Vague Soft Sets Research Articles

Effective vague soft environment-based decision-making

<abstract><p>The soft idea has a crucial impact on facing uncertainty, but extending soft, fuzzy soft, and vague soft settings is more comprehensive in expressing the problem ambiguity parameters than the soft set. Despite this advancement, the vague soft set falls short in addressing certain decision-making issues. This occurs when we have some external factors that can impact our final decision. These external factors can be represented in the effective parameter set. So, the objective of the current article is to incorporate the new concept of effectiveness into the concept of vague sets. This approach leads the researchers to create a novel and expanded framework for effective decision-making, surpassing any previously introduced methods in applicability. The article also provides an exploration of the types, concepts, and operations of effective vague soft sets, each illustrated with examples. Furthermore, the study delves into the examination of properties like De Morgan's laws, distributive, commutative, absorption, and associative properties for those new sets. Moreover, the framework of effective vague soft sets is used to develop a decision-making methodology. This technique simplifies the process of determining whether a student meets the requirements for a particular level of education or if a patient has a specific disease, among other applications. Additionally, to clarify the proposed algorithm, a detailed case study representing how to classify students toward specializations is examined in detail. Using matrix processes in this example, in addition to $ Wolfram \; Mathematica^{\circledR} $, not only renders computations simpler and quicker but also results in more precise optimum effective decisions. In the end, a detailed comparison with existing techniques is performed and summed up in a chart to illustrate the difference between them and the present one.</p></abstract>

Multi-criteria group decision making approach based on a new type of neutrosophic vague approach is used to select the shares of the companies for purchase

In this paper, we introduce the neutrosophic vague soft set, a combination of vague and neutrosophic soft sets. With the help of aggregated operations, we discuss neutrosophic vague soft sets. Multi-criteria group decision making can be evaluated effectively using the VIKOR approach. In this approach, the score function is generated by aggregating the VIKOR method to a neutrosophic vague soft approach. With the help of closeness values, alternative solutions are presented as optimal ones. To invest some money into the top five companies on the stock exchange, an investment company intends to purchase shares of the companies. Their investment strategy was to allocate some of their cash in percentages of 30 dollars, 25 dollars, 20 dollars, 15 dollars, and 10 dollars according to the top five ranked companies to minimize this effect.

Representing complex vague soft set by quaternion numbers

Based on the quaternion system, we give a new representation of the complex vague soft set, and related logical operations. This new representation contains more information than before. Three quaternion distance measures are proposed and a decision model is established. The disease diagnosis of breast cancer is applied to the model to reflect the superiority of the model. By comparing the diagnostic errors under the different distance measures, the most suitable distance measure for this dataset is selected.

Applications on Bipolar Vague Soft Sets

The purpose of this research is to interpolate bipolarity into the definition of the vague soft set. This gives a new more applicable, flexible, and generalized extension of the soft set, the fuzzy soft set, or even the vague soft set, which is the bipolar vague soft set. In addition, types of bipolar vague soft sets, as well as some new related concepts and operations are established with examples. Moreover, properties of bipolar vague soft sets including absorption, commutative, associative, distributive, and De Morgan’s laws are discussed in detail. Furthermore, a bipolar vague soft set-designed decision-making algorithm is provided generalizing Roy and Maji method. This allows making more effective decisions to choose the optimal alternative. Finally, an applied problem is introduced with a comparative analysis to illustrate how the proposed algorithm works more successfully than the previous models for problems that contain uncertain ambiguous data.

Generalized complex vague soft set and its applications

Generalized complex vague soft set and its applications

Development of methods for identifying an appropriate benchmarking peer to establish information security policy

Benchmarking methodology provides organizations with appropriate information security policy. However, selecting an appropriate organization as a benchmarking peer can be a challenge due to firms’ heterogeneous implementation and usage of information systems. Our goal is to develop and propose methods to appropriately identify a benchmarking peer organization by incorporating machine learning methods and mathematics set theory. We incorporate vague soft set, entropy, dynamic time warping, and Gaussian process. We use log data from information security management systems in multiple companies to validate our methods. Our experimental results indicate that the combined use of Gaussian process, vague soft set, and dynamic time warping can be more effective in identifying an appropriate benchmarking peer than conventional machine learning methods.

Transitive Closure of Vague Soft Set Relations and its Operators

Yousef Al-Qudah, Khaleed Alhazaymeh, Nasruddin Hassan, Hamza Qoqazeh, Mohammad Almousa, and Mohammad Alaroud. International Journal of Fuzzy Logic and Intelligent Systems 2022;22:59-68. https://doi.org/10.5391/IJFIS.2022.22.1.59

A new approach to vague soft toplogical structures concerning soft points

This paper concerns the study of the notion of vague soft β-open set and vague soft separation axioms in vague soft topological spaces. By using such notions and that of the vague soft pints, we study the separation axioms βi (with i = 0, 1, 2, 3, 4) in vague soft topological spaces. We give some peculiar examples about them and we prove some relationships between them. The relationship of βi (with i = , 1, 2, 3, 4) spaces with the closer of vague soft β-open set by means of soft points, vague soft countable spaces and their relationship with βi (with i = , 1, 2) spaces by means of soft points are addressed. In continuation, vague soft topological, vague soft inverse topological spaces properties, Bolzano Weirstrass Property(BVP) and its topological characteristics, compact spaces and sequentially compact spaces and their relationship with separation axioms by means soft points are addressed in vague soft topological spaces.

A New Approach to Vague Soft Bi-Topological Spaces

Fuzzy soft topology considers only membership value. It has nothing to do with the non-membership value. So an extension was needed in this direction. Vague soft topology addresses both membership and non-membership values simultaneously. Sometimes vague soft topology (single structure) is unable to address some complex structures. So an extension to vague soft bi-topology (double structure) was needed in this direction. To make this situation more meaningful, a new concept of vague soft bi-topological space is introduced and its structural characteristics are attempted with a new definition. In this article, new concept of vague soft bi-topological space (VSBTS) is initiated and its structural behaviors are attempted. This approach is based on generalized vague soft open sets, known as vague soft open sets. An ample of examples are given to understand the structures. For the non-validity of some results, counter examples are provided to pay the price. Pair-wise vague soft open and pair-wise vague soft close sets are also addressed with examples in (VSBTS). Vague soft separation axioms are initiated in (VSBTS) concerning soft points of the space. Other separation axioms are also addressed relative to soft points of the space. Vague soft bi-topological properties are studied with the application of vague soft open sets with respect to soft points of the spaces. The characterization of vague soft close as well as vague soft open sets, characteristics of Bolzano Weirstrass property, vague soft compactness and its marriage with sequences, interconnection between sequential compactness and countable compactness in (VSBTS) with respect to soft open sets are addressed.

An Absolutely New Attempt to Vague Soft Bitopological Spaces Basis at Newly Defined Operations regarding Vague Soft Points

In this study, new operations of union, intersection, and complement are defined with the help of vague soft sets in a new way that is in both true and false statements, union is defined with maximum, and intersection is defined with minimum. On the basis of these operations, vague soft topology is defined. Pairwise vague soft open sets and pairwise vague soft closed sets are defined in vague soft bitopological structures (VSBTS). Moreover, generalized vague soft open sets are introduced in VSBTS concerning soft points of the space. On the basis of generalized vague soft open sets, separation axioms are also introduced. In continuation, these separations axioms are engaged with other important results in VSBTS.

Path guidance based on landmark user preference fuzzy entropy weight model

Compared with electronic map or static point of interest (POI), the path guidance integrating landmarks with salience features can reduce the cognitive burden better. However, due to the influence of various factors on the significance of landmarks, specific mathematical formulas need to be constructed, and there is no unified formula construction standard. To solve this problem, considering the consistency of the idea between multiple factor comprehensive of landmark and multiple constraint optimal scheme decision of fuzzy decision, this paper constructs a fuzzy entropy weight model of landmark based on user preferences, which the actual values of landmark significance are converted to vague set values, and the weights of landmark factors are determined by fuzzy entropy of Vague soft sets. Subsequently, the landmark preference model and path guidance model are obtained and applied in the case of path guidance. Compared with the mathematical formula, the constructed landmark user preference model by fuzzy entropy of Vague soft sets reduces the construction complexity, and is an effective method to realize landmark preference and apply in path guidance.

애매한 소프트 집합상의 쇼케이 적분과 그 응용에 관한 연구

Wang-Qu [9]는 패턴 인식, 이미지 처리, 근사 추론, 퍼지 제어 등 다양한 분야에서 광범위하게 적용할 수 있는 애매한 소프트 집합의 엔트로피, 유사성 측도 및 거리 측도를 도입했다. 또한, Jang-Kwon [3]에서 처음으로 구간값 함수의 쇼케이 적분을 정의하고 이와 관련된 성질을 조사하였다. 그이후 많은 논문에서 구간값 쇼케이적분의 응용을 연구해 왔다. 애매한 집합의 속성이 구간값 소속함수의 성질을 가지고 있음을 이용하고자 한다. 본 논문에서는 애매한 소프트 집합상에서 쇼케이 적분을 정의하고, 이들 적분에 의해 정의된 구간값 거리 측도를 조사한다.

CUBIC VAGUE SOFT SET AND ITS APPLICATION

CUBIC VAGUE SOFT SET AND ITS APPLICATION

Neutrosophic Bipolar Vague Soft Set and Its Application to Decision Making Problems

In this paper we study the concept of neutrosophic bipolar vague soft setsand some of its operations. It is the combination of neutrosophic bipolar vague setsand soft sets.Further we develop a decision making method based on neutrosophic bipolar vague soft set. A numerical example has been shown. Some new operations on neutrosophic bipolar vague soft set havealsobeen designed.

Operations on vague soft matrices and its applications in decision making

In this paper, we introduce the notion of vague soft matrix to represent vague soft sets in matrix form. By using this representation it is easy to store and manipulate vague soft sets in a computer. We then define basic operations like union, intersection, complement and product of vague soft matrices and their properties. Using vague soft product, we define the score matrix of two vague soft sets which will be useful in decision making problems. At the end, we provide a decision making algorithm using vague soft matrices and applied it for two real life problems.

RELIABILITY EVALUATION IN CONSTRUCTION QUALITY BASED ON COMPLEX VAGUE SOFT EXPERT SET METHOD

The control of the construction quality is very important in the construction industry. In this paper, the fuzzy reliability and construction quality are linked together to establish a specific quantitative evaluation model, which not only can help to make up for the lack of the traditional reliability qualitative evaluation methods, but also can avoid the inaccuracy of fuzzy quantitative evaluation of construction quality to a certain extent. This paper firstly selects some influencing factors of construction quality, and then makes use of complex vague soft expert set theory to study the construction quality and reliability. By the operational relationship and quantitative evaluation index, the membership functions of each subset are obtained, and different evaluation intervals are divided, it is helpful to draw the quantitative evaluation results of quality within a reasonable range and improve the accuracy of the quality and reliability. The presented hybrid method and detailed steps can provide some references for the reliability evaluation of construction quality.

A type of similarity measure for vague soft sets and its application to landmark preference

A type of similarity measure for vague soft sets and its application to landmark preference

Similarity Measure of Complex Vague Soft Sets and Its Application to Pattern Recognition

The precise representation and analysis of complex data sets have become an increasingly important concern in areas such as medical diagnosis, economics, stock market analysis and pattern recognition. The advent of digital technology has resulted in the ubiquity of digitalized images and patterns. Unlike analog images and patterns, digital images and patterns are defined multi-dimensional data that consists of information pertaining to the physical and non-physical attributes of the images. This calls for a suitable complex fuzzy-based model that has the ability to represent multi-dimensional data in a succinct and concise manner. This paper achieves this goal using the complex vague soft set (CVSS) model to represent the multi-dimensional information for digital images. The information measures of CVSSs pertaining to the measures of distance and similarity are then established with the aim of solving pattern recognition problems involving digital images. The axiomatic definition of the distance-based similarity measure of CVSSs is introduced and the relations between this similarity measure and the distance measure of CVSSs are proposed and verified. The utility of this measure is demonstrated by applying it in a pattern recognition problem involving digitalized images that are defined by multi-dimensional data pertaining to the physical features and non-physical features such as the geographical data and timestamp of the images.

Vague Entropy Measure for Complex Vague Soft Sets.

The complex vague soft set (CVSS) model is a hybrid of complex fuzzy sets and soft sets that have the ability to accurately represent and model two-dimensional information for real-life phenomena that are periodic in nature. In the existing studies of fuzzy and its extensions, the uncertainties which are present in the data are handled with the help of membership degree which is the subset of real numbers. However, in the present work, this condition has been relaxed with the degrees whose ranges are a subset of the complex subset with unit disc and hence handle the information in a better way. Under this environment, we developed some entropy measures of the CVSS model induced by the axiomatic definition of distance measure. Some desirable relations between them are also investigated. A numerical example related to detection of an image by the robot is given to illustrate the proposed entropy measure.

A Comprehensive Evaluation Method of Network Public Opinion Based On Similarity Measure Between Vague Soft Sets

Aiming at the limitation of existing similarity measure method based on Vague soft sets, the similarity measure formula between Vague soft sets is modified and a novel similarity measure between Vague soft sets in consideration of the difference of interval center of Vague values is introduced, the axiomatic proof is given too. The experimental results of comprehensive evaluation of the network public opinion show that this method is reasonable, effective and practical, which has a good application prospect and effect in the study of internet public opinion.