The development of the model of the expert system on the basis of fuzzy sets for panning of agricultural work
Розроблено структурну схему експертної системи в контексті системи автоматизованого управління для складання виконавчого плану виконання сільськогосподарських робіт для поля, на якому вирощується певна культура. Проектування моделі експертної системи проводилося за алгоритмом нечіткого логічного вив...
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Інститут проблем математичних машин і систем НАН України
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irk-123456789-844562015-07-09T03:02:08Z The development of the model of the expert system on the basis of fuzzy sets for panning of agricultural work Balchenko, I.V. Lytvynov, V.V. Lytvyn, S.V. Моделювання і управління Розроблено структурну схему експертної системи в контексті системи автоматизованого управління для складання виконавчого плану виконання сільськогосподарських робіт для поля, на якому вирощується певна культура. Проектування моделі експертної системи проводилося за алгоритмом нечіткого логічного виведення Мамдані в пакеті Fuzzy Logic Toolbox обчислювального середовища MATLAB. Показано реалізацію модуля експертної системи на прикладі ідентифікації сприятливих умов для виконання посіву цукрових буряків. Разработана структурная схема экспертной системы в контексте системы автоматизированного управления для составления исполнительного плана выполнения сельскохозяйственных работ для поля, на котором возделывается определенная культура. Проектирование модели экспертной системы производилось по алгоритму нечёткого логического вывода Мамдани в пакете Fuzzy Logic Toolbox вычислительной среды MATLAB. Показана реализация модуля экспертной системы на примере идентификации благоприятных условий для выполнения посева сахарной свеклы. The structural scheme of the expert system in the context of the automated control system for the preparation of the executive plan of agricultural work for the field, that is cultivated a culture, has been developed. Designing of the expert system model performed by the algorithm of fuzzy logical deduction of the Mamdani in the packet Fuzzy Logic Toolbox of the computing environment MATLAB. The realization of the module of the expert system on an example for identification of favorable conditions for sugar beet seeding has been shown. 2014 Article The development of the model of the expert system on the basis of fuzzy sets for panning of agricultural work / I.V. Balchenko, V.V. Lytvynov, S.V. Lytvyn // Математичні машини і системи. — 2014. — № 4. — 118-128. — Бібліогр.: 4 назв. — англ. 1028-9763 http://dspace.nbuv.gov.ua/handle/123456789/84456 004.942: 631,15 en Математичні машини і системи Інститут проблем математичних машин і систем НАН України |
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English |
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Моделювання і управління Моделювання і управління |
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Моделювання і управління Моделювання і управління Balchenko, I.V. Lytvynov, V.V. Lytvyn, S.V. The development of the model of the expert system on the basis of fuzzy sets for panning of agricultural work Математичні машини і системи |
| description |
Розроблено структурну схему експертної системи в контексті системи автоматизованого управління для складання виконавчого плану виконання сільськогосподарських робіт для поля, на якому вирощується певна культура. Проектування моделі експертної системи проводилося за алгоритмом нечіткого логічного виведення Мамдані в пакеті Fuzzy Logic Toolbox обчислювального середовища MATLAB. Показано реалізацію модуля експертної системи на прикладі ідентифікації сприятливих умов для виконання посіву цукрових буряків. |
| format |
Article |
| author |
Balchenko, I.V. Lytvynov, V.V. Lytvyn, S.V. |
| author_facet |
Balchenko, I.V. Lytvynov, V.V. Lytvyn, S.V. |
| author_sort |
Balchenko, I.V. |
| title |
The development of the model of the expert system on the basis of fuzzy sets for panning of agricultural work |
| title_short |
The development of the model of the expert system on the basis of fuzzy sets for panning of agricultural work |
| title_full |
The development of the model of the expert system on the basis of fuzzy sets for panning of agricultural work |
| title_fullStr |
The development of the model of the expert system on the basis of fuzzy sets for panning of agricultural work |
| title_full_unstemmed |
The development of the model of the expert system on the basis of fuzzy sets for panning of agricultural work |
| title_sort |
development of the model of the expert system on the basis of fuzzy sets for panning of agricultural work |
| publisher |
Інститут проблем математичних машин і систем НАН України |
| publishDate |
2014 |
| topic_facet |
Моделювання і управління |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/84456 |
| citation_txt |
The development of the model of the expert system on the basis of fuzzy sets for panning of agricultural work / I.V. Balchenko, V.V. Lytvynov, S.V. Lytvyn // Математичні машини і системи. — 2014. — № 4. — 118-128. — Бібліогр.: 4 назв. — англ. |
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118 © Balchenko I.V., Lytvynov V.V., Lytvyn S.V., 2014
ISSN 1028-9763. Математичні машини і системи, 2014, № 4
МОДЕЛЮВАННЯ І УПРАВЛІННЯ
UDC 004.942: 631.15
I.V. BALCHENKO*, V.V. LYTVYNOV*, S.V. LYTVYN*
THE DEVELOPMENT OF THE MODEL OF THE EXPERT SYSTEM ON THE BASIS
OF FUZZY SETS FOR PANNING OF AGRICULTURAL WORK
*Chernihiv National University of Technology, Chernihiv, Ukraine
Анотація. Розроблено структурну схему експертної системи в контексті системи автоматизо-
ваного управління для складання виконавчого плану виконання сільськогосподарських робіт для по-
ля, на якому вирощується певна культура. Проектування моделі експертної системи проводилося
за алгоритмом нечіткого логічного виведення Мамдані в пакеті Fuzzy Logic Toolbox обчислюваль-
ного середовища MATLAB. Показано реалізацію модуля експертної системи на прикладі ідентифі-
кації сприятливих умов для виконання посіву цукрових буряків.
Ключові слова: нечітка логіка, лінгвістична змінна, функція належності, експертна система, ви-
конавчий план, агрофірма.
Аннотация. Разработана структурная схема экспертной системы в контексте системы авто-
матизированного управления для составления исполнительного плана выполнения сельскохозяйст-
венных работ для поля, на котором возделывается определенная культура. Проектирование моде-
ли экспертной системы производилось по алгоритму нечёткого логического вывода Мамдани в
пакете Fuzzy Logic Toolbox вычислительной среды MATLAB. Показана реализация модуля экспер-
тной системы на примере идентификации благоприятных условий для выполнения посева сахар-
ной свеклы.
Ключевые слова: нечёткая логика, лингвистическая переменная, функция принадлежности, экс-
пертная система, исполнительный план, агрофирма.
Abstract. The structural scheme of the expert system in the context of the automated control system for the
preparation of the executive plan of agricultural work for the field, that is cultivated a culture, has been
developed. Designing of the expert system model performed by the algorithm of fuzzy logical deduction of
the Mamdani in the packet Fuzzy Logic Toolbox of the computing environment MATLAB. The realization
of the module of the expert system on an example for identification of favorable conditions for sugar beet
seeding has been shown.
Keywords: a fuzzy logic, a linguistic variable, a membership function, an expert system, an executive plan,
an agrarian firm.
1. The problem statement
A development conception for the computer-aided management system of an agricultural enter-
prise was proposed by authors in the work [1]. It was showed, that incompleteness factors and a
large amount of primary qualitative information should be considered when algorithmization of
problems statements of a system.
The design principles of the functional subsystem of planning for automating management
of a crop cultivating agricultural enterprise are shown in the work [2]. When planning the agricul-
tural work it is necessary to correlate the current condition of the soil or crop with the terms, the
cost of the additional work and the extent of possible improvement of the soil or crop condition.
Thus, it is necessary an expert participation in a decision on an inclusion in the executive plan of
agricultural works.
The feature of a work planning is the relative noncriticality to the runtime term. The fuz-
ziness in relation start time of work’s performance and duration, which is comparable with the
ISSN 1028-9763. Математичні машини і системи, 2014, № 4 119
individual characteristics of fields and the time of a technic concentration in the work area, is al-
lowed [1]. Using an apparatus of a fuzzy logic in the development of a knowledge base and infe-
rence engines of an expert system allows to formalize the procedure for evaluating the condition
of the field by fragmentary, unreliable and possibly inaccurate information and to make decisions
about the need for work performance with deep arguments.
Fuzzy expert systems allow not only to consider the uncertainty, but also to simulate rea-
soning, that is difficult to implement in systems on a traditional logic. Therefore, the main pur-
pose of the fuzzy logic application is a creation apparatus that is able to model human reasoning
based on the experts experience and to explain decision-making methods [3].
In this connection it became necessary to construct the expert system based on a fuzzy
logic. This system must allow to form an executive plan for the field on which the culture is cul-
tivated.
2. The development of the model of the expert system
The computer-aided management system of an agricultural enterprise can be viewed as an adap-
tive fuzzy automatic control system relative to the field as a control object. The system is
represented as a closed control system with feedback. In it live circuit the fuzzy controller is used
as a regulator. The fuzzy controller is an expert system with input signals that describe conditions
of the field. The fuzzy controller generates a control action in the form of executive plans of
works through implementation schemes of a fuzzy inference. In this scheme, pre-entered know-
ledge, that is received from experts at the design stage, are used and presented in a form of the
rule base of a fuzzy inference system. Any next change in a rule base expert is implemented from
the outside by an expert.
In the figure 1 the generalized structural scheme of a fuzzy computer-aided management
system of an agricultural enterprise is presented.
Fig. 1. The structural scheme of a fuzzy computer-aided management system
of an agricultural enterprise
The generalized control object is a field where the culture is cultivated. The control object
includes directly controlled technological process in the form of executive plans of works, ampli-
fying transforming mechanisms in the form of control over the execution of plans, the regulatory
authorities in the form of planning and dispatching services, and methods for measuring of the
field condition [1]. Input variables that charactering the real field condition are exposed by the
fuzzification and are used in the fuzzy inference system. Fuzzy inference system contains a base
of fuzzy production rules of a generalized form “IF {“The field condition1”, … , “The field con-
dition N”} THEN “The effect on the field””. Experts’ knowledge about management work is
The field
Sensors
Real conditions
A fuzzi-
fication
A defazzi-
fication
A fuzzy
inference
An interface A rule base
(desired conditions) A plan of
agricultural
works
An agriculturist
120 ISSN 1028-9763. Математичні машини і системи, 2014, № 4
represented in the rule base in the fuzzy form to achieve the desired condition of the object on the
basis of knowledge about the values that characterize the actual object condition. Crisp output
values are received as a result of fuzzy inference and the subsequent defuzzification use in the
description of the work and its inclusion in the executive plan.
Special tools of fuzzy modeling in MATLAB allow performing the full range of research
on the development and application of fuzzy models [4]. For these reasons, MATLAB was cho-
sen as software tools, within which it is possible realize theoretical concepts of fuzzy sets and
fuzzy inference procedure.
The module for identification of favorable conditions for sugar beet seeding was realized
using the configuration package Fuzzy Logic Toolbox of the computing environment MATLAB
(fig. 2).
Fig. 2. Functional scheme for identification of favorable conditions for sugar beet
seeding in the editor window of the MATLAB
The main stages of fuzzy inference are: a fuzzification of the input variables, a formation
of the rule base, an aggregation of sub-conditions, an activation of sub-conclusions, an accumula-
tion of conclusions, and a defuzzification of output variables. We show the implementation of
these steps on the example of the identification of favorable conditions for sugar beet seeding.
2.1. The fuzzification
The fuzzification is a transformation of a crisp set of an input data to a fuzzy set, which is deter-
mined by the values of membership functions. Fuzzification allows to present objective presence
inaccurate measurement of object conditions. The purpose of fuzzification stage is the establish-
ment of a correspondence between a specific numerical value of the input variable of the fuzzy
inference system and the value of a membership function of the term of the input linguistic varia-
ble. The input data { }1 2, ... ix x x ϵ X , where i is the number of the field conditions, are values,
which are received from sensors or by agriculturist evaluating. Then a linguistic evaluation of an
each crisp parameter is carried according to membership functions that are specified in the sys-
tem. After this, a crisp set of input parameters is transformed into fuzzy set Ã, which is characte-
rized by a membership function µÃ (x), and is used as linguistic variables in logical rules of a
knowledge base.
In the development of the knowledge base of the expert system to plan for sugar beet
seeding the knowledge base was used, and it is presented in table 1. The values of the input con-
ditions were amended according to their fuzzy linguistic variables (table 1) at the fuzzification
stage, and then the variation of the membership function was chosen.
ISSN 1028-9763. Математичні машини і системи, 2014, № 4 121
The parameter values for a range of a linguistic variable were calculated on the permissi-
ble deviations of parameters from the mean values in accordance with norms.
Table 1 shows that possible values for the soil moisture are the following set:
V = (40; 45; 50; 55; 60; 65; 70; 75; 80; 85; 90). (1)
Each element of the set has its own degree of membership: the higher the degree of mem-
bership, the greater the probability that the parameter value is in the norm. Membership functions
or information for their construction are given by experts by subjective preferences and are not
random.
Table 1. The knowledge base for the work “Sugar beet seeding”
A parameter name A symbol A parameter value
The soil humidity, % V Low Middle High
40−50 60−70 80−90
The soil temperature,
˚С
T Low Middle High
2−4 5−7 8−9
The soil density,
gm/cm3
ρ Low Middle High
0.6−0.9 1−1.3 1.4−1.7
The runtime term of
work (April)
τ Early Average Late
1−10 11−20 21−30
The resulting fuzzy set can be represented as follows:
Vmiddle
0 0 0,5 1 1 1 0,5 0 0 0
A ( , , , , , , , , , ).
40 45 50 60 65 70 75 80 85 90
=ɶ (2)
Because the set of a humidity parameter is finite, the fuzzy set à is written as:
N
V n 1
( )
A nA
n
V
V=
µ
= ∑ ɶɶ , (3)
where
� ( )nA
Vµ is a membership degree of the element nV ϵV to fuzzy set Ã. The membership
degree is a value from range [0 1]. The higher degree of a membership, the more element of the
set corresponds to the properties of a fuzzy set.
Considering all other parameters, it is possible to consider the system to be type of MISO
(Multiple Input Single Output). In this case, the system depends on the values of all input para-
meters, and will be described in the rules, which take into account all of input parameters of the
system. There is generalized record of the MISO system that is the following:
].
~~~~
[ τρ AAAAy TV ∧∧∧= (4)
Each parameter has a range of variation. Linguistic assessment of the value of each input
variable is performed by three terms, and the output variable is performed by five terms. Mem-
bership function is trapezoidal: y=trapmf (x, [a, b, c, d]). The argument а is a minimal valid value
of the parameter with zero probability of a norm. Interval between the arguments b and c shows
the parameter belonging to the norm with probability 1. And, accordingly, the argument d is a
maximum valid value with zero probability of a norm.
Let us consider the definition of the membership function for example soil humidity pa-
rameter (V) in more detail. The low value for the parameter is the range of [40 60], the average
value is the range of [50 80] and the high value is the range of [60 70]. Selecting a trapezoid form
of the membership function is conditioned by the fact that the parameter membership to the norm
with probability 1 isn’t determined by a single value of the variable, but determined by range of
acceptable values.
122 ISSN 1028-9763. Математичні машини і системи, 2014, № 4
For input condition of the soil humidity, the membership function has three qualitative re-
presentations, for which the mechanism of fuzzy inference is mathematically formalized as:
>
∈
−
−
∈
=
60,0
]60..50[,
5060
60
]50..40[,1
)(
Vif
Vif
V
Vif
Vlowµ . (5)
><
∈
−
−
∈
∈
−
−
=
8050,0
]80..70[,
7080
80
]70..60[,1
]60..50[,
5060
50
)(
VandVif
Vif
V
Vif
Vif
V
Vlmiddleµ . (6)
<
∈
−
−
∈
=
70,0
]80..70[,
7080
70
]90..80[,1
)(
Vif
Vif
V
Vif
Vhighµ . (7)
For each input conditions trapezoidal fuzzy sets were given. Membership functions are
normal (normalized) and take values in the range from 0 to 1. Graphical view of the membership
functions is shown in figures 3a−f.
a) b)
c) d)
f)
Fig. 3. Membership functions of input variables of the humidity а), the temperature b), the density c), the
runtime term d), the output variable of seeding conditions f)
ISSN 1028-9763. Математичні машини і системи, 2014, № 4 123
After completion of the fuzzification stage for all input variables must concrete values of
membership functions for each of the linguistic terms were determined, and they are used in the
conditions of the rule base of the fuzzy inference.
Let us assume that the state of the field, where sugar beet cultivation is planned, is charac-
terized by the conditions: the humidity level is 59%, the density is 1.1 gm/cm3, the temperature is
7.52 ˚C, the runtime term is April 8th. After fuzzification we got truth degree of elementary fuzzy
statements, which are presented in table 2.
Table 2. Truth degrees of fuzzy sets after fuzzification
A fuzzy set A truth
degree
A fuzzy set A truth
degree
“The low humidity” 0,11 “The low density” 0
“The middle humidity” 0,89 “The middle density” 1
“The high humidity” 0 “The high density” 0
“The low temperature” 0 “The early runtime term” 0,4
“The middle temperature” 0,48 “The average runtime term” 0,6
“The high temperature” 0,52 “The late runtime term” 0
2.2. The formation of fuzzy production rules
Causal relationships between the parameters and conditions of seeding are formalized in the form
of the set of fuzzy logic rules. Format basic rules of inference “if – then” is called a fuzzy impli-
cation. The rule condition may be the statement “The humidity is low”, the term “low” is given
by the fuzzy set of the universal set of the linguistic parameter “The humidity”. The consequence
for this condition may be one of the terms of the output parameter of seeding conditions.
The fuzzy knowledge base including information about the relation of the "values of the
parameters – conditions for seeding" and contains by the following linguistic rules:
1) If (The humidity is Low) and (The temperature is Low) and (The density is low) and
(The runtime term is Early) then (Conditions for seeding are Unsatisfactory) (1);
2) If (The humidity is Low) and (The temperature is Low) and (The density is Low) and
(The runtime term is Average) then (Conditions for seeding are Below satisfactory) (1);
3) If (The humidity is Low) and (The temperature is Low) and (The density is Low) and
(The runtime term is Late) then (Conditions for seeding are Below satisfactory) (1);
4) If (The humidity is Low) and (The temperature is Low) and (The density is Low) and
(The runtime term is Late) then (Conditions for seeding are Below satisfactory) (1);
5) If (The humidity is Low) and (The temperature is High) and (The density is Low) and
(The runtime term is Early) then (Conditions for seeding are Satisfactory) (1);
6) If (The humidity is Low) and (The temperature is Middle) and (The density is Low)
and (The runtime term is Average) then (Conditions for seeding are Satisfactory) (1);
7) If (The humidity is Low) and (The temperature is High) and (The density is Low) and
(The runtime term is Average) then (Conditions for seeding are Satisfactory) (1)
8) If (The humidity is Low) and (The temperature is Middle) and (The density is Low)
and (The runtime term is Late) then (Conditions for seeding are Satisfactory) (1);
9) If (The humidity is Low) and (The temperature is High) and (The density is Low) and
(The runtime term is Late) then (Conditions for seeding are Satisfactory) (1);
10) If (The humidity is Middle) and (The temperature is Low) and (The density is Low)
and (The runtime term is Early) then (Conditions for seeding are Below satisfactory) (1);
11) If (The humidity is High) and (The temperature is Low) and (The density is Low) and
(The runtime term is Early) then (Conditions for seeding are Unsatisfactory) (1);
12) If (The humidity is Middle) and (The temperature is Middle) and (The density is Low)
and (The runtime term is Early) then (Conditions for seeding are Above satisfactory) (1);
124 ISSN 1028-9763. Математичні машини і системи, 2014, № 4
13) If (The humidity is Middle) and (The temperature is Middle) and (The density is Mid-
dle) and (The runtime term is Early) then (Conditions for seeding are Optimal) (1);
14) If (The humidity is Middle) and (The temperature is Middle) and (The density is Mid-
dle) and (The runtime term is Average) then (Conditions for seeding are Optimal) (1);
15) If (The humidity is High) and (The temperature is High) and (The density is Middle)
and (The runtime term is Early) then (Conditions for seeding are Above satisfactory) (1);
16) If (The humidity is High) and (The temperature is High) and (The density is High)
and (The runtime term is Average) then (Conditions for seeding are Above satisfactory) (1);
17) If (The humidity is High) and (The temperature is High) and (The density is High)
and (The runtime term is Late) then (Conditions for seeding are Satisfactory) (1);
18) If (The humidity is Middle) and (The temperature is High) and (The density is Mid-
dle) and (The runtime term is Late) then (Conditions for seeding are Optimal) (1);
19) If (The humidity is Middle) and (The temperature is Middle) and (The density is
High) and (The runtime term is Late) then (Conditions for seeding are Above satisfactory) (1);
20) If (The humidity is Middle) and (The temperature is High) and (The density is Mid-
dle) and (The runtime term is Low) then (Conditions for seeding are Optimal) (1);
21) If (The humidity is High) and (The temperature is High) and (The density is High)
and (The runtime term is Late) then (Conditions for seeding are Satisfactory) (1);
22) If (The humidity is Middle) and (The temperature is High) and (The density is Mid-
dle) and (The runtime term is Average) then (Conditions for seeding are Optimal) (1).
2.3. The aggregation of sub-conditions
The aggregation is a procedure for determining the truth degrees of conditions for each of the
rules of the fuzzy inference system. Here are used values of membership functions of the terms of
the linguistic variables that make up the nuclei of the antecedents of fuzzy production rules and
were received at the fuzzification stage.
In MISO system the condition is a compound statement, its truth degree is based on the
known truth values of its elementary statements using fuzzy logic operation «AND»:
µ(V ∩ T ∩ ρ ∩ τ)=min{µ(V); µ(T); µ(ρ);µ(τ)} . (8)
After aggregation on the basis of truth degree of the input parameters, obtained in sec. 2.1,
were received the truth degree of conditions (table 3).
Table 3. Truth degrees of conditions1
ρ 0 0 0 1 1 1 0 0 0
V T \ τ 0,4 0,6 0 0,4 0,6 0 0,4 0,6 0
0,11 0 0(1) 0(2) 0(3) 0 0 0 0 0 0
0,11 0,48 0(4) 0(6) 0(8) 0,11 0,11 0 0 0 0
0,11 0,52 0(5) 0(7) 0(9) 0,11 0,11 0 0 0 0
0,89 0 0(10) 0 0 0 0 0 0 0 0
0,89 0,48 0(12) 0 0 0,4(13) 0,48(14) 0 0 0 0
0,89 0,52 0 0 0 0,4(20) 0,52(22) 0(18) 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0,48 0 0 0 0 0 0 0 0 0
0 0,52 0 0 0 0 0 0 0 0 0
1 In table 3 in parentheses is indicated number of the rule for which was evaluated the truth degree of con-
ditions.
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2.4. The activation of sub-conclusions
The activation of fuzzy inference systems is a procedure or process of finding the truth degree of
each of the elementary logic statements (sub-conclusions), which make up the nuclei of conse-
quents of all the fuzzy production rules. Because conclusions are made regarding the output lin-
guistic variables, on activation the truth degree of elementary sub-conclusions are associated with
basic membership functions.
Membership functions ( )yµ of each of the elementary sub-conclusions of consequents of
all production rules are received using the method of min-activation of fuzzy composition:
( ) ( ){ }min ;y c xµ = µ (9)
where ( )xµ is membership functions of the terms of linguistic variables;
c is fuzzy truth degree of statements, which form the corresponding nuclei consequent of
fuzzy production rules.
Using the procedure of activation, we received the following non-zero membership func-
tions ( )yµ :
by rules 13,20:
13
0,4, [0,79..1]
0,75
( ) , [0,75..0,79],
0,79 0,75
0, 0,75
if y
y
y if y
if y
∈
−µ = ∈ −
<
(10)
by the rule 14:
14
0,48, [0,798..1]
0,75
( ) , [0,75..0,798],
0,798 0,75
0, 0,75
if y
y
y if y
if y
∈
−µ = ∈ −
<
(11)
by the rule 22:
122
0,52, [0,802..1]
0,75
( ) , [0,75..0,802].
0,802 0,75
0, 0,75
if y
y
y if y
if y
∈
−µ = ∈ −
<
(12)
2.5. The accumulation of conclusions
The accumulation in the fuzzy inference system is a process of finding the membership function
for output linguistic variables. The aim of the accumulation is in a union of all truth degrees of
sub-conclusions for the membership function of the output variables. The result of the accumula-
tion is defined as a union of fuzzy sets of all sub-conclusions of a fuzzy rule base with respect to
the corresponding linguistic variable using the max-union:
( ) ( ) ( ) ( ) ( ){ }13 20 14 22max ; ; ;y y y y yµ = µ µ µ µ . (13)
In accumulating all truth degrees of the output parameter, which were presented in sec.
2.4, the fuzzy set of the output variable was obtained, and is identical to the formula 12.
The fuzzy inference of rules in the MATLAB editor is shown in figure 4.
126 ISSN 1028-9763. Математичні машини і системи, 2014, № 4
Fig. 4. The fuzzy inference of rules in the MATLAB editor
2.6. The defuzzification
The defuzzification is an inverse transformation of the fuzzy set à in the crisp set B. The aim of a
defuzzification is to obtain quantitative values, using the results of the accumulation of output
linguistic variables. These values can be used by external to the fuzzy inference system devices
(executive mechanisms of the computer-aided management system of an agricultural enterprise).
In this model, the identification of conditions for seeding (probability of favorable conditions) is
performed by the method of the center of gravity, which calculates the centroid of the area:
max max
min min
( ) / ( )
y y
y y
y y y dy y dy= µ µ∫ ∫ , (14)
where [ ]max min;y y – is a medium of a fuzzy set of an output linguistic variable.
So, when the humidity level is 59%, the density is 1.1 gm/cm3, the temperature is 7.52 ˚C,
the runtime term is April 8th, after defuzzification the output parameter was 0.89. There are op-
timal conditions for sugar beet seeding, and may be used by agriculturist for making the decision
about including work «seeding» in the executive plan on date April 8th.
Moreover, the surface of the "input-output" was obtained by the results of the fuzzy infe-
rence. The surface shows the dynamics of the execution conditions for sugar beet seeding (see
fig. 5 a–d).
Thus, the dynamics of the computer-aided management system of an agricultural enter-
prise with fuzzy controller is totally based on the architecture of the fuzzy inference system: on
method of construction and content of base production rules and on the method of implementa-
tion of the algorithm of the fuzzy inference. In the design of the fuzzy system the experts and ex-
pert poll methodologies must be carefully chosen and the rule base formed. The choice of imple-
ment ways of each stages of the algorithm of fuzzy inference is made to greater extent intuitively,
since there are no complete and holistic methods of synthesis of the fuzzy inference algorithm on
the basis of production rules, which is allowed to realize fuzzy control in accordance to any pre-
set assessment of the required quality of the control. Typically, the choice of the specific fuzzy
inference algorithm is carried out empirically from a limited number of possible implementations.
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a b
c d
Fig. 5. Dependence of favorable conditions for sugar beet seeding from the runtime term and the tempera-
ture a), from the temperature and the humidity b), from the density and the humidity c), from the runtime
term and the density d)
The above given inference system is a system of Mamdani-Zadeh. The choice of fuzzy
model of type Mamdani is caused by the fact that the rules of the knowledge base are clear and
intuitive, whereas for Sugeno-type models it is not always clear which linear dependences "input
– output" should be used and how to get them.
3. Conclusion
The developed model of the expert system on the basis of a fuzzy logic and field conditions al-
lows finding the best solution of the problem of formulation and correction of the executive plan
of work when field conditions are being changed in real time.
The main advantages of designing of a model of the expert system on the basis of a fuzzy
logic are:
1) a support of the development of a rapid prototype of the expert system with an increas-
ing complexity of a functionality;
2) for an agronomist it is more understandable a fuzzy logic model than the similar ma-
thematical model on the basis of differential or difference equations;
3) a method of fuzzy sets allows to include qualitative variables in the analysis and to op-
erate with fuzzy input data and linguistic criteria;
4) fuzzy models are simpler to implement in comparison with traditional control algo-
rithms of technical systems.
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Стаття надійшла до редакції 23.10.2014
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