Application Of Set Theory Research Articles

Attribute selection for heterogeneous data based on information entropy

Attribute selection in an information system is one of the important applications of rough set theory. This paper studies attribute selection for heterogeneous data based on information entropy. We first define information entropy in an information system with heterogeneous data and then put forward the notions of joint information entropy, conditional information entropy and mutual information entropy in a decision information system with heterogeneous data. We apply information entropy to perform attribute selection in a decision information system with heterogeneous data. We propose two attribute selection algorithms based on information entropy. Finally, we make experimental analysis and comparisons to illustrate the feasibility and efficiency of the proposed algorithms.

An approach for supplier selection problem based on picture cubic fuzzy aggregation operators

This article is an advanced approach to picture fuzzy set through the application of cubic set theory. For instance, we establish the idea of the picture cubic fuzzy sets (PCFSs) theory and define several operations for PCFS. Also, presented some weighted aggregation operators under picture cubic fuzzy information, so called picture cubic fuzzy weighted averaging (PCFWA) operator, picture cubic fuzzy order weighted averaging (PCFOWA) operator, picture cubic fuzzy weighted geometric (PCFWG) operator, and picture cubic fuzzy order weighted geometric (PCFOWG) operator. Further, we study their fundamental properties and showed the relationship among these aggregation operators. In order to determine the feasibility and practicality of the mentioned new technique, we developed multi-attribute group decision -making algorithm with picture cubic fuzzy environment. Further, the developed method applied to supply chain management and for implementation, consider numerical application of supply chain management. Compared the developed approach with other preexisting aggregation operators, and we concluded that the defined technique is better, reliable and effective.

О криптографических мерах защиты информации при внедрении информационных технологий в решение задач управления в социальных и экономических системах

In theory and in practice, there is uncertainty in the existence of measures for cryptographic protection of information due to the fuzzy legal regulation of the classification of information protection measures associated with the use of cryptographic methods and encryption (cryptographic) information protection tools to ensure the security of data automatically processed in information systems. Cryptographic methods are widely used not only to protect information from unauthorized access, but also as the basis for a number of modern information technologies. The author proposed to introduce the concept of "cryptographic measures of information protection" into scientific circulation, and to include this concept in the basic law on information protection. Information protection in the Federal Law "About Information, Information Technologies and Information Protection" is the adoption of legal, organizational and technical measures. In the article, based on the application of set theory, a model of groups of measures to ensure information security, including cryptographic ones, is proposed.

Application of SET Theory in the Study of Oraon Festivals

Application of SET Theory in the Study of Oraon Festivals

The application of braden scale and rough set theory for pressure injury risk in elderly male population

Background: The elderly with a limited body or bedridden are prone to pressure injury, and the Braden scale is often used as a risk assessment tool. However, few studies have explained the relationship between risk factors and risk levels using machine learning methods from Braden clinical observation data. Additionally, nearly half of the elderly over 75 years old in China are men. Purpose: This study aimed to establish a pressure injury risk prediction model for elderly male patients using a machine learning method based on hospital clinical data. It further analyses the importance of risk factors and risk levels. Methods: This study's Braden observation data were obtained from the electronic medical records of elderly male patients from 27 October 2019 to 1 November 2020 in the case hospital. Rough set theory was used to identify the perception patterns between risk factors and risk levels based on the data. Results: The importance of rough set theory showed that sensory perception and nutrition are key risk factors for identifying elderly male inpatients. Therefore, nurses should pay special attention to the measurement scores of these two risk factors. Moreover, this method also revealed conditions/decision rules for different risk levels. Among elderly male inpatients at risk of severe pressure injury, 42% of the observation data showed that their physical condition is completely limited in sensory perception, possibly insufficient nutrition, friction and shearing problems, and bedridden activities. Conclusion: This model can effectively identify the critical risk factors and decision rules for different risk levels for pressure injury in elderly male inpatients. This allows nurses to focus on patients at a high risk of possible pressure injury in the future without increasing their workload. This study also provides a way to solve the problem that the Braden scale shows insufficient predictive validity and poor accuracy in identifying patients with different pressure injury risk levels, so it cannot fully reflect patients' characteristics.

Invariance of separation in covering approximation spaces

<abstract> In this paper, the invariance of separation in covering approximation spaces are discussed. This paper proves that some separations in covering approximation spaces are invariant to reducts of coverings, invariant to covering approximation subspaces and invariant under <italic>CAP</italic>-transformations of covering approximation spaces. These results deepen and enrich theory of separations in covering approximation spaces, which is helpful to give further researches and applications of Pawlak rough set theory in information sciences. </abstract>

Application of the rough set theory to the analysis of food safety in fish processing

Food safety is a set of conditions and actions that must be carried out during all stages of the food production and trading process in order to ensure the safety and the health of consumers. This also applies to fish processing.Some parasite species which live in fish are especially dangerous to humans. Therefore, the aim of the article was to build a model that would take the biological characteristics of fish as well as environmental data into account and then be used to predict the presence of parasites in raw fish and fish products. Intelligent systems, based on artificial intelligence methods, are ideally suited for this type of task. Rough sets, an artificial intelligence methods was used to build a model with this aim.

An application of soft set theory in decision making problem by parameterization reduction

In this paper, we concentrate the application of parametric reduction of soft set in decision making problem. The main purpose of the paper is to select the key parameters for selection or purchase of objects. Using key parameters person or selection committee will select the optimal choice object. We put forward an algorithm in decision making problem and provide some examples. We focus on parameter reduction of soft set and how it helpful in effective and efficient decision making of the people in a short time.

Capabilities of the Maple computer algebra system in the study of set theory and combinatorics

The basic branch of both discrete and continuous mathematics is Set theory, the study of which is a difficult task. Designed and developed in the Maple computer algebra system, the Maplets package–the set theory application–enables to provide assistance both in teaching (by demonstrating the performance of operations on sets, testing knowledge and skills in using operations), and in studying set theory and solving the simplest combinatorial tasks (can be used as a simulator for students). By using interactive worksheets and animated images in Maple, students are given the opportunity for numerous experiments that will contribute to the development of their math education as well as computational skills. The application will form a sustainable need for the use of computer systems by students in the study of various branches of mathematics.

Multi-criteria decision support systems based on linguistic intuitionistic cubic fuzzy aggregation operators

This article is an advanced approach to linguistic intuitionistic fuzzy variable through application of cubic set theory. For instance, we establish the idea of the linguistic intuitionistic cubic fuzzy variable (LICFV) theory and define several operations for LICFV; also establish a series of weighted aggregation operators under linguistic intuitionistic cubic fuzzy information, so called linguistic intuitionistic cubic fuzzy weighted averaging (LICFWA) operator, linguistic intuitionistic cubic fuzzy order weighted averaging (LICFOWA) operator, linguistic intuitionistic cubic fuzzy weighted geometric (LICFWG) operator, linguistic intuitionistic cubic fuzzy order weighted geometric (LICFOWG) operator, linguistic intuitionistic cubic fuzzy hybrid averaging (LICFHA) operator, and linguistic intuitionistic cubic fuzzy hybrid geometric (LICFHG) operator; and further study their fundamental properties and showed the relationship among these aggregation operators. In order to demonstrate the feasibility and practicality of the mentioned new technique, we develop multi-criteria decision-making algorithm under linguistic intuitionistic cubic fuzzy environment. Further, the proposed method applied to mobile phone selection, consider numerical application of mobile phone. Comparing the proposed techniques with other pre-existing aggregation operators, we concluded that the proposed technique is better, reliable, and effective.

A rough set theory application in forecasting models

This paper introduces the performance of different forecasting methods for tourism demand, which can be employed as one of the statistical tools for time series forecasting. The Holt-Winters (HW), Seasonal Autoregressive Integrated Moving Average (SARIMA) and Grey model (GM (1, 1)) are three important statistical models in time-series forecasting. This paper analyzes and compare the performance of forecasting models using rough set methods, Total Roughness (TR), Min-Min Roughness (MMR) and Maximum Dependency of attributes (MDA). Current research identifies the best time series forecasting model among the three studied time series forecasting models. Comparative study shows that HW and SARIMA are superior models than GM (1, 1) for forecasting seasonal time series under TR, MMR and MDA criteria. In addition, the authors of this study showed that GM (1, 1) grey model is unqualified for seasonal time series data.

Topological structures in rough set theory: A survey

Rough set theory provides a mathematical tool to study vague, imprecise, inconsistent and uncertain knowledge. The topological notions are closely related to the notions and results of rough set theory, so the conjoint study of rough set theory and topology becomes essential. Researchers have widely discussed the topological aspects and their applications in rough set theory. This study highlights the interdependencies of topology and classical rough set theory and the significant work done in this area during the last twenty years.

О проблеме технических мер в системе мер по обеспечению информационной безопасности

In theory and in practice, there is a problem of removing uncertainty in the implementation of technical measures due to the unclear right-hand regulation of classification of measures to ensure the security of data automatically processed in information systems. In the article, based on the application of set theory, it is proposed to remove this uncertainty by selecting groups of measures to ensure the security of information. Information protection in the Federal law "on information, information technologies and information protection" is the adoption of legal, organizational and technical measures. However, in practice, in the system of measures to ensure the information security of objects of protection, they are found not only in a "pure" form, but also in a close relationship, interaction with each other (organizational-legal, organizational-technical, technical-legal), and very often can not be implemented independently.

Rough Set Theory and its Applications: A recent Survey

Rough set theory is a mathematical method proposed by Pawlak . Rough set theory has been developed to manage uncertainties in information that presents missing and noises. Rough set theory is an expansion of the conventional set theory that supports approximations in decision making process. Fundamental of assumption of rough set theory is that with every object of the universe has some information associated it. Rough set theory is correlate two crisp sets, called lower and upper approximation. The lower approximation of a set consists of all elements that surely belong to the set, and the upper approximation of the set constitutes of all elements that possibly belong to the set. The boundary region of the set consists of all elements that cannot be classified uniquely as belonging to the set or as belonging to its complement, with respect to the available knowledge Rough sets are applied in several domains, such as, pattern recognition, medicine, finance, intelligent agents, telecommunication, control theory ,vibration analysis, conflict resolution, image analysis, process industry, marketing, banking risk assessment etc. This paper gives detail survey of rough set theory and its properties and various applications of rough set theory.

Application of Rough Set Theory (RST) to Forecast Energy Consumption in Buildings Undergoing Thermal Modernization

In many regions, the heat used for space heating is a basic item in the energy balance of a building and significantly affects its operating costs. The accuracy of the assessment of heat consumption in an existing building and the determination of the main components of heat loss depends to a large extent on whether the energy efficiency improvement targets set in the thermal upgrading project are achieved. A frequent problem in the case of energy calculations is the lack of complete architectural and construction documentation of the analyzed objects. Therefore, there is a need to search for methods that will be suitable for a quick technical analysis of measures taken to improve energy efficiency in existing buildings. These methods should have satisfactory results in predicting energy consumption where the input is limited, inaccurate, or uncertain. Therefore, the aim of this work was to test the usefulness of a model based on Rough Set Theory (RST) for estimating the thermal energy consumption of buildings undergoing an energy renovation. The research was carried out on a group of 109 thermally improved residential buildings, for which energy performance was based on actual energy consumption before and after thermal modernization. Specific sets of important variables characterizing the examined buildings were distinguished. The groups of variables were used to estimate energy consumption in such a way as to obtain a compromise between the effort of obtaining them and the quality of the forecast. This has allowed the construction of a prediction model that allows the use of a fast, relatively simple procedure to estimate the final energy demand rate for heating buildings.

Knowledge granularity based incremental attribute reduction for incomplete decision systems

Attribute reduction is an important application of rough set theory. With the dynamic changes of data becoming more and more common, traditional attribute reduction, also called static attribute reduction, is no longer efficient. How to update attribute reducts efficiently gets more and more attention. In the light of the variation about the number of objects, we focus on incremental attribute reduction approaches based on knowledge granularity which can be used to measure the uncertainty in incomplete decision systems. We first introduce incremental mechanisms to calculate knowledge granularity for incomplete decision systems when multiple objects vary dynamically. Then, incremental attribute reduction algorithms for incomplete decision systems when adding multiple objects and when deleting multiple objects are proposed respectively. Finally, comparative experiments on different real-life data sets are conducted to demonstrate the effectiveness and efficiency of the proposed incremental algorithms for updating attribute reducts with the variation of multiple objects in incomplete decision systems.

Multicriteria Group Decision-Making for Supplier Selection Based on Intuitionistic Cubic Fuzzy Aggregation Operators

This article is an advanced approach to intuitionistic fuzzy set through application of cubic set theory. For instance, we establish the idea of the intuitionistic cubic fuzzy set (ICFS) theory and define several operations for ICFS ; also establish a series of weighted aggregation operators under intuitionistic cubic fuzzy information, so-called intuitionistic cubic fuzzy weighted averaging (ICFWA) operator, intuitionistic cubic fuzzy order weighted averaging (ICFOWA) operator, intuitionistic cubic fuzzy weighted geometric (ICFWG) operator, intuitionistic cubic fuzzy order weighted geometric (ICFOWG) operator, intuitionistic cubic fuzzy hybrid averaging (ICFHA) operator, and intuitionistic cubic fuzzy hybrid geometric (ICFHG) operator; and further study their fundamental properties and showed the relationship among these aggregation operators. In order to demonstrate the feasibility and practicality of the mentioned new technique, we develop multicriteria group decision-making algorithm under intuitionistic cubic fuzzy environment. Further, the proposed method applied to supply chain management and for implementation, consider numerical application of supply chain management. Also the selected supplier by ICFD aggregation operators is verified by VIKOR method. Comparing the proposed techniques with other pre-existing aggregation operators, we concluded that the proposed technique is better, reliable, and effective.

A Note on Neutrosophic Submodule of an R-module M

The paper focuses on the applications of neutrosophic set theory in the domain of classical algebraic structures, especially R-module. This study discusses some algebraic operations of neutrosophic sets of an R-moduleM, induced by the operations in M and demonstrates certain properties of the neutrosophic submodules of an R-module. The ideas of R module’s non-empty arbitrary family of neutrosophic submodules are characterized, and related outcomes are proved. The last section of this paper also derives a necessary and sufficient condition for a neutrosophic set of an R-module M.

Application of Soft Computing Techniques Rough Set Theory and Formal Concept Analysis for analysing Investment Decisions in Gold-ETF

Complex and noisy financial eco-system requires reliable models and proven techniques to predict the market movements and investor decisions. This study uses competent soft computing techniques: rough set theory (RST) and formal concept analysis (FCA) to study the investors' preferences, behavioural drivers and their actual behaviour in Gold-ETF (G-ETF) market. G-ETF, though a safe-haven and an alternate for reducing portfolio risks, inherits all complexities of financial markets. The employed RST helps in generating decision rules; and FCA to identify key factors affecting investment decision. This study is first of its kind, as integration of the foresaid techniques was not employed to study financial behaviour, earlier. The study has analysed 250 responses of G-ETF investors, in 12 listed G-ETFs, to conclude with a rich insight on the investment decisions discretised by different decision rules, strongly recommending the combined use of RST and FCA for data driven decisions.

Determination of the type of repair work based on the results of survey and monitoring of the technical condition of buildings

This article is devoted to structural scrutiny of a building. The technical condition of buildings affects such characteristics of a building as safety, reliability, durability and maintainability. However, in the absence of reliable information on the technical condition of buildings, structural survey or monitoring of а building in order to determine the category of technical condition is necessary. The purpose of this work is to develop an economic and mathematical model for determining the type of maintenance work based on the results of structural scrutiny and monitoring of a building. The article is of importance because the final stage of the survey gives a qualified opinion on the level of structural scrutiny of a building, and on the basis of this opinion repair work eliminating physical and moral deterioration and providing in accordance with specifications renovation of the building are planned. The scientific novelty of the economic and mathematical model developed by the authors on the results of building structural scrutiny lies in the application of the fuzzy set theory and fuzzy logic method for determining of the level of physical and moral deterioration of a building consistent with a certain type of repair work and followed by the necessary capital investments.