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Technology of modeling of integrity and fuzzy model of
knowledge – IFMK
Fatma khanim Bynyatova
Intellect school Azerbaijan
fatmaxanum@rambler.ru
Gulbala Salamov
Hacettepe University, Turkey
g.salamov@gmail.com
Abstract Rapid development of technology requires high intellectual and social skills from the growing
generation. But it is impossible to acquire these skills mastered at school. One of the reasons is that the system
requires only acquiring knowledge. Acquisition is the elementary level of cognitive activity, and even though
ICT is used in this structure, high-level cognitive skills are not formed in students’ minds. ICT is based on the
artificial cognition, and the content of the knowledge is constructed illogically i.e. from its parts to the whole
content.Artificial intelligence was created by Lutfi-Zadeh. Piaget worked on the human beings’ ability of
constructing cognitive skills in the cognitive theory. In order to form high level cognitive abilities in students’
minds, the model of artificial cognition and the model of natural cognition should be modeled and the knowledge
should be placed logically in IFMK i.e. in the model integrity and fuzzy model.
IFMK modeling technology.
1. The model will be modeled as a normative model and will eventually reflect the structure of knowledge
relevant to the development of the individual’s cognition. This structure is an integrity and fuzzy model of
subject programs.
2. The model will be modeled conceptually. Special symbols and signs are used and operations are carried
out on them. The main idea is explained by the language of integrity logic created by Piaget for natural cognition
at the same time by the language of artificial intelligence i.e. by the fuzzy logic.
3. The model is modeled in 3 model.
Formation
• Establish a coordinate network of the model with the psychological tools used by Piaget to reflect the
development of the cognition.
• To show compatibility between the logical tools created by Piaget and Zadeh.
• Replacing the psychological concepts of the constructed model of integrity by the fuzzy notions created
by Zadeh and creating IFMK.
Model study.
Interpretation
Steps to model IFMK
• Piaget’s psychological concepts are interpreted as didactic concepts.
• Knowledge units are regarded as knowledge structures and divided into variables and invariables. Variable
knowledge is marked by y, invariable knowledge is marked by with x.
• The knowledge of x and y is classified and numbered by x1-x9 v y1-y9ə.
• The coordinate network for the model is created. Invariable x1-x9 knowledge is placed on the horizontal X –axis,
variable y1-y9 knowledge is placed on the vertical Y axis.
The obtained coordinate network is a logical integrity model of knowledge.
• As the concepts of integrity logic coincide with the fuzzy concepts by Zadeh, the psychological concepts of
the model are substituted by the fuzzy logic concepts. Variable knowledge y1-y9 are substituted by the linguistic
variables and it is marked as y0,1-y0,9, and the knowledge in the slot is numbered. Invariable knowledge x1-x9 is
substituted by the by mathematical cluster and its elements are marked as x0,1-x0,9 . The knowledge within the
elements is numbered according to the internal rules.
Exploring IFMK
• Each x0,1-x0,9 knowledge is also a cluster of knowledge structures. They can be merged and separated from
logical conditions, associated with logical conditions or disappeared in accordance with the rules of linguistic
variation.
• The affiliation of y0,1-y0,9 to the elements x0,1-x0,9 creates conditions for carrying out logical operations.
• The digital features of the knowledge x0,1-x0,9 and y0,1-y0,9 allow to determine the students’ knowledge
coordinates and so on.
3. Interpretation
• As IFMK provides a complete set of knowledge, program materials are constructed in the complete scheme
and expanded every year.
• IFMK can be used as a technological model in secondary schools, in every form of electronic education, in
program structure of electronic and digital schools, and in constructing individual programs for talented children.
Key words: integrity logic, fuzzy logic, modeling, variable, invariable, model
I INTRODUCTION.
Rapid development of technology requires high intellectual and social skills from the growing generation. And this
development does not ensure the generation that grew up in the environment of traditional education system.
The required skills are: analyzing, creating, transforming knowledge from one level to another, carrying out
operations on knowledge, working in the team, being responsible, in short, high intellectual and social skills.
However, these skills cannot be acquired by the growing generation in the traditional teaching environment, and in
the content structure of the knowledge they study as it is impossible to acquire these skills at school. One of the
reasons is that the system requires only acquiring knowledge. Acquisition is the elementary level of cognitive
activity, and even though ICT is used in this structure, high-level cognitive skills are not formed in students’ minds.
ICT is based on the artificial cognition, and the content of the knowledge is constructed illogically i.e. from its parts
to the whole content.
Artificial intelligence was created by Lutfi-Zadeh [3]. J. Piaget worked on the human beings’ ability of
constructing cognitive skills in the cognitive theory [4] They created it in different languages: Lutfi-Zadeh
created it in mathematical language, J. Piaget created it in psychological language. In order to form high level
cognitive abilities in students’ minds, the model of artificial cognition and the model of natural cognition should
be modeled and the knowledge should be placed logically in IFMK i.e. in the model integrity and fuzzy model.
If we model the knowledge as isomorphic by modeling human thinking through Piaget’s integrity logic, in
the obtained, thinking way of natural cognition may coincide with the thinking way of artificial cognition. With
the help of this integrity and fuzzy knowledge, every individual builds his / her own thinking way and creates
adequate knowledge structures.
II. MODELING OF INTEGRITY AND FUZZY MODEL OF KNOWLEDGE – IFMK
1. The model will be modeled as a normative model and will eventually reflect the structure of knowledge
relevant to the development of the individual’s cognition. This structure is an integrity and fuzzy model of
subject programs. As the model is modeled in conformity with normative rules, it is pragmatic and its
purpose is to adequately build the structure of the content of the teaching to the human thinking structure
and to improve logically the individual’s thinking and acquire high mental abilities.
2. The model will be modeled conceptually[6]. Special symbols and signs are used and operations are carried
out on them. The main idea is explained by the language of integrity logic created by Piaget for natural
cognition at the same time by the language of artificial intelligence i.e. by the fuzzy logic.
3. The model is modeled in 3 levels.
a) Formation
• Establish a coordinate network of the model with the psychological tools used by Piaget to reflect the
development of the cognition.[2]
b) To show compatibility between the logical tools created by Piaget and Zadeh.
c) Replacing the psychological concepts of the constructed model of integrity by the fuzzy
notions created by Zadeh and creating integrity and fuzzy model.
d) Model study.
e) Interpretation – transition of the results of the model to the programs.
The following steps are taken in order to model integrity and fuzzy model of knowledge - IFMK:
1. Piaget’s psychological concepts are interpreted as didactic concepts.
2. Intelligent structures - didactic knowledge structures (didactic knowledge units)[1].
Invariant cognitive structures - the structure of the invariant knowledge.
Variable Cognitive Structures - Variable Knowledge Structures.
Integrity scheme of cognitive structures - Integrity scheme of knowledge
3. Knowledge units are regarded as knowledge structures and divided into variables and invariables. Variable
knowledge is marked by y, invariable knowledge is marked by with x.
4. The knowledge of x and y is classified and numbered by x1-x9 and y1-y9.
5. The coordinate network for the model is created.
6. Invariable x1-x9 knowledge is placed on the horizontal X –axis, variable y1-y9 knowledge is placed on the
vertical Y axis.
The obtained coordinate network is a logical integrity model of knowledge. (Scheme 1)
Y
9
8
7
6
5
4
3
2
1
X
0 1 2 3 4 5 6 7 8 9
Scheme 1.
7. As the concepts of integrity logic coincide with the fuzzy concepts by Zadeh, the psychological concepts
of the model are substituted by the fuzzy logic concepts.
a) Intelligence Structures - Elements of Cluster.
b) Variable Cognitive Structures - Universal Cluster.
c) Variable cognitive structures - Linguistic variability
d) When we take into account Lutfi-Zadeh’s linguistic concept, the function of possession has two
rules.
e) Syntactical rule. This rule is given in grammatical form, and it creates the name of a variable or
categorical of knowledge.
h) Semantic rule. This rule defines the meaning of each variable that changes with the algorithmic
procedure.
7. Modeling of the integrity-logical and logical model of knowledge on the basis of J. Piaget’s and
Zadeh’s theories
a) The notion of variable knowledge by J. Piaget is substituted by the linguistic variable by Lutfi-
Zadeh and y1-y9 knowledge is marked as y0,1-y0,9.
b) Invariable knowledge structures is substituted by the by mathematical cluster and x1-x9 knowledge
is marked as x0,1-x0,9 .
c) The coordinate network is created for the model.
d) The universal cluster x0,1-x0,9 knowledge is placed on horizontal X-axis. Linguistic variable
knowledge y0,1-y0,9 is placed on the vertical Y-axis.
The obtained coordinate network is an integrity and fuzzy model of knowledge. (Scheme 2)
Y
0,9
0,8
0,7
0,6
0,5
0,4
0,3
0,2
0,1
X
0
0,
1
0,
2
0,
3
0,
4
0,
5
0,
6
0,
7
0,
8
0,
9
Scheme 2
EXPLORING IFMK - INTEGRITY AND FUZZY MODEL OF KNOWLEDGE
1. According to scientists the formation of the variables i.e. category, is a single theory of scientific
researches. When the elements of knowledge cluster are numbered with the categorical-linguistic
knowledge, we can describe the knowledge with its features. Every feature of knowledge accepts
consecutive numbers. Such marking can be called “fuzzy” language of knowledge.
2. Knowledge of each class or elements of cluster knowledge is also a cluster of knowledge structures
(knowledge base). Each of them has their own rules. Cluster structures can be merged and separated into
logical conditions in accordance with the rules of linguistic variation, entering into the association or
disappear. The linguistic variables belong to the elements of the majority are determined by logical
operations with substitution, multiplication, enrichment and identical operations. In such a case, the rules
of linguistic variables are always as mobile as the rules of cluster. These rules are transformed into the
nano-structure of knowledge by integrating with the help of mobile movement around the knowledge
structures on the basis of logical conditions.
3. INTERPRETATION – TRANSFORMATION OF THE RESULTS OF THE MODEL INTO PROGRAMS
Based on the results of the logic and fuzzy model of the subject knowledge, Azerbaijani language [5]
curriculum program for primary education is created.
The following steps should be taken inorder to build this program:
1. It is necessary to divide the knowledge structure of Azerbaijani language [5] into the linguistic variables
and the invariant, i. e. Universal cluster.
2. Invariant knowledge, or the universal cluster i.e. the word stock of the language, is marked by x is
classified and devided into classes i.e. into parts of speech.
Every part of speech is -x0,1-noun, x0,2-adjective; x0,3-numeral; x0,4-pronoun; x0,5-verb; x0,6-adverb; x0,7- x0,8-
x0,9 are structural parts of are placed horizontally coordinate. Invariable knowledge or “cluster of knowledge” can
be finite along the classes and endless within the classes.
3. linguistic variable knowledge - that is y is the knowledge of Azerbaijani grammar. There were 6 variable
knowledge in the Azerbaijani language: y-0,1 the category of singlular and plural; y-0,2- the category of
declining; y-0.3 the category of person; y-0,4- the category of time, y-0,5- the category of possession,
y-0,6- the category of quantity
Category knowledge is plased vertically in the coordinate (scheme 3)
Scheme 3 is a coordinate network of the Azerbaijani language program and 4 categorial knowledge are studied
during this teaching period. The coordinate network is a genetic program of linguistic knowledge. Knowledge in the
slots of this program is divided into levels according to the classes.
Scheme 3
parts of speech
categories
y
x
0,2 hal
1isim 2sif t 3say 4 v zlik 5fel 6z rfə ə ə ə köm kçi nitqə
hiss l riə ə
0,4 zaman
0,3 ş xsə
0,1 t k v c mə ə ə
x0,1noun , x0,2 adjective, x0.3 numeral, x0,4 pronoun, x0.5 verb, x0,6 adverb x0,7-x0,9 auxiliary parts of speech
y0,1the category of singlular and plural; y0,2 the category of declining
y0,3 the category of person; y0,4the category of time
As it is seen in the scheme, in accordance with the categorical knowledge structures, they can be logially
combined with the parts of speech <y0.1x0.1> and can be separated <y0.1> <x0.1>. They can be associated
<y0,1x0,1, x0,2, x0,3> and so on. The categorial knowledge belings to the parts of speech. It allow to carry out
some operations on the parts of speech, such as multiplicative , enrichment and identity and othe logical
operations. In such cases, categorical rules are always as mobile as parts of speech. The created co-ordinate
network can be regarded as an integral part of the artificial language along with natural language knowledge. For
example, the phrase “It has been snowing heavily since evening” was expressed in a natural language. This
sentence will be written in the artificial language like : <x0.6> <x0,6> <y0,1x0,1> <y0,1x0,5>
Digital features of categorial and invariant knowledge make it possible to define the knowledge coordinate of each
student. Based on these technological bases, the standard program framework can be programmed corresponding to
every student’s individual development level. In this approach, individuality, diversity and overall work are built on
technological basis. All subject knowledge can be modeled with the help of IFMK technology, because there are
variable and invariable knowledge in it.
4. If pupil’s thinking carries out operations on knowledge, if his thinking is connected with knowledge
structures, clustering ability of knowledge structures is formed. Each student finds the relationships among
these knowledge, classifies or substitutes them with other knowledge with the help of logical operations.
For this reason, his knowledge is dynamic, relatated, declined to vary and and renew.
WHAT INNOVATION WILL BRING IN THE PROPOSED MODELING TECHNOLOGY IN EDUCATION
1. By placing the knowledge in the technological framework of new generation technologies,
ICT can be oriented to self-development rather than memory.
2. Integrity logic by J. Piaget and fuzzy logic by Zadeh destroy the traditional structure of
teaching knowledge and gives it a new structure - horizontal structure. Such a structure of
knowledge makes it possible for each student to succeed in education. Depending on the
inner ability of every pupil the duration of being successful within the framework of the
program may be longer or shorter.
3. IFMK can be used as a technological model in secondary schools, in every form
of electronic education, in program structure of electronic and digital schools, and
in constructing individual programs for talented children.
4. If the proposed model is implemented in a constructive teaching process, the model will
make a person “to think ” as anobject of knowledge (4)
References
1.F.Bunyatova. The use of fuzzy logic in educatiotionnal technology and machine
translation.. Copyright Agency of the AzerbaijanRepublic № 328. 01.07.02. Baku.
2.Fatma Khanum Bunyatova Chapter 7 “Logic of Integrity, Fuzzy Logic and Knowledge
Modeling for Machine Education” . in the book "Intelligent Systems" edited by Vladimir
Mikhailovich Koleshko, ISBN 978-953-51-0054-6, 7 2012
http://www.intechopen.com/books/intelligent-systems/logic-of-integrity-fuzzy-
logic-and-knowledge-modeling-for-machine-education
3. The concept of a linguistic variable and its application to making approximate decisions.
M. Mir 1976 Lotfi Asker Zade Понятие лингвистической переменной и его применение
к принятию приближенных решений..
4. JEAN PIAGET: THEORY, EXPERIMENTS, DISCUSSIONS. MOSCOW 2001
5.F.Bunyatova .Constructive teaching.:root , principles, problems and examples from lessons.”
Baku 2008
6.Topic 15 Modeling as a method of knowledge. Classification and forms
model viewshttps://www.altstu.ru/media/f/Tema-15-Modelirovanie.pdf
