The modern approaches to the classification of satellites was analyzed, the relevance of the use of the fuzzy logic apparatus and the main stages of solving the given problem using the theory of fuzzy sets was determined. The features of the classification of satellites, which can be obtained both from the analysis of a priori and a posteriori information about satellites, and can be numerical, categorical or linguistic, was determined. The need to define linguistic variables and their linguistic terms for those features of the classification of satellites that can be presented in a linguistic form was substantiated. The choice of the method of constructing the membership function of a fuzzy set of defined features of the satellites classification, which can be presented in a linguistic form, was justified. Further steps to solve the problem of satellites classification based on fuzzy logic was outlined: building a system of fuzzy rules for satellites identification and creating a fuzzy knowledge base for their classification.
The composition of the space systems of the world’s leading states that carry out space activities is actively changing today. The number of satellites is increasing, their functional capabilities are improving due to the development of the material, technical and scientific base.
Considering the martial law introduced in Ukraine from February 24, 2022, space support and, in particular, space situational awareness (space situation analysis) is an urgent need in the process of planning the activities of national security and defense entities, which requires a clear classification of satellites, which is determined by their purpose.
A clear understanding of the purpose of satellites allows you to take into account the peculiarities
of their functioning and influence on various spheres of activity of state authorities, especially to
ensure the national security and defense of Ukraine [
The development of technologies and the appearance of new satellites may require the expansion of existing classification features, that is, such as the satellites classes defined for a certain period of time which are not static. Under such conditions, classification features obtained from both a priori and a posteriori information about satellites can be numerical, categorical or linguistic.
Taking into account heterogeneous features requires the use of appropriate mathematical apparatus, which will allow them to be formalized for the further classification of satellites, which is an current scientific task.
Many scientific works are devoted to the issue of object classification. Diferent approaches have
been proposed to solve the classification task, for example, using of the backpropagation algorithm
of artificial neural networks for the classification of GPS satellites and the calculation of geometric
accuracy coeficients of their positioning [
But most of the attention is given to the classification of satellites from the point of view of their further application or the use of data that can be obtained from satellites.
Thus, the classification of GPS satellites using improved learning algorithms is considered to solve the
problem of calculating the geometric accuracy coeficients of GPS satellites positioning [
In Ukrainian works, options for the satellites classification are considered using the example of species
observation satellites based on the analysis of their features and the systematization of information
about space systems, a generalized classification of satellites is proposed [
Thus, in modern scientific works, the results of research on the classification of satellites by individual features are reflected, and the specified task by a set of features is almost not considered.
In the case when there is no clear boundary separating the classes (for example, heterogeneous
features belong to several classes), the approach using fuzzy logic [
The purpose of the article is to determine the linguistic variables and the membership function of a set of features for the further satellites classification using the theory of fuzzy sets.
In the modern conditions of using information about the state and changes of the space situation,
there is an urgent need for reliable and complete information about the purpose of satellites, which is
complicated by certain limitations in the use of measuring tools, etc. [
In order to increase the accuracy of determining the purpose of satellites, the reliability of their classification, it is proposed to use the mathematical apparatus of the theory of fuzzy sets to classify satellites based on a priori and a posteriori information that can be obtained from open sources.
The initial stage in the task of satellites classification using fuzzy set theory is the determination of the features of satellites that will be used for classification. These features can be numerical, categorical or linguistic.
It is possible to classify satellites according to the information that precedes their launch and the information that is available for analysis after the launch. Thus, it is possible to distinguish a priori (pre-launch) and a posteriori (post-launch) features of classification, which, in turn, can be direct and indirect [18].
The initial information before launch for classification is the satellite launch plan. Information from the satellite launch plan can be interpreted accordingly to table 1.
After launch, the satellite classification is refined based on the use of a posteriori information and its orbital parameters obtained from oficial sources or from measuring devices.
Taking into account that all features are diferent, it is possible to obtain a generalized conclusion and make a decision regarding the belonging of satellite to a certain class with a certain degree of truth using a mathematical apparatus of fuzzy derivation.
The problem of data classification can be solved by the fuzzy inference system, which is based on the algorithm of obtaining fuzzy conclusions based on fuzzy premises using concepts of fuzzy logic [16]. The process of fuzzy derivation combines the main concepts of fuzzy set theory: membership functions, linguistic variables, fuzzy logical operations, methods of fuzzy implication, and fuzzy composition [18].
The general scheme of the fuzzy inference system is presented in figure 1.
Fuzzy inference systems are defeaturesed to transform the values of input variables into output variables based on the use of fuzzy rules. For this, fuzzy inference systems should contain a base of fuzzy rules and initial term sets [18].
The main stages of fuzzy derivation (figure 1) are [18]: • fuzzification of input variables; • aggregation of preconditions in fuzzy rules; • activation or composition of subconclusions in fuzzy rules; • accumulation of conclusions of fuzzy rules.
In general, the classification of objects based on fuzzy logic is a complex process and requires a large amount of input data, but the main advantage of applying the proposed approach is the ability to use information that may be fuzzy, but still useful for decision-making.
Consider the first stage of the process of fuzzy derivation – fuzzification of input variables – establishing correspondence between the specific (usually numerical) value of a separate input variable of the system of fuzzy derivation and the value of the membership function of the corresponding term of the input linguistic variable. After that, specific values of membership functions for each of the linguistic terms used in the prerequisites of the fuzzy inference system rule base must be determined for all input variables [18].
Formally, the fuzzification procedure is performed as follows. At the beginning of fuzzification, the specific values of all input variables of the fuzzy inference system are determined, that is, the set of values = 1, 2, ..., .
In the general case, each ∈ , where is the universe of the linguistic variable .
Next, we consider each of the subconditions of the form ∈ of the fuzzy derivation system rules, where is some term with the corresponding membership function (), which can be analytically specified, for example, in the following form: or
⎧ (, , ) = ⎨
⎧ (, , ) = ⎨ ⎩ ⎩
1, ⩽ ⎫ −− , < < ⎬ , 0, ⩽ ⎭ 1, ⩽ ⎫ −− , < < ⎬ . 0, ⩽ ⎭
At the same time, the value is used as an argument of () and the quantitative value is found, which is the result of fuzzification of the subcondition.
The specified approach can be used to solve the task of satellites classification taking into account the majority of disparate features.
Suppose that the launch of the ViaSat 3.2 satellite (ViaSat 3 EMEA) is planned for 2024, which is about 6.4 tons, using an Atlas-5 launch vehicle in an orbit with an altitude of about 35,790 km [19].
For example, consider the features “Type of launch vehicle” and “Type of orbit”, which are indirect linguistic a priori features for further classification of the satellites.
Correspondence between the type of launch vehicle and its payload is shown in table 2 [19, 20, 21]. Correspondence between the type of orbit and its altitude is shown in table 3 [19, 20, 21].
Let’s define the linguistic variable “Type of launch vehicle” as 1. Then “Small, Medium, Heavy, Overweight” will be the set of terms 1 of this linguistic variable 1:
1 = {, , , ℎ} .
The set of all ranges of values of the variable 1: 1 = [0, > 50] . (4)
The set of all ranges of values of the variable 2: 2 = {, , ℎ} .
Consider the process of fuzzification of four fuzzy statements for the input linguistic variable 1 – “Type of launch vehicle”: “Type of launch vehicle small”, “Type of launch vehicle medium”, “Type of launch vehicle heavy”, “Type of launch vehicle overweight”. The fuzzification of the first fuzzy statement gives the value “0”, which is obtained by substituting the value 1 = 6.4 into of the argument of the membership function. The fuzzification of the second fuzzy statement gives the value “0.24”, which is obtained by substituting the value 1 = 6.4 into the argument of the function accessories. The fuzzification of the third and fourth fuzzy statement gives the value “0”, which is obtained by substituting the value 1 = 6.4 into the argument of the function accessories. The result of fuzzification for the input linguistic variable 1 on figure 2. (5) (6)
Consider the fuzzification process of three fuzzy statements for the input linguistic variable 2 – “Type of orbit“: “Orbit type is low”, “Orbit type is medium”, “Orbit type is high”. The fuzzification of the first and second fuzzy statements gives the value “0”, which is obtained by substituting the value 2 = 35790 to the argument of the membership function for linguistic variable “Orbit type is low” and “Orbit type is medium”. The fuzzification of the third fuzzy statement gives the value “0.84”, which is obtained by substituting the value 2 = 35790 to the argument of the membership function for linguistic variable “Orbit type is high”. The result of fuzzification for the input linguistic variable 1 on ifgure 3.
With the known values of the variables “Payload weight” = 6.4 tons and “Orbital height” = 35790 km, a preliminary conclusion can be made about the type of launch vehicle that can be used during the launch of the satellites and the likely type of orbit to which it will be possible the satellites will be launched.
Thus, using the theory of fuzzy sets, the linguistic variables of some features of the satellites classification were formalized and an example of the calculation of their membership functions was given. The following steps in the classification process are: 1) finding the degrees of truth of the simplest statements based on the given values of the input parameters; 2) calculation of the truth of the prerequisites of the rules; 3) determination of membership functions of each of the conclusions for the general linguistic variable; 4) unification of membership functions through the construction of their maximum; 5) obtaining a specific value of the output variable.
The proposed approach can be used to solve the problem of complex classification of satellites, taking into account the majority of heterogeneous features.
The author’s contribution to the article is distributed as follows: • Conceptualisation of reseach, formulation of the research idea, Dmytro V. Pekariev and Iryna A.
Bespalko; • Formal analysis, preparing data for analysis, Leonid M. Naumchak; • Research of satellites classification, Leonid M. Naumchak; • Methodology for defining linguistic variables and terms, Iryna A. Bespalko and Leonid M. Naumchak; • Project administration, Ihor A. Pilkevych; • Software of modeling membership function, Iryna A. Bespalko; • Supervision throughout the research process, Ihor A. Pilkevych and Dmytro V. Pekariev; • Writing – original draft, Iryna A. Bespalko and Leonid M. Naumchak; • Writing – review and editing, Iryna A. Bespalko. [15] A. V. Ryabko, O. V. Zaika, R. P. Kukharchuk, T. A. Vakaliuk, V. V. Osadchyi, Methods for predicting the assessment of the quality of educational programs and educational activities using a neurofuzzy approach, CTE Workshop Proceedings 9 (2022) 154–169. doi:10.55056/cte.112. [16] O. Khorozov, Application of fuzzy logic for telemedicine systems, Kybernetyka y vychyslytelnaia tekhnyka 2 (2017) 36–48. doi:10.15407/kvt188.02.036. [17] O. Pisarchuk, Modeling of situational management and identification processes in energetic information and management systems, Bulletin of ZhSTU, Technical sciences 71 (2014) 98–105.
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htm. [21] European Space Agency, Types of orbits, 2023. URL: https://www.esa.int/Enabling_Support/Space_ Transportation/Types_of_orbits.