Situational solution of the spatial location problem

2018 ◽  
Vol 939 (9) ◽  
pp. 45-51
Author(s):  
V.V. Oznamets
Keyword(s):  
Comparative Analysis ◽  
Fuzzy Sets ◽  
Spatial Information ◽  
Spatial Location ◽  
Linguistic Variables ◽  
Membership Functions ◽  
Fuzzy Information ◽  
Reference Information ◽  
Number Of Factors ◽  
Theory Of Fuzzy Sets

The rational allocation of resources is the basis for sustainable development of the territories. In reality, spatial planning often does not have clear information for decision- making. This factor puts the task of allocating resources under fuzzy information. The author suggests such a placement method. The basis for the solution and analysis is a well-known model of the informational situation. The author develops this concept and introduces a new one, of the informational spatial situation. Fuzzy spatial information makes grounds to introduce a new concept of fuzzy information situation. A comparative analysis is used to solve the problem. At the first stage of the solution, an ideal reference information situation is introduced. This model can not be realized in reality completely. Real conditions differ from ideal ones, therefore in practice there is a set of fuzzy information situations, each of which is close to the reference information situation for a number of factors. For the comparative analysis, the theory of fuzzy sets is applied. The author uses the concepts of linguistic variables and membership functions to describe an unclear information situation. Linguistic variables and membership functions determine for the whole set of fuzzy situations are determined. This approach translates the description of real fuzzy situations into the area of linguistic variables. A new description of fuzzy situations makes it possible to perform analysis using the theory of fuzzy sets. The analysis using the theory of fuzzy sets showed how a situation that maximally satisfies the placement requirements is singled out from a given set. The author proves that optimal solutions do not apply to fuzzy analysis, and that the solution obtained using the theory of fuzzy sets is rational.

scholarly journals RESEARCH OF THE BANKRUPTCY PREDICTION RELIABILITY IN CASE TO INTRODUCE A NEW CATEGORY OF THE COMPANIES FINANCIAL POSITION

2020 ◽  
pp. 105-122
Author(s):  
Aleksandra Noskova ◽  
◽  
Aleksander Alekseev
Keyword(s):  
Fuzzy Sets ◽  
Balance Sheet ◽  
Point Of View ◽  
Linguistic Variables ◽  
Membership Functions ◽  
Financial Position ◽  
Fixed Assets ◽  
Theoretical Significance ◽  
Prediction Reliability ◽  
Accuracy Increase

The motivation for this research was the result obtained earlier by the authors in the field of developing industry models for predicting bankruptcy with high prognostic ability. The article examines the prediction reliability of the financial position of companies in the case of introducing an additional category of financial position that reflects the position between financial solvency and insolvency (bankruptcy). The authors hypothesize that the reliability of models decreases if the requirements for their accuracy increase due to the introduction of an additional category of financial position. Hypothesis testing is performed using a non-entropic approach. This approach should reduce the measure of uncertainty in terms of the uncharacteristic nature of some of the identified features of financial position relative to the initial categories. At the same time, features of financial position are defined as ranges of specific weight of balance sheet items that have positive or negative information importance. Information importance is determined based on the methods of system-cognitive analysis, implemented automatically in the EIDOS X++ system, as well as by reproducing information models using MS Excel tools. Normalization of the informational importance values of features and their interpolation allowed us to obtain functions similar to the membership functions in the theory of fuzzy sets. When constructing membership functions relative to ranges of significant balance sheet items ("Fixed assets", "Inventory", "Accounts Receivable", "Short-Term financial investments", "Retained earnings (uncovered loss)", "Accounts payable"), ranges with zero or insignificant values of characteristic functions corresponding to the initial categories of financial position are identified. This actually meant a high level of uncertainty in the prediction. The authors propose to introduce additional linguistic variables and their corresponding fuzzy sets, whose carriers are the relative scales of the above balance items, this will reduce uncertainty. A total of 5 such fuzzy sets were identified, where the researchers used the concept of "gray zone" as a linguistic variable, which was actually used as a new category of financial position. All calculations are shown on the example of fixed assets. The prognostic ability of models based on an optimized sample, where the category of the position of companies that have at least 3 out of 5 features of the "gray zone" has been replaced, is reduced, as expected, but only slightly. And in the case of reproducing algorithms of system-cognitive analysis using MS Excel tools, there is even an increase in the prognostic ability of one of the models. In fact, the hypothesis that the reliability of models decreases if the requirements for their accuracy increase was not confirmed. From an economic point of view, the theoretical significance of the obtained result is that with the help of a non-entropic approach it was possible to show the need to introduce a new category of financial position. From a mathematical point of view, the theoretical significance lies in the fact that membership functions for linguistic variables are obtained based on real data on the financial position of almost two hundred Russian companies, these reduction functions can be used by specialists in the field of fuzzy set theory in the future. The results obtained are applicable at least for the construction industry, but can also be replicated relative to other sectors of the economy when forming the corresponding samples.

scholarly journals Construction of the method for building analytical membership functions in order to apply operations of mathematical analysis in the theory of fuzzy sets

2018 ◽  
Vol 5 (4 (95)) ◽  
pp. 22-29 ◽  
Author(s):  
Leonid Dykhta ◽  
Nataliia Kozub ◽  
Alexander Malcheniuk ◽  
Oleksii Novosadovskyi ◽  
Alexander Trunov ◽  
...  
Keyword(s):  
Fuzzy Sets ◽  
Mathematical Analysis ◽  
Membership Functions ◽  
Theory Of Fuzzy Sets

scholarly journals METHOD FOR OBTAINING THE PARAMETERS OF MEMBERSHIP FUNCTIONS OF FUZZY SETS BASED ON REAL DATA FOR AUTOMATED INFORMATION PROCESSING SYSTEMS

2019 ◽  
Vol 46 (3) ◽  
pp. 79-86
Author(s):  
E. E. Bisyanov ◽  
A. A. Gutnik
Keyword(s):  
Information Processing ◽  
Fuzzy Sets ◽  
Real Data ◽  
Linguistic Variables ◽  
Membership Functions ◽  
Automated Systems ◽  
Accessory Function ◽  
Different Types ◽  
Automated Processing ◽  
The Membership Function

Objectives Development of a method for selecting the type of accessory function and obtaining its parameters to allow subjective personal influences in automated information processing to be excluded.Method. Existing methods for constructing membership functions were analysed. The research was based on the methods of fuzzy logic and data analysis.Results. A method for obtaining the parameters of membership functions of fuzzy sets using real data is suggested. It is proposed to use the data obtained from the object under study to determine the kernel of the fuzzy number, as well as derive theoretical information about the object for the carrier. Triangular, trapezoidal, bell-shaped and Gaussian membership functions are considered. The appearance of the membership function can be defined using the criterion of the relations of the kernel to the carrier of a fuzzy set. The results of calculations for obtaining the membership functions based on data on the power consumption of electric motors of different types are given.Conclusion. The developed method can be used both in decision support systems as well as in automated systems for controlling technological processes. If necessary, the values of the criterion proposed in the article can be revised to take the values included in the set of measured real data into account or to simplify the procedure of automated processing. Further research will use the described method to obtain the terms of linguistic variables. 

scholarly journals Methods of fuzzy sets theory for statistical analysis of mass service systems.

2020 ◽  
pp. 23-32
Author(s):  
В. Заяць ◽  
O. Рибицька ◽  
Я. Маєвський ◽  
Т. Марциняк ◽  
М. Заяць
Keyword(s):  
Statistical Analysis ◽  
Fuzzy Sets ◽  
Service Systems ◽  
Fuzzy Sets Theory ◽  
Fuzzy Information ◽  
Fuzzy Measures ◽  
Mass Service ◽  
Sets Theory ◽  
Theory Of Fuzzy Sets

Approaches to the processing of fuzzy information are proposed in the conditions of incomplete determination of the vector of input characteristics, which are based on the theory of fuzzy sets and fuzzy measures. Their analysis have been carried out, the limits of their use, and areas of effective application, in particular, regarding mass service systems.

scholarly journals The Formal Construction of Fuzzy Numbers

2014 ◽  
Vol 22 (4) ◽  
pp. 321-327 ◽  
Author(s):  
Adam Grabowski
Keyword(s):  
Fuzzy Sets ◽  
Rough Set ◽  
Fuzzy Numbers ◽  
Membership Functions ◽  
The Core ◽  
Current State ◽  
Fuzzy Objects ◽  
Mizar Mathematical Library ◽  
Theory Of Fuzzy Sets ◽  
Formal Construction

Summary In this article, we continue the development of the theory of fuzzy sets [23], started with [14] with the future aim to provide the formalization of fuzzy numbers [8] in terms reflecting the current state of the Mizar Mathematical Library. Note that in order to have more usable approach in [14], we revised that article as well; some of the ideas were described in [12]. As we can actually understand fuzzy sets just as their membership functions (via the equality of membership function and their set-theoretic counterpart), all the calculations are much simpler. To test our newly proposed approach, we give the notions of (normal) triangular and trapezoidal fuzzy sets as the examples of concrete fuzzy objects. Also -cuts, the core of a fuzzy set, and normalized fuzzy sets were defined. Main technical obstacle was to prove continuity of the glued maps, and in fact we did this not through its topological counterpart, but extensively reusing properties of the real line (with loss of generality of the approach, though), because we aim at formalizing fuzzy numbers in our future submissions, as well as merging with rough set approach as introduced in [13] and [11]. Our base for formalization was [9] and [10].

Hesitant fuzzy β covering rough sets and applications in multi-attribute decision making

2021 ◽  
pp. 1-16
Author(s):  
Jia-Jia Zhou ◽  
Xiang-Yang Li
Keyword(s):  
Decision Making ◽  
Comparative Analysis ◽  
Fuzzy Sets ◽  
Rough Sets ◽  
Fuzzy Information ◽  
Hesitant Fuzzy Sets ◽  
Application Model ◽  
Rough Approximation ◽  
Multi Attribute Decision Making ◽  
The Universe

 In present paper, we put forward four types of hesitant fuzzy β covering rough sets (HFβCRSs) by uniting covering based rough sets (CBRSs) and hesitant fuzzy sets (HFSs). We firstly originate hesitant fuzzy β covering of the universe, which can induce two types of neighborhood to produce four types of HFβCRSs. We then make further efforts to probe into the properties of each type of HFβCRSs. Particularly, the relationships of each type of rough approximation operators w.r.t. two different hesitant fuzzy β coverings are groped. Moreover, the relationships between our proposed models and some other existing related models are established. Finally, we give an application model, an algorithm, and an illustrative example to elaborate the applications of HFβCRSs in multi-attribute decision making (MADM) problems. By making comparative analysis, the HFβCRSs models proposed by us are more general than the existing models of Ma and Yang and are more applicable than the existing models of Ma and Yang when handling hesitant fuzzy information.

scholarly journals Technique for Evaluating the Security of Relational Databases Based on the Enhanced Clements–Hoffman Model

2021 ◽  
Vol 11 (23) ◽  
pp. 11175
Author(s):  
Vitalii Yesin ◽  
Mikolaj Karpinski ◽  
Maryna Yesina ◽  
Vladyslav Vilihura ◽  
Stanislaw A. Rajba
Keyword(s):  
Fuzzy Sets ◽  
Quantitative Evaluation ◽  
Relational Databases ◽  
Database Security ◽  
Convincing Evidence ◽  
Residual Risk ◽  
Linguistic Variables ◽  
Traditional Technology ◽  
Main Components ◽  
Theory Of Fuzzy Sets

Obtaining convincing evidence of database security, as the basic corporate resource, is extremely important. However, in order to verify the conclusions about the degree of security, it must be measured. To solve this challenge, the authors of the paper enhanced the Clements–Hoffman model, determined the integral security metric and, on this basis, developed a technique for evaluating the security of relational databases. The essence of improving the Clements–Hoffmann model is to expand it by including a set of object vulnerabilities. Vulnerability is considered as a separate objectively existing category. This makes it possible to evaluate both the likelihood of an unwanted incident and the database security as a whole more adequately. The technique for evaluating the main components of the security barriers and the database security as a whole, proposed by the authors, is based on the theory of fuzzy sets and risk. As an integral metric of database security, the reciprocal of the total residual risk is used, the constituent components of which are presented in the form of certain linguistic variables. In accordance with the developed technique, the authors presented the results of a quantitative evaluation of the effectiveness of the protection of databases built on the basis of the schema with the universal basis of relations and designed in accordance with the traditional technology of relational databases.

DEVELOPMENT OF VALUATION METHOD OF THE STATUS OF BASE STATIONS FOR DETERMINING THE NEED OF THEIR UPGRADING

2017 ◽  
pp. 60-70
Author(s):  
Natalya Ivanovna Shaposhnikova ◽  
Alexander Aleksandrovich Sorokin
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Cellular Network ◽  
New Technologies ◽  
Base Station ◽  
Base Stations ◽  
Valuation Method ◽  
The Status ◽  
Telecommunications Services ◽  
Theory Of Fuzzy Sets

The article consideres the problems of determining the need to modernize the base stations of the cellular network based on the mathematical apparatus of the theory of fuzzy sets. To improve the quality of telecommunications services the operators should send significant funding for upgrading the equipment of base stations. Modernization can improve and extend the functions of base stations to provide cellular communication, increase the reliability of the base station in operation and the functionality of its individual elements, and reduce the cost of maintenance and repair when working on a cellular network. The complexity in collecting information about the equipment condition is determined by a large number of factors that affect its operation, as well as the imperfection of obtaining and processing the information received. For a comprehensive assessment of the need for modernization, it is necessary to take into account a number of indicators. In the structure of indicators of the need for modernization, there were introduced the parameters reflecting both the degree of aging and obsolescence(the technical gap and the backlog in connection with the emergence of new technologies and standards). In the process of a problem solving, the basic stages of decision-making on modernization have been allocated. Decision-making on the need for modernization is based not only on measuring information that takes into account the decision-makers, but also on linguistic and verbal information. Therefore, to determine the need for upgrading the base stations, the theory of fuzzy sets is used, with the help of which experts can be attracted to this issue. They will be able to formulate additional fuzzy judgments that help to take into account not only measuring characteristics, but also poorly formalized fuzzy information. To do this, the main indicators of the modernization need have been defined, and fuzzy estimates of the need for modernization for all indicators and a set of indicators reflecting the need for upgrading the base stations have been formulated.

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