a class of neural fuzzy networks built upon a general neuron model. The neural fuzzy networks can formally represent and process both the qualitative (linguistic) and quantitative information, which usually describe a complex, multidimensional systems or decision making processes. Presented the results of tests and a practical implementation of applications of fuzzy-neuro system for decision-making in strategic management and determination of product development strategy. |
| first_indexed | 2025-07-17T10:25:58Z |
| format | Article |
| fulltext |
© G. Setlak, 2003
72 ISSN 1681–6048 System Research & Information Technologies, 2003, № 1
УДК 683:519
FUZZY-NEURO SYSTEM FOR DECISION-MAKING IN
MANAGEMENT
GALINA SETLAK
This paper introduces a systematic approach for intelligent decision support system
design based on a class of neural fuzzy networks built upon a general neuron model.
The neural fuzzy networks can formally represent and process both the qualitative
(linguistic) and quantitative information, which usually describe a complex, multi-
dimensional systems or decision making processes. Presented the results of tests and
a practical implementation of applications of fuzzy-neuro system for decision-
making in strategic management and determination of product development strategy.
INTRODUCTION
Computer integrated manufacturing (CIM) provides manufacturing industry with the
means to produce a variety of products efficiently. Effective planning, scheduling and
control in the CIM environment depend largely on proper design of the decision sup-
port system (DSS). A manufacturing system is driven by input stimuli from the mar-
ket in the form of direct product demand, market conditions and feedback on
production with a variety of information perspectives. The activities of this system
may be broadly classified as management (including strategic planning), design, pro-
duction planning and production operation. Intelligent DSS have evolved as tools that
attempt to support decision-making processes in problem contexts characterized by
novelty and large search spaces. Problems with these characteristics are known as
unstructured problems. The managerial problem domain is composed of dynamic,
temporal relationships between variables. Solving many problems concerned with
modern manufacturing management is connected with processing of incomplete, in-
exact information. First of all, these problems are mainly aspects of strategic man-
agement: market analysis, choice of product strategy and of manufacturing system
development, choice of strategy for manufacturing arrangement, and others. To solve
such tasks it is necessary to apply unstructured procedures for decision making, which
use experimental data, skills and human intuition. To model and process fuzzy, lin-
guistic or so called qualitative information fuzzy sets theory and mathematical appa-
ratus of fuzzy logic are used [1, 2, 3, 4]. In such systems of decision making support,
the process of obtaining explanations and inference engine operation during process-
ing of fuzzy knowledge is highly complicated.
This paper aims at development of procedures and algorithms for application
of artificial intelligence tools to acquire and process various types of knowledge
(quantitative, qualitative, linguistic, fuzzy) and to solve selected unstructured
problems and tasks in decision support systems. The proposed environment inte-
grates techniques and methods of knowledge and decision process modeling such
as artificial neural networks and fuzzy logic-based reasoning methods.
In this paper possibilities are presented of an approach which combines
methods based on fuzzy logic and artificial neural networks, which results in crea-
Fuzzy-neuro system for decision-making in management
Системні дослідження та інформаційні технології, 2003, № 1 73
tion of a structure called a fuzzy neural network. The structure of a fuzzy neural
network combines the best properties of an artificial neural network, the ability to
learn from examples, and fuzzy logic, i.e. conversion of fuzzy knowledge. Com-
bination of these artificial intelligence technologies allows creation of compre-
hensive programming tools that can be used to solve complex decision problems
when incomplete, uncertain or contradictory knowledge has to be processed or it
is hard to formalize the knowledge. Fuzzy neural networks presented in this paper
are a generalization and expansion of classical neural networks. These networks
are able to process qualitative and linguistic information apart from quantitative
information through the application of the fuzzy set theory and mechanisms of
fuzzy decision making.
In this paper the results of the tests and a practical implementation of appli-
cations for decision support systems based on fuzzy neural networks used for stra-
tegic management and determination of product development strategy will be
presented.
CLASSICAL ARTIFICIAL NEURAL NETWORK
The original source of fuzzy neural networks is a multilayer perceptron, which is
a feedforward neural network characterized by transferring of information from
the input level through K additional hidden layers to the output layer. Fig.1 pre-
sents the structure of a two-layer perceptron, i.e. a perceptron with one additional
(hidden) layer. In the standard structure of a multilayer perceptron each i-th node
in k-th layer is connected through synaptic weights ijW with all the nodes of the
previous layer )1( −k .
Output signals are calculated as follows:
Fig. 1. Model of multilayer perceptron [2]
11W ′
iNW ′21
W ′
Y1 Y2 Yi Yn. . .
NnW ′
11W 12W inW
NnW
1Y ′ 2Y ′ iY ′ NY ′
1
X
2
X
n
X. . .
Output layer
Hidden layer
Input layer
G. Setlak
ISSN 1681–6048 System Research & Information Technologies, 2003, № 1 74
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−=′ ∑
=
N
j
jjiji xWfY
1
θ — for hidden layer neurons, (1)
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
′−′′= ∑
=
N
j
jjiji YWfY
1
θ — for output layer neurons, (2)
where ijW , ijW ′ — synaptic weights;
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
∑
=
N
j
jij xWf
1
— activation function;
jj θθ ′, — shift values; ),...,2,1( Njx j = — input signals.
In hidden perceptron layers transformation of nonlinear information takes
place. For processing of non-linearity in the hidden layers sigmoid function is of-
ten used, which can be described as follows:
αα
−+
=
e
f
1
1)( . (3)
In practice, the main Back-Propagation algorithm, as well as its different
modifications, is used for training neural networks of the multilayer perceptron
type [4, 5]. Details of the network training process will be presented in the further
part of this paper concerned with fuzzy neural networks, which is the object of the
research.
MODEL OF A FUZZY NEURAL NETWORK
Let us consider a system with n inputs: nxxx ,...,, 21 ( niXx ii ,...,2,1, =∈ )
and m outputs: myyy ,...,, 21 ( mjYy jj ,...,2,1, =∈ ), respectively, where =x
nn XXXxxx ×××∈= ...),...,,( 21
T
21 and jj Yy ∈ are linguistic variables. Quali-
tative information, which describes the behavior of this system, is presented as a
number of K fuzzy IF – THEN rules in the following form:
IF )is(andand)is(and)is( 1212111 nn AxAxAx ′′′ …
THEN )is(andand)is(and)is( 1212111 mm ByByBy ′′′ …
and … and
IF )is(andand)is(and)is( 2211 nknkk AxAxAx ′′′ …
THEN )is(andand)is(and)is( 2211 mkmkk ByByBy ′′′ … (4)
where jkik BA ′′ , , ( ni ,...,2,1= ), ( mj ,...,2,1= ) and ( Kk ,...,2,1= ) are certain
linguistic notions which describe appropriate system inputs and outputs. ikA′ and
jkB′ are fuzzy sets, where )( iik XRA ∈′ and )( jjk YRB ∈′ and )( iXR and )( jYR
mean clusters of all fuzzy sets which are determined on the sets iX and jY re-
spectively.
Fuzzy-neuro system for decision-making in management
Системні дослідження та інформаційні технології, 2003, № 1 75
Quantitative information that describes the behavior of the system may be
presented as a number of L sets with numerical data of the following type:
),...,,,,...,,( 2121 mlllnlll yyyxxx ′′′′′′ , where Ll ,...,2,1= , and )( iil Xx ∈′ , )( jjl Yy ∈
(yjl
’
∈ Yj ). Quantitative information may also be presented as a system of L
conditional rules in the following form:
IF )(andand)( 1111 nn xxxx ′=′= …
THEN Llyyyy nn ,...,2,1)(andand)( 1111 =′=′= … . (5)
The methodology of processing the above-presented information (i.e.
qualitative, quantitative, and mixed) is based on the application of a fuzzy neural
network. In accordance with the main idea the details of which are presented in
papers [1, 3], all types of the input information are as if «built into» the structure
of a fuzzy neural network during the process of network training. Another
important task is development of the inference engine, which will be able to
generate responses of the system to the types of input data determined above.
These problems according to the approach presented are solved in the
following way: the input information and the corresponding output information is
processed by means of two interfaces, which are developed on the basis of the
fuzzy sets theory and fuzzy logic. These interfaces have the same structure. Main
conception for processing of input and output fuzzy information may be presented
by executing of such operations in the following sequence (Fig. 2).
The task of the interfaces is transformation of the input information to the
form allowing for classical neural network processing. For performing this task,
let us determine the following notions from the theory of fuzzy logic and fuzzy
decision-making [4, 5].
Fuzzy input data
Fuzzy rule base
Output fuzzy sets
mm Yyy ∈′′ ,...,1
Algorithm
of correction
Interface for processing
of output data
Determination of
membership functions
Determination of
outputs for fuzzy set
Fuzzy inference engine
MULTILAYER
PERCEPTION
Fuzzyfication
Fig. 2. Conception of fuzzy neural system
G. Setlak
ISSN 1681–6048 System Research & Information Technologies, 2003, № 1 76
• Membership function is a function which assigns a degree of membership
(mostly, in the interval [0, 1]) to the fuzzy set: )(),( iAiA xx
iik ′µµ .
• Assuming that AAAAAAA nkkkn =′××′×′××′××′×′ ……… 2112111 and
BBBBBBB mkkkm =′××′×′××′××′×′ ……… 2112111 , the fuzzy rules (4) and (5)
can be interpreted by the product-operation rule of fuzzy implication:
)()(),( jAiAjiBA yxyx µµµ =→ . (6)
• Each fuzzy set )( ii xRA ∈′ can be described by means of primary fuzzy
sets included in the set χi, and also with the use of compatibility measure of two
fuzzy sets iA′ and ikA :
[ ]{ })(),(minsup),( iAiA
Xx
iki xxAA
iki
ii
µµπ ′=′
∈
, iak ,...,2,1= . (7)
• If the input data is quantitative ii Xx ∈′ , then they are described by the
membership function 1)( =′ ix x
i
µ , if ii xx ′= and 0)( =′ ix x
i
µ , if ii xx ′≠ (so
called fuzzy singleton). Subsequently, the compatibility measure is used:
[ ]{ } )()(),(minsup),( iAiAix
Xx
iki xxxAx
ikiki
ii
′=′=′
∈
µµµπ . (8)
Let us transform the output data in the same way too, by means of primary
fuzzy sets, the membership function, and fuzzy logic.
• Let j be the number of output jY and, respectively, fuzzy sets
)(0
jj YFC ∈ , which is determined by the composition «measure of activation»
( )ijk akv ,1}{ = and composition primary fuzzy sets in the following form:
{ …]),([min]),([minmax)( 21
0
21 jjBjjBjj vyvyyc
jj
µµµ =
} mjvy jkjB jk
,...,2,1,]),([min =µ… . (9)
NEURAL NETWORK TRAINING
A multilayer perceptron is subjected to the process of training, i.e. a classical neu-
ral network, which is a component of the fuzzy neural network model described
above.
For other research [2, 3, 5, 6], the Back Propagation algorithm and its
modifications are used for training of this neural network. As it has been known,
the above-presented algorithm for network training does not guarantee the
obtaining of global minimum for quality evaluation (for error). Nevertheless, in
research on solving a number of practical tasks, it is possible to obtain a very
Fuzzy-neuro system for decision-making in management
Системні дослідження та інформаційні технології, 2003, № 1 77
exact approximation of the training data, while the training process is taking
place, by execution of calculations for various parameter values (η , α and, what
is most important — the quantity of neurons in the hidden layer — 1N ), after
which the optimal variant is chosen. Consequently, a conclusion may be drawn
that for solving of a number of practical tasks, the obtaining of global minimum
for quality evaluation is not a necessary and indispensable condition of receiving
satisfactory results. To avoid the problem referred to above, in this paper research
on the use of genetic algorithms is carried out for solving the task of neural
network training, and also for determination of the optimal topological network
structure.
AN EXAMPLE OF A APPLICATION OF A INTELLIGENT DECISION
SUPPORT SYSTEM
The fuzzy neural network presented above has been used for development of an
intelligent decision support system. The decision support system has been applied
to select a product strategy in the area of household equipment.
In this paper, the selection method of market-assortment-strategy has been
applied for the choice of the product development strategy.
For development of the market-assortment-strategy basic notions of the Business
Portfolio Models have been applied. Business Portfolio Models are tools for
product classification used for determination of a competitive position of a busi-
ness on the market, and assessment of the market possibilities. In this paper one
of the most popular GE (General Electric) methods is applied, otherwise called
the GE’s Multifactor Portfolio Matrix. This approach has a variety of names, in-
cluding the nine-cell GE matrix, GE’s nine-cell business portfolio matrix, and the
market attractiveness-business strength matrix [8]. The basic approach is shown
in Fig. 3.
Each circle in this matrix
represents the entire
market and the shaded
portion represents the
organization’s business
market share. Each of
an organization’s busi-
nesses is plotted in the
matrix on two dimen-
sions, industry attrac-
tiveness and business
strength. Each of these
two major dimensions is
a composite measure of
a variety of factors. The
two dimensions make
good sense for strategy
formulation, because a
successful business is
Business Strength
High Medium Low
5 4 3 2 1
I I S
I S H
In
du
st
ry
A
ttr
ac
tiv
en
es
s
5
High
4
3
Medium
2
Low 1
S H
H
Fig. 3. GE Multifactor Portfolio Matrix [8]
G. Setlak
ISSN 1681–6048 System Research & Information Technologies, 2003, № 1 78
typically one that is an attractive industry and has a particular business strength
required for succeeding in it. To use this approach, an organization must deter-
mine what factors are most critical for defining industry attractiveness and busi-
ness strength. In this paper a list of the factors that are commonly used for placing
businesses on the aforesaid dimensions has been used, which is presented in [8].
Depending on where businesses are plotted on the matrix, three basic strategies
are formulated: I — invest/grow, S — Selective investment and H — Har-
vest/divest. The next step is to weigh each variable on the basis of its perceived
importance relative to the other factors (hence the total of the weights must be
1,0). Subsequently, a fuzzy-neural system must indicate, on a scale of 1 to 5, how
low or high the business scores on that factor. Table 1 presents this analysis for
one business.
T a b l e . Illustration of Industry Attractiveness and Business Strength Computa-
tions (source [8])
Industry
Attractiveness Weight Value Business strength Weight Value
Overall market
size 0,20 0,8 Market share 0,10 0,40
Annual market
growth rate 0,20 1,0 Share growth 0,15 0,60
Historical profit
margin 0,15 0,6 Product quality 0,15 0,60
Competitive
intensity 0,15 0,45 Brand reputation 0,10 0,50
Technological
requirements 0,15 0,45 Distribution net-
work 0,05 0,20
Inflationary
vulnerability 0,05 0,10 Promotional effec-
tiveness 0,05 0,25
Energy re-
quirements 0,05 0,15 Productive
capasity 0,05 0,15
Environmental
impact 0,05 0,05 Productive ef-
feciency 0,05 0,10
Must be
acceptable Unit costs 0,15 0,45 Social/political
/legal
1,00 3,60 Material supplies 0,05 0,25
R&D performance 0,10 0,40
Managerial personel 0,05 0,20
∑ 1,00 4,30
Performance of a fuzzy neural expert system has been tested on the
following input data:
• 22=N — number neurons in input layer; 68=L — rules.
• Fuzzyfication with 3 linguistic variables — 3=K has been applied to the
system (Fig. 3).
Fuzzy-neuro system for decision-making in management
Системні дослідження та інформаційні технології, 2003, № 1 79
• Number neurons in hidden layer: 10, 15, 25, 30, 35 (Fig.5).
• Number neurons in output layer: 3.
• The fuzzy set defined in )( iXR is characterized by a membership
function ]1,0[:)( →Ry jB jk
µ , and is labeled by a linguistic term ikA , such as
«high», «medium», «low» (industry attractiveness and business strength). The
membership function for the fuzzy set inputs, is shown in Fig. 4.
Fuzzy set conformity metrics (or activation levels in other words) are inputs
to the neural network, accord-
ing to (7)–(8) formulas. Next,
they are processed by the neu-
ral network and compared to
the required activation levels
for outputs. A fuzzy neural
network accepts both quantita-
tive and qualitative informa-
tion in the learning data set.
Qualitative information is rep-
resented by the fuzzy set appa-
ratus in the form of an
appropriate set of membership
functions for each linguistic
variable. In the case of the gen-
eration of quantitative output data, defuzzyfication is carried out with the use of
the center average method:
∑
∑
=
== m
j
B
m
j
B
j
y
yy
y
j
j
1
10
)(
)(
µ
µ
. (10)
During the system testing, mean absolute error was used as a criterion of
quality evaluation and the assessment of the system, which for the training data
assumes the form:
∑∑
=
−
=
=−=
P
p
M
l
p
l
p
l Ppvd
PM
Q
1
1
1
2 ,...,2,1,)(1 . (11)
Another such criterion of system assessment with respect both to the training
and testing data is the maximum system error
maxBQ , defined as follows:
p
l
p
l
ML
Pp
B vdQ −=
−=
=
1,...,1,0
,...,2,1
max
max
. (12)
The structure of the neural network, namely the number of additional layers
and quantity of neurons in an additional layer, has been chosen experimentally.
The structures with one, two and three additional layers have been evaluated. A
neural network with one additional layer and non-linear sigmoidal activation
Fig. 4. Membership function for the inputs fuzzy set
0 1 2 3 4 5
1
0,5
µ
3Bµ2Bµ
3Bµ
Y
G. Setlak
ISSN 1681–6048 System Research & Information Technologies, 2003, № 1 80
function returns as good results as does a network with two additional layers. A
neural network with more additional layers requires large amount of training data
in order to learn effectively. It is not necessary then to extend the network struc-
ture as it leads to increased quantity of data and learning time. That is why this
paper presents the results for the neural network with one additional layer and
with a layer with various quantities of neurons. All experiments have been run
with various quantity of neurons in the additional layer (N1). The results of simu-
lation researches are shown on Fig.5. This very important problem has been
widely discussed in the literature. The present research just confirm the opinion
that the neural network with one additional layer and with non-linear sigmoidal
activation function is able to approximate any function, practically, with required
accuracy.
The training data are prepared for a specific decision problem on the basis of
data received from an expert (strategic management division). The data form a set
of fuzzy rules for preparing a Multifactor Portfolio Matrix).
CONCLUSIONS
The paper uses fuzzy neural networks to model and process fuzzy, linguistic or
mixed knowledge. The developed programming modules provide user interfaces
that (based on fuzzy logic theories) allow conversion of the input information into
numeric form and subsequent processing by a classic neural network.
On the basis of the results it may be supposed that fuzzy neural networks are a
more universal theoretical instrument, which can be used for complex processes mod-
eling and for developing intelligent decision support systems, characterized by the
ability to process quantitative, as well as qualitative, and linguistic information, and
thus to solve unstructured tasks in a fuzzy environment. Fuzzy neural network models
show very good features for interpolation and extrapolation of training data used dur-
ing the training process. The research conducted proves that fuzzy neural networks
are a very effective and useful instrument of implementation of intelligent managerial
systems.
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Fig. 5. Results of training phase for fuzzy neural network
0 5 10 15 20 25 30 35
N1
Qmin
0,04
0,03
0,02
0,01
Fuzzy-neuro system for decision-making in management
Системні дослідження та інформаційні технології, 2003, № 1 81
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Received 28.11.2002
|
| id | journaliasakpiua-article-175326 |
| institution | System research and information technologies |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2025-07-17T10:25:58Z |
| publishDate | 2019 |
| publisher | The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" |
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| resource_txt_mv | journaliasakpiua/9c/d6101d41d8faa4043b56595ec2b80d9c.pdf |
| spelling | journaliasakpiua-article-1753262019-08-07T15:26:01Z Fuzzy-neuro system for decision-making in management Нечеткая нейронная система для принятия решений в менеджменте Нечітка нейронна система для прийняття рішень у менеджменті Setlak, G. This paper introduces a systematic approach for intelligent decision support system design based on a class of neural fuzzy networks built upon a general neuron model. The neural fuzzy networks can formally represent and process both the qualitative (linguistic) and quantitative information, which usually describe a complex, multidimensional systems or decision making processes. Presented the results of tests and a practical implementation of applications of fuzzy-neuro system for decision-making in strategic management and determination of product development strategy. Изложен систематизированный подход к проектированию интеллектуальной системы поддержки принятия решений, основанной на классе нечетких нейронных сетей, построенных на базе общей модели нейронной сети. Нечеткие нейронные сети могут формально представлять и обрабатывать как количественную , так и качественную (лингвистическую) информацию, которая обычно описывает сложные многомерные системы или процессы принятия решений. Приведены результаты тестов и практического внедрения нечеткой нейронной системы для принятия решений в стратегическом менеджменте и определении стратегии развития производства. Описано систематизований підхід до проектування інтелектуальної системи підтримки рішень, яка заснована на класі нечітких нейронних мереж, побудованих на загальній моделі нейронної мережі. Нечіткі нейронні мережі можуть представляти формалізовано як кількісну, так і якісну інформацію, яка звичайно описує складні багатовимірні системи та процеси прийняття рішень Наведено результати тестів та практичного застосування нечітких нейронних систем для прийняття рішень у стратегічному менеджменті та визначенні стратегії розвитку виробництва. The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" 2019-08-07 Article Article application/pdf https://journal.iasa.kpi.ua/article/view/175326 System research and information technologies; No. 1 (2003); 72-81 Системные исследования и информационные технологии; № 1 (2003); 72-81 Системні дослідження та інформаційні технології; № 1 (2003); 72-81 2308-8893 1681-6048 en https://journal.iasa.kpi.ua/article/view/175326/175259 Copyright (c) 2021 System research and information technologies |
| spellingShingle | Setlak, G. Нечітка нейронна система для прийняття рішень у менеджменті |
| title | Нечітка нейронна система для прийняття рішень у менеджменті |
| title_alt | Fuzzy-neuro system for decision-making in management Нечеткая нейронная система для принятия решений в менеджменте |
| title_full | Нечітка нейронна система для прийняття рішень у менеджменті |
| title_fullStr | Нечітка нейронна система для прийняття рішень у менеджменті |
| title_full_unstemmed | Нечітка нейронна система для прийняття рішень у менеджменті |
| title_short | Нечітка нейронна система для прийняття рішень у менеджменті |
| title_sort | нечітка нейронна система для прийняття рішень у менеджменті |
| url | https://journal.iasa.kpi.ua/article/view/175326 |
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