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Assabayev Rauan Assetuly, Abiyr Maira Meirbekkyzy
Kazakh-British technical university
Faculty of information technologies
Kazakhstan , Almaty
Abstract: This article describes the use of fuzzy logic to solve machine learning problems. The methods of fuzzy logic, the theory of fuzzy sets and relations are currently widely used in modeling control and recognition systems, that is, where it is necessary to assess the situation and make a decision in conditions of inaccurate information or in the presence of fuzzy goals and restrictions. The apparatus of fuzzy mathematics allows you to formalize and transform quantitatively fuzzy (qualitative) concepts that an expert operates when describing their ideas about the real system, their wishes, recommendations, and management goals. The precondition for the creation of the theory of fuzzy sets was that the human mind, in contrast to the machine, operates in assessing situations with fuzzy categories. Therefore, when developing and creating automated control systems, recognition and decision-making, the use of a fuzzy approach provides a number of advantages, and sometimes is the only possible one. Fuzzy logic is a superset of traditional logic that has been extended to handle the notion of partial truth values ​​between the Boolean function of true and false. Fuzzy logic usually takes the form of a fuzzy system of reasoning, and its components are fuzzy variables, fuzzy rules and fuzzy inference mechanisms.
Key words: Fuzzy sets, fuzzy logic, machine learning systems, artificial intelligence, model optimization.
            The knowledge that a person has to some extent is always incomplete, approximate, not reliable. Nevertheless, on the basis of such knowledge, people manage to draw reasonably grounded conclusions and make reasonable decisions. Therefore, for intelligent information systems to be really useful, they must take into account the incomplete certainty of knowledge and operate successfully in such conditions [1]. Thus, incomplete certainty and vagueness of existing knowledge is more a typical picture when analyzing and assessing the state of affairs, when drawing conclusions and recommendations, than an exception. In the process of research on artificial intelligence, several approaches have been developed to solve this problem.
            One of such approaches is L. Zadeh's fuzzy logic. In his work the concept of a set was extended by the assumption that the function of an element's membership in a set can take any values in the interval [0..1], and not just 0 or 1. Such sets were called fuzzy. Also L. Zadeh proposed logical operations on fuzzy sets and proposed the concept of a linguistic variable, the values of which are fuzzy sets.
            The fuzzy logic model makes it possible to implement intellectual functions in the system based on the analysis of incomplete information about the subject area, and to build a convenient user interface in which the data output has such similarities to the results of human reasoning as proximity, uncertainty and subjectivity. In addition, due to the continuity of the membership function, there are advantages in data processing speed. The functional diagram of the fuzzy inference process is shown in Figure 1.
Figure 1: Functional diagram of the fuzzy inference process
Source: Authoring
Fuzzy models have a number of features in comparison with traditional ones, the most significant of which are:
  • fuzzy models are more flexible, since they allow to take into account the experience and intuition of a specialist in a certain area to a greater extent;
  • fuzzy models of control and recognition of complex systems are more adequate to the simulated reality and allow obtaining a solution in terms of accuracy correlated with the initial data;
  • fuzzy models in some cases require less time to obtain a result;
  • fuzzy models allow to increase the speed of processing high-quality information when using relatively simple specialized devices;
  • fuzzy models are created in cases when the construction of clear ones is impossible or difficult.
A fuzzy approach to modeling control and recognition systems has the following distinctive features:
  • it uses so-called "linguistic" variables, instead of numeric variables or in addition to them;
  • simple relationships between variables are described using fuzzy statements;
  • complex relations are described by fuzzy algorithms [2].
The theoretical basis for the use of fuzzy approaches in modeling control and recognition systems is a well-developed apparatus of fuzzy mathematics, including fuzzy arithmetic, fuzzy and linguistic logic, theory of possibilities.
Intelligent systems for processing and representing knowledge are developing along the path of integrating symbolic and figurative representations of scientific knowledge. This direction in knowledge engineering in combination with advanced hardware and software multimedia is of great practical importance, especially at the stage of translating paper documents into their computer equivalents. In this case, problems arise associated with the forms of knowledge representation, with the construction of the user interface, with the recognition of the entered information, with the provision of a high speed of its search and processing.
In connection with a significant increase in the volume of information systems (in local networks, in electronic libraries, electronic catalogs, etc.) and the limited capabilities of tools for navigation and information retrieval, the tasks of developing new approaches and increasing the efficiency of existing methods of information retrieval are becoming urgent. Recently, research in this area has been actively carried out in Ukraine and abroad. The following main directions of these studies can be distinguished:
  • extraction of information objects from documents, determination of their characteristics (statistical, linguistic, semantic);
  •  building the semantic structure of documents;
  •  thematic analysis and thematic search for information in the repository of documents;
  •  thematic classification, clustering and filtering of documents.
When solving the listed tasks, elements of information systems theory, the apparatus of graph theory, and fuzzy mathematics, decision theory are used.
In this regard, the problem of designing artificial intelligence systems using fuzzy logic is extremely relevant. The paper proposes one of the approaches to solving this problem.
Clear and fuzzy graphs are widely used as models for the representation and transformation of knowledge in intelligent systems for information processing, control, recognition, forecasting, training and other artificial intelligence systems. The language of clear and fuzzy directed graphs is convenient not only for representing knowledge, but also for a mathematically correct solution of the problem of semantic information compression with a fuzzy analogy based on a fuzzy homomorphism of a general type. The questions of homomorphism of fuzzy graphs are obviously applicable to the study of homomorphisms of fuzzy hypergraphs, since any fuzzy hypergraph can be uniquely represented by a fuzzy bipartite or König graph, as well as a fuzzy vertex adjacency graph and a fuzzy edge adjacency graph.
When developing highly professional intelligent decision-making, control, recognition systems, the knowledge representation models of which are built on the basis of situational-frame networks, and even more so when developing global intelligent systems using hybrid knowledge models to transform conceptual concepts, it is necessary to be able to quickly, albeit approximately evaluate the influence of certain facts on the behavior of the system in the world around it. In order for the forecast and assessment to be effective, in the knowledge base of such an intelligent system, in addition to the usual and fuzzy inference, it is desirable to have an accelerated inference. As such a logical conclusion, it is proposed to use an inference based on a fuzzy analogy. The word analogy is understood as such a form of inference, in which, on the basis of the similarity of two objects, phenomena or concepts in some respect, a logical conclusion is made about their similarity in another respect. Fuzzy analogy means the following. Let there be a model of the initial knowledge base, given in the form of a fuzzy graph and one or more fuzzy homomorphic images of it. To obtain a conclusion based on a fuzzy analogy of a linear type, it is necessary to establish a fuzzy isomorphism, if it exists, of the original model of the system and its fuzzy isomorphic image, that is, find fuzzy substitutions that transfer one model to another and paths of the same length from the initial vertex to the final one in an isomorphic image and the original model. These paths correspond to inference by a fuzzy linear analogy. The essence of a fuzzy nonlinear, more precisely, homomorphic, analogy is that if there is a homomorphism between the graph of a model of the original knowledge base and its fuzzy homomorphic image, then you can build a fast, but rather rough express inference based on the homomorphic image of the system, and then, having determined the effective direction search. solutions, it is possible to refine it using inference in a certain area of ​​the original knowledge base. The procedure for refining the obtained solution is repeated the required number of times [3].
In this case, logical inference can be understood as various methods, for example, such as inference based on a compositional inference rule, inference based on generalized rules modus ponens and modus tollens, arising from conditional fuzzy inference, or inference based on recognition of fuzzy reference situations. When implementing fuzzy inference in systems of fuzzy implicative rules and fuzzy descriptions of situations, the stage of logical inference is preceded by the stage of identifying the input fuzzy situation, at which, if required, quantitative information is converted into its qualitative description. In other words, a transition is made from the numbers characterizing the parameters of the decision-making object to the corresponding fuzzy sets. Fuzzy sets obtained as a result of fuzzy logical inference can be interpreted depending on the established requirements, either by their linguistic approximation, that is, by the description of linguistic variables, or by transition to specific numbers characterizing the parameters of the decision. In both cases, it is required to perform a number of special operations and transformations on fuzzy sets.
Operations on fuzzy sets are of a specific nature, due, on the one hand, to the need to perform mass transformations on the sets of their vector representations, and on the other, to their relative simplicity (the most frequently used operations are reduced to pairwise execution of operations on the elements of two fuzzy sets for determining the maximum and minimum ).
The use of the proposed method of inference based on fuzzy homomorphism will significantly increase the intellectual capabilities of existing and developed hybrid and global intelligent decision-making systems.
Successful applications of fuzzy logic and fuzzy algorithms lie in the field of building decision-making systems and managing complex technological and organizational processes. Since these systems are human-machine, the time of their reaction to the user's request is strictly limited by the psychological characteristics of the dialogue. Control of technological processes should naturally occur in real or accelerated time.
For practical tasks, the amount of processed fuzzy information is usually significant, and one of the main operators for processing fuzzy information is memory access and checking logical conditions. In this regard, there may be cases when the software implementation of fuzzy algorithms does not meet the requirements for a comfortable user experience, or the requirements of the technological process regarding the decision-making time and must be supported by hardware.
Research carried out in the field of fuzzy information processing has shown that the basic operations of fuzzy logic used to transform fuzzy sets have natural parallelism, since they are performed on each element of the fuzzy set independently of each other. In addition, in fuzzy algorithms, the operations applied to all elements of a fuzzy set are, in most cases, the same or the same type at each specific step. And finally, regardless of the basis of the operations used, more complex operations are formed as a collection of several simple operations.
For hardware support for the inference of decisions in systems called situational, it is proposed to use the ideology of vector or matrix processors used independently or as a coprocessor. Decision inference in such systems is based on fuzzy recognition of input information by comparing its description with descriptions of reference fuzzy situations that characterize the state of the decision-making object. Fuzzy situational inference of decisions is quite simple to implement and, at the same time, has a number of advantages over compositional inference:
  • no need to perform linguistic interpretation of the resulting composition of fuzzy sets;
  • reducing the amount of stored information, since for the implementation of fuzzy compositional inference it is necessary to store at least one matrix of the fuzzy “input-output” relationship for each rule, or to obtain them in the process of solving;
  • simplicity of hardware implementation, since fuzzy situational inference is reduced to the definition of fuzzy proximity of pairs of fuzzy sets of the second level.
A parallel fuzzy inference processor can process fuzzy information specified directly on the verbal scale, bypassing the first (subject) level of processing. At the same time, the option of using a fuzzy processor in a single-level inference scheme that does not use a verbal scale of feature values is allowed.
Compared to the available processors of fuzzy compositional decision inference, the speed of fuzzy logical situational inference in a parallel fuzzy processor increases three times with a two-level inference scheme and an order of magnitude with a single-level inference scheme and reaches 200 thousand logical inferences per second. The same temporal relationships are preserved when the fuzzy compositional inference of solutions is implemented on a fuzzy processor. In addition, the scope of the set of reference situations used by the proposed fuzzy processor is limited only by the technological capabilities of its manufacturer, since the reference situations are stored in external memory and do not affect the timing of the processor. The basis of fuzzy logical operations, unlike known processors, is not essential for the architecture of a parallel fuzzy inference processor. When the basis of fuzzy logical operations changes, only the architecture of the elementary processor changes [4].
The fuzzy inference coprocessor is intended for hardware support of decision-making systems. It can also be used as a fuzzy controller of complex technical objects, technological processes and robotic systems, accelerators of expert and predictive systems operating on the basis of fuzzy logic.
In the developed countries of the world, work is being intensively carried out on the practical implementation of fuzzy controllers and regulators, on the creation of intelligent control systems based on them, expert systems with fuzzy logic in the industrial and non-industrial spheres. To date, more than 400 practical applications of fuzzy controllers and control systems are known. According to experts, in the coming years, about 70% of all developments on intelligent systems will be based on fuzzy logic. Despite various architectural solutions and the associated different speed of the software and hardware tools for processing fuzzy knowledge developed and being developed at present, all of them are united by an orientation towards the implementation of one of the possible modifications of fuzzy inference algorithms, namely, compositional inference. This algorithm is effectively used in systems of fuzzy control of dynamic objects operating on the principle of a regulator. At the same time, the vast class of systems based on decision-making and situational management is not covered at all. For the design and programming of fuzzy processors used in such systems, as well as in control systems for dynamic objects, the software and hardware complex FuzEx - FuzCop can be used [1].
FuzEx is an integrated system design complex based on fuzzy knowledge using an accelerator or its software emulator for efficient fuzzy inference. The fuzzy inference accelerator, built on the basis of the FuzCop fuzzy processor, is intended for hardware support of intelligent systems with fuzzy logic, operating both on the basis of fuzzy situational inference and fuzzy compositional inference.
FuzEx contains five main components: a dictionary editor, a production editor, a fuzzy knowledge system constructor, a library of standard modules, and system accelerator support tools. The dictionary editor is used to describe linguistic variables related to the subject area. The production editor allows you to create and modify knowledge base rules. The constructor is intended for setting requirements for the designed system and for assembling executable modules. The library of standard modules contains a set of procedures for information input-output and fuzzy logical inference. The system support for the accelerator is a software shell for the input language compiler, the accelerator firmware loader, and the accelerator emulator. The input language compiler is used to translate a program written in an input language close to high-level languages ​​into fuzzy accelerator microprograms. The firmware loader is used to transfer (load) the received code into the accelerator's own memory. The emulator is designed to execute a sequence of commands of the input language without using an accelerator.
FuzShell system software that is part of FuzEx allows you to load data and internal microinstructions into the internal memory of a fuzzy controller or read them, initialize a fuzzy processor included in the controller to process fuzzy data, configure the processor for one or another type of logical inference, to distribute the internal memory of the accelerator depending on the number of features of the assessment of the current situation and fuzzy productions. The FuzShell software shell has tools for multi-window editing of both the source code of programs and the firmware generated by the compiler. It is possible to configure the I / O ports of the accelerator, read memory cells. The current situation can be entered by transferring data based on the DDE standard from another application (program) that reads information from the input sensors, and then loading the received situation into the controller for processing.
The FuzEx-FuzCop hardware and software complex can be used to build decision-making systems based on fuzzy knowledge, control systems for complex processes and objects, pattern recognition, forecasting, expert opinions, as well as in robotics, medicine, ecology, and household appliances.
In the field of software systems of fuzzy situational control and decision-making, the following results were obtained:
  • a decision-making system based on fuzzy knowledge has been developed to control the launch - release for metallization and cutting in the production of precision resistors (implemented at one of the enterprises of the electronic industry);
  • a demonstration prototype of a control system for a robot-manipulator in the “eye-hand” system based on fuzzy recognition has been developed;
  • a system of fuzzy situational management of a section of flexible automated production was developed (implemented at one of the enterprises of electronic
  • a demonstration prototype of the instrumental software complex for supporting the design of intelligent systems based on fuzzy logic was developed;
  • the structure of an intelligent decision-making system for diagnostics and prescription of natural medicine drugs has been developed [3];
  • a fuzzy knowledge base for this system has been developed, built on the basis of a composition of fuzzy meta-implications and on the basis of fuzzy relations on a set of fuzzy situations.
Currently, research and development of economic advisory systems and distance learning systems are being actively pursued. The need for such developments is confirmed both by the presence of a stable demand for them, and by the works that have recently appeared in the scientific literature in Kazakhstan and abroad [5].
In the context of a deep reform of the higher education system, one of the most important issues is to ensure the competitiveness of the university, that is, to ensure high quality training of specialists and create conditions for national and international academic mobility. Entering the world market of educational services is an objective necessity that ensures the competitiveness of the university, requiring the development of methods for assessing the results of pedagogical work and measuring the degree of student learning.
An important feature of the ongoing reform of higher education is the introduction of a certified education quality management system in universities, while universities are given the opportunity to independently choose the forms and pace of reform. The role of the state in this process is the creation of conditions and control over the results of the reform.
The problems of assessing the quality of knowledge and determining the effectiveness of the teacher's activities are relevant for any educational institution, from school to higher educational institution. This explains the large number of developed methods for determining the indicators of student learning and the creation of knowledge control systems using modern information technologies. Computerization in this area helps to reduce the degree of subjectivity in assessing the performance of an educational institution, in determining the effectiveness of each teacher, in determining the degree of learning of each student. The use of modern computer technologies makes it possible to create intelligent systems for controlling the quality of knowledge, taking into account the degree of learning of each individual or their group in specific academic disciplines. The absence of averaging in determining the degree of learning makes it possible to assess the actually achieved learning outcomes and the actual effectiveness of the teacher's activities, that is, to conduct a qualitative monitoring of the educational process.
            The main components of any intelligent system are a knowledge base that adequately reflects objective reality, and a logical conclusion that provides an optimal search for solutions. Unlike a database, information stored in a knowledge base is linked, that is, it is structured. Moreover, this connection is carried out due to those relationships between factors (parameters) that are observed in the control object or in the environment. In knowledge models, relationships are defined by semantics, which is defined outside the system. Such relationships are data in themselves, as are the environmental factors of the domain.
            To build a system for monitoring the educational process, the apparatus of fuzzy mathematics is used, which allows one to formalize and transform quantitatively qualitative (fuzzy) concepts. As you know, a fuzzy approach to modeling intelligent systems has the following distinctive features:
  • it uses so-called “linguistic” variables;
  • simple relationships between variables are described using fuzzy statements;
  • complex relationships are described by fuzzy algorithms
A meaningfully fuzzy algorithm can be defined as an ordered sequence of fuzzy instructions or operators that lead to the solution of a given problem. A fuzzy operator is one that contains at least one fuzzy or linguistic variable, fuzzy function or fuzzy relation.
Building a monitoring system of the educational process includes three main stages.
At the first stage of building the system, learning goals are formulated, that is, a list of knowledge, abilities and skills of students for each discipline is determined. At the same stage, the level of requirements of each teacher is determined. Three levels of requirements are well known. If the teacher works according to the first (highest) level of requirements, then the mark "excellent" is given to the student for the creative application of a well-mastered theory in practice. A teacher working at the second (intermediate) level of requirements gives an “excellent” mark for reproductive skills. A teacher working at the third (lowest) level of requirements gives an “excellent” mark for knowledge of theory without applying the knowledge gained in practice.
At the second stage of building a monitoring system, the degree of student learning in each discipline is determined. The second stage of monitoring also includes mathematical processing of the results of educational activities, which makes it possible to determine the degree of learners' learning, taking into account the level of the teacher's requirements for each discipline. The use of information technology greatly facilitates and speeds up such calculations.
At the third stage of monitoring, the actual effectiveness of the teacher's activities is determined based on the indicators of the degree of learners' learning. The main indicators of the teacher's effectiveness are the strength, depth and awareness of the students' knowledge. The same indicators determine the quality of education.
When building a monitoring system, the main problem is the creation of a knowledge base containing information about the goals of learning, the level of requirements of each teacher, the actual degree of learning of each student and the effectiveness of the teacher.
A system of fuzzy implicative rules (productions) is used as models for representing knowledge of a quantitative and qualitative nature. This system of rules is a set of fuzzy implications of the form: if <premise>, then <conclusion>, possessing the properties of completeness and consistency for an unambiguous description of a given subject area. A situation in this case is a description of the state of an object (for example, a student) at a certain point in time, characterized by a set of features (indicators of the degree of learning). A fuzzy description of a situation is understood as one that reflects not only quantitative, but also a number of qualitative characteristics of the situation. For example, if the level of the teacher's requirements is "average", the number of students with excellent marks is equal to K5, the number of students at “good” is K4, etc., then the student's learning ability (SDA) is determined by the formula:
SDA = ((0,64К5+0,36К4+0,16К3)/N)≤0,64
where N is the total number of students in this discipline for a given teacher, including those who have unsatisfactory grades. Similarly, according to the corresponding formulas, the SDA is calculated for the lowest and highest levels of teacher requirements.
            The actual effectiveness of the teacher's activity (Eph), expressed as a percentage, is determined as follows:
            if the degree of learning is equal to P1 and P2, then Eph≤16;
if the degree of learning is equal to P1 and P2 and P3 and P4, then Eph≤64;
if the degree of learning is equal to P1 and P2 and P3 and P4 and P5, then Eph≤100.
The highest level of teacher requirements ensures a high quality education, characterized by greater strength, depth and awareness.
Inference in a production system is a multi-step procedure for comparing the current description of the situation with the premise of each rule. As a conclusion that changes the current situation at each step, as a rule, the one with the highest degree of truth is used. The result will be that current situation, called the final one, which cannot be modified by any rule with a given degree of truth. The logical inference in the system of fuzzy situations is based on a one-step or multi-step procedure for determining the maximum degree of equality of the initial (current) fuzzy situation with situations taken as reference situations to which the decisions made are assigned. Inference based on fuzzy rules is a generalization of traditional deductive inference (modus ponens rule). It can be implemented in two ways. The first is based on the use of a fuzzy relation R, which is a matrix that formalizes a given system of fuzzy rules. The result of inference is a fuzzy set obtained by the maximin composition of a fuzzy description of the input situation on the matrix R. The second method involves obtaining the same result, but without preliminary convolution of the system of fuzzy rules into the matrix R. The first method requires less memory for storing the original system of rules and significantly less time to implement the inference engine. The second method is justified when, in the process of inference of decisions, fuzzy rules must be modified, and their aggregates must change.
When implementing fuzzy inference in systems of fuzzy implicative rules and fuzzy descriptions, the stage of inference is preceded by the stage of identifying the input fuzzy situation, at which the transformation of quantitative information into its qualitative description is carried out, that is, the transition from numbers characterizing the parameters of an object to the corresponding fuzzy sets is carried out. On the other hand, fuzzy sets resulting from logical inference can be interpreted by linguistic variables or specific numbers characterizing the parameters of the decision. In both cases, it is required to perform a number of special operations and transformations on fuzzy sets.
The proposed construction of a knowledge base based on the composition of fuzzy meta-implications allows storing and processing both clear and fuzzy information from monitoring the educational process, eliminating the subjectivity of assessing the work of an educational institution when determining its status. Using the proposed system makes it possible to assess the level of requirements of each teacher and outline a program for the gradual transition of an individual teacher from a lower level to a higher level of requirements. The ability and desire of the teacher to work at the highest level of requirements is a condition for overcoming formalism in assessing the knowledge, abilities and skills of students and meets the implementation of those social tasks that are determined by the mission of each educational institution.
            Theoretical and practical research of the foundations of designing intelligent systems in the conditions of fuzzy or incomplete, poorly structured information made it possible to solve some of the problems in the organization of electronic archives, in the development of an adaptive user interface for graphic operating systems, in the creation of monitoring systems for the educational process and other practical applications.
The main theoretical and practical results are as follows:
  • features of knowledge representation and logical inference in decision-making and recognition control systems have been investigated;
  • the structure of the monitoring system of the educational process has been developed;
  • principles of building search engines for electronic archives have been investigated;
  • developed an algorithm for extracting terms from text based on morphological information about words;
  • a classification method based on fuzzy sets and fuzzy logic theory has been developed;
  • the analysis of the main stages in the implementation of the system of thematic cataloging of documents was carried out;
  • built a model of the system of morphological analysis.
[1] Brachman R., Sefridge P. Knowledge representation support for data archeology // Intelligent and Cooperative Information Systems. – 1993. – № 2. – P. 113–120.
[2] Miroshnik, M.A. Development of information security tools in distributed computer systems and networks / M.A. Miroshnik // Information and control systems for railway transport, - Kharkiv. - 2015. - No. 1. - P. 18-25.
[3] Miroshnik, M.A. Development of intelligent diagnostic infrastructure in distributed computer systems / M.A. Miroshnik // Ibid. - No. 3. - P. 3-9.
[4] Miroshnik, M.A. Application of software complex for query processing in the database management system with a view of dispatching problem solving in Grid systems / Miroshnik M.A. Kotukh V.G., Selevko S.N. // Telecommunications and radio engineering. – 2013. – Vol.27, № 10. – P. 875-891.
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