On some logical relation properties for rough neutrosophic set

<p>In this study, we give some concepts concerning the neutrosophic sets, single valued neutrosophic sets, interval-valued neutrosophic sets, bipolar neutrosophic sets, neutrosophic hesitant fuzzy sets, inter-valued neutrosophic hesitant fuzzy sets, refined neutrosophic sets, bipolar neutrosophic refined sets, multi-valued neutrosophic sets, simplified<br>\nneutrosophic linguistic sets, neutrosophic over/off/under sets, rough neutrosophic sets, rough bipolar neutrosophic sets, rough neutrosophic hyper-complex set, and their basic operations. Then we introduce triangular neutrosophic numbers, trapezoidal neutrosophic fuzzy number and their basic operations. Also some comparative studies between the existing neutrosophic sets and neutrosophic number are provided.</p>

Neutrosophic sets (NSs) handle uncertain information while fuzzy sets (FSs) and intuitionistic fuzzy sets (IFs) fail to handle indeterminate information. Soft set theory, neutrosophic set theory, and rough set theory are different mathematical models for handling uncertainties and they are mutually related. The neutrosophic soft rough set (NSRS) model is a hybrid model by combining neutrosophic soft sets with rough sets. We apply neutrosophic soft rough sets to graphs. In this research paper, we introduce the idea of neutrosophic soft rough graphs (NSRGs) and describe different methods of their construction. We consider the application of NSRG in decision-making problems. In particular, we develop efficient algorithms to solve decision-making problems.

Roughness measures for uncertainty data occur with less consideration since the data involve indeterminacy and inconsistency. The indeterminacy plus inconsistency can be solved by a rough neutrosophic set with roughness approximation. Therefore, a binary logarithm similarity measure for a rough neutrosophic set with roughness approximation was proposed in this research. A rough neutrosophic set was chosen as the uncertainty set theory information, which includes the upper and lower approximation with a boundary set approximation. The objectives of this research are to define a binary logarithm similarity measure for a rough neutrosophic set, to formulate the properties satisfied by the proposed similarity measure, and to develop a decision-making model by using a binary logarithm similarity measure for a case study (COVID-19). The roughness approximation was used in the derivation of the binary logarithm similarity measure. The proving result was finalized. Then, the derivation of binary logarithm similarity measures of a rough neutrosophic set was well defined. As a validation process, the similarity properties for identifying the most important priority group for COVID-19 vaccines were used such as age, health state, women, and job types. Following that, the decision-making for identifying the most important priority group for COVID-19 vaccines is presented.

Graph theory has numerous applications in various disciplines, including computer networks, neural networks, expert systems, cluster analysis, and image capturing. Rough neutrosophic set (NS) theory is a hybrid tool for handling uncertain information that exists in real life. In this research paper, we apply the concept of rough NS theory to graphs and present a new kind of graph structure, rough neutrosophic digraphs. We present certain operations, including lexicographic products, strong products, rejection and tensor products on rough neutrosophic digraphs. We investigate some of their properties. We also present an application of a rough neutrosophic digraph in decision-making.

Rough sets and single-valued neutrosophic sets are mathematical models to deal with incomplete and vague information. These two models can be combined into two frameworks for modelling and processing incomplete information in information systems. Thus, single-valued neutrosophic rough set model and rough single-valued neutrosophic set model are hybrid models, which give more precision, flexibility and compatibility to the system as compared to the classic and fuzzy models. In this chapter, we present rough single-valued neutrosophic digraphs (rough neutrosophic digraphs, for short) and neutrosophic rough digraphs and describe methods of their construction. We consider the concept of self-complementary rough neutrosophic digraphs. We discuss regular neutrosophic rough digraphs. We also give a comparative analysis of rough neutrosophic digraphs and neutrosophic rough digraphs.

Rough set concept is a methodology of information processing for relational databases. It is a unique uncertainty mathematics topic closely connected to fuzzy set theory. When the rough set is combined with neutrosophic set theory, an effective tool for working with indeterminacy arises. In this study, we defined a multi-valued rough neutrosophic set and a multi-valued rough neutrosophic matrix. Using separation measures, we introduced a new approach for a multi-valued neutrosophic with a rough structure. We consider the problem of determining the condition of dengue-affected patients in a specific hospital. Using this method, we create a multi-valued rough neutrosophic decision matrix that clearly displays the relationship between patient conditions and symptoms. We can determine which one has a serious condition by solving this problem and presenting it on the graph.

Soft rough fuzzy sets and soft fuzzy rough sets

During the recent years the smart cities knows a great extension as a modern shape of sustainable expansion. It's a urban area that utilize various devices connected with internet and integrates them with ICTs to promote goodness and execution of services for the best interaction among citizens and city's government. The basic for smart cities is distributed and independent information infrastructure. Using information effectively is going to be a main factor for success in the smart cities. The sources of information's (models, experts, and sensors) must be reason, perfect and complete. The generated information from independent and distributed sources can be imprecise, uncertain, and/or incomplete in real life. Any deficiency in gathered information will have a negative effect on the performance of services and decision making process within smart cities. So, we need a general framework to represent all types of imperfect and incomplete information. Since the classical methods fails to deal with vague, inconsistent and incomplete information, the fuzzy set was introduced to solve this drawback. The fuzzy set was not the perfect method for dealing with these drawbacks because it considers only truthiness and fails to deal with indeterminacy. The efficient mathematical tool for dealing with uncertain, vague and inconsistent objects is rough sets theory which introduced by Pawlak. The theory of neutrosophic rough sets is powerful for dealing with incompleteness and neutrosophic set deals with indeterminate and inconsistent data efficiently through considering truthiness, indeterminacy and falsity degrees. So, in this research we will propose a general framework for dealing with imperfect and incomplete information through using single valued neutrosophic and rough set theories. The combination of two sets will deal with all aspects of vagueness, inconsistency and incompleteness of data and information, and then will enhance the quality of introduced services and decisions from smart cities to their citizens. As experimentation, we applied the proposed framework for modeling imperfect and incomplete data in healthcare field.

Rough set theory for the interval-valued fuzzy information systems

This papers proposes a reflexion on the concept of vagueness. We relate the different kinds of vagueness to relevant mathematical frameworks with particular emphasis on recent works on neutrosophic logic, Dezert-Smarandache theory, and rough sets. The different facets of vagueness are illustrated through a case study on Ambrosia artemisiifolia predictive cartography

Theories of fuzzy sets and rough sets are powerful mathematical tools for modelling various types of uncertainty. Dubois and Prade investigated the problem of combining fuzzy sets with rough sets. Soft set theory was proposed by Molodtsov as a general framework for reasoning about vague concepts. The present paper is devoted to a possible fusion of these distinct but closely related soft computing approaches. Based on a Pawlak approximation space, the approximation of a soft set is proposed to obtain a hybrid model called rough soft sets. Alternatively, a soft set instead of an equivalence relation can be used to granulate the universe. This leads to a deviation of Pawlak approximation space called a soft approximation space, in which soft rough approximations and soft rough sets can be introduced accordingly. Furthermore, we also consider approximation of a fuzzy set in a soft approximation space, and initiate a concept called soft---rough fuzzy sets, which extends Dubois and Prade's rough fuzzy sets. Further research will be needed to establish whether the notions put forth in this paper may lead to a fruitful theory.

In this paper, we study the application of fuzzy set theory, genetic algorithms and rough set theory techniques to the control of the rectifier. A fuzzy adaptive control scheme with the aid of rough set theory via genetic algorithms (GAs) finding the center parameters in place of the classical control is proposed. On the one hand, genetic algorithm gets optimal parameters of an accurate domain model, which tunes the scaling factors of fuzzy adaptive control but is hardly established in a non-liner system. On the other hand, fuzzy adaptive control deals with the dynamics and complexity of responses from rectifier of a HVDC system in the operation points, by adjusting its control parameters with the aid of rough tuner adaptively. Our study includes a brief introduction to fuzzy control and rough set algorithms, both theory and application. We also evaluate the performance of rough fuzzy control by simulation in the paper. The focus of our experiments is on the constant current control in rectifier side of HVDC system. The result shows there are many improvements offered by the fuzzy control scheme based on rough set theory in comparison with the only fuzzy control scheme in the rectifier side of HVDC system.

Theories of fuzzy sets and rough sets are powerful mathematical tools for modelling various types of uncertainty. Molodtsov (Comput Math Appl 37:19–31, 1999 [6]) initiated a novel concept called soft sets, a new mathematical tool for dealing with uncertainties. It has been found that fuzzy sets, rough sets, and soft sets are closely related concepts (Aktas and Cagman in Inf Sci 1(77):2726–2735, 2007 [1]). Research works on soft sets are very active and progressing rapidly in these years. In 2001, Maji et al. (J Fuzzy Math 9(3):589–602, 2001 [5]) proposed the idea of intuitionistic fuzzy soft set theory and established some results on them. Based on an equivalence relation on the universe of discourse, Dubois and Prade (Int J Gen Syst 17:191–209, 1990 [3]) introduced the lower and upper approximation of fuzzy sets in a Pawlak approximation space and obtained a new notion called rough fuzzy sets. Feng et al. (Soft Compt 14:899–911, 2009 [4]) introduced lower and upper soft rough approximation of fuzzy sets in a soft approximation space and obtained a new hybrid model called soft rough fuzzy sets which is the extension of Dubois and Prade’s rough fuzzy sets. The aim of this chapter is to consider lower and upper soft rough intuitionistic fuzzy approximation of intuitionistic fuzzy sets in intuitionistic fuzzy soft approximation space (IF soft approximation space) and obtain a new hybrid model called soft rough intuitionistic fuzzy sets which can be seen as extension of both the previous work by Dubois and Prade and Feng et al.

Based on rough set and basic theory of data fusion, the data fusion algorithm combining rough set theory and BP neural network is studied. Since rough set theory can effectively simplify information, cut down the tagged dimension . This paper will be rough set theory and neural networks combined, using channel capacity of knowledge relative reduction algorithms to simplify the input information. Rough set theory is first used to process the sample data, and eliminate the redundant information, then reduce the scale of neural network, improve the identification rate, and improve the efficiency of the whole data fusion system. The effectiveness of the improved algorithm is demonstrated by an example compared with the traditional neural network system.

With the requirements of the power load predicting accuracy becoming higher and higher, and the actual power load is also a complex nonlinear system limited by various uncertain factors. Given only considering the influence of a single model on the load forecasting, the predicting accuracy is absolutely not high under the comprehensive effects of multiple factors. Ensuring to make the electrical model satisfy the requirements, there is access to improving the accuracy of load predicting results through analysis of the relationship between load and multiple factors in power load forecasting. This paper combines the rough set theory with information fusion, firstly a decision table of attributes is established on the basis of historical datum, for the purpose of simplifying the attribute index in mining to obtain important information. Following step is to rank the importance of the factors influencing the load according to the degree of effect, with grouping these sorted factors into attributes combination and using the same kind of load forecasting method to predict each combination's own results, and finally all groups of the predicting results are integrated by fusion, where then final predicting result can be obtained. The results of the algorithmic example show that groups of predicting results integrated based on information fusion theory are better than the results got through any casual single attribute combination. And fusion results are a combined action of a variety of related factors, enhancing the favorable trend, where at the same time it has reduced the uncertainty brought by multiple factor comprehensive effect. Based on information fusion the predicting results are helpful to reduce the prediction error, which is feasible and effective. With the explosive growth on the amount of in today's information age, the wave of data is coming, fast and furious. The era of big proposes a new challenge for the development in electricity industry. With the advance of electricity industry, intelligence, automation and interaction will bring many datum casing electrical big generation. Due to the numerous index of power load forecasting, different goals of all kinds of power load forecasting, even with the same kind of theory, the forecast model to predict no matter from the form, content or effect also vary widely. The load in the medium and long-term prediction of power system is greatly influenced by economy, society and meteorology factors and other uncertainties, etc. How to extract the key factor from multiple factors and reduce the results' uncertainty arising from the comprehensive effect of multiple factors, and improving the precision has been becoming a serious problem to be solved. Aiming at these problems, the paper based on the literature (8) proposing medium-and long- term load forecasting based on partial least squares regression analysis, an more optimized and advanced method is put forward to improve accuracy of prediction. The rough set theory and information fusion are introduced into the model, which respectively advance pre-processing and optimize the integration of multiple sets of results after prediction, in order to reduce uncertainty caused by varieties factors affecting and improve accuracy of forecasting results. II. THE ROUGH SET THEORY In the era of big data, on account of the characteristics on grid volume, which is large amount, variety type, and more speed, the traditional attribute simplified methods have been unable to complete the pre-processing on electrical big data. To this end the paper proposes a method on power big simplified processing based on cloud computing technology. The rough set theory which offers a new way for mining, is a new mathematical tool to deal with uncertain and imprecise problems. In this paper, rough sets method is used in power load forecasting to analyze the dependence of load on each factor and the importance of various properties in condition attribute set. In the decision system R={U, A}, the rough set divides A(attribute) into two categories C and D, where C is condition attribute, D is decision attribute, and U is domain. The ternary collection R={U,C,D} is known as a decision-making system. An important application of rough set in the analysis is to find the dependence among attributes from a known decision system R={U,C,D}. The dependency is defined as follows.