A new expert system in prediction of lung cancer disease based on fuzzy soft sets

Power Aggregation Operators of Interval-Valued Atanassov-Intuitionistic Fuzzy Sets Based on Aczel–Alsina t-Norm and t-Conorm and Their Applications in Decision Making

Aczel–Alsina t-norm and t-conorm are important t-norm and t-conorm, and they are extended from algebraic t-norm and t-conorm. Obviously, Aczel–Alsina t-norm and t-conorm are more general than some existing t-norm and t-conorm. Furthermore, the power aggregation (PA) operator is also a very famous and valuable operator which can consider the power relation between any two input parameters. In addition, Interval-valued Atanassov-intuitionistic fuzzy set (IVA-IFS) can easily express uncertain information. In order to fully use their advantages, in this analysis, we extend the PA operators based on Aczel–Alsina t-norm and t-conorm to IVA-IFS and propose the interval-valued Atanassov-intuitionistic fuzzy Aczel–Alsina power averaging (IVA-IFAAPA), interval-valued Atanassov-intuitionistic fuzzy Aczel–Alsina power ordered averaging (IVA-IFAAPOA), interval-valued Atanassov-intuitionistic fuzzy Aczel–Alsina power geometric (IVA-IFAAPG) and interval-valued Atanassov-intuitionistic fuzzy Aczel–Alsina power ordered geometric (IVA-IFAAPOG) operators. Moreover, we discuss the properties of the presented operators such as idempotency, monotonicity, and boundedness. In addition, a multi-attribute decision-making (MADM) procedure is proposed to process the IVA-IF information. Finally, a practical example is used to show the effectiveness and superiority of the proposed method by comparing it with some existing operators.

Possibility Fermatean fuzzy soft set and its application in decision-making

This paper aims to introduce a new multiple attribute decision-making model named possibility Fermatean fuzzy soft set (PFFSS), which is a combination of the generalized fuzzy soft sets and Fermatean fuzzy sets. Some operations and properties of the new model, including complement, restricted union, and extended intersection are discussed. Further, an application of PFFSSs is modeled for multiple attribute decision-making and solved with the help of our newly launched algorithm, that is, the selection of the best eco-system model based on a computer simulation report. Finally, a comparative analysis between the initiated PFFSS model and some existing approaches is provided to show its reliability over them.

An improved D-S evidence theory based neighborhood rough classification approach

Neighborhood classifier, a common classification method, is applied in pattern recognition and data mining. The neighborhood classifier mainly relies on the majority voting strategy to judge each category. This strategy only considers the number of samples in the neighborhood but ignores the distribution of samples, which leads to a decreased classification accuracy. To overcome the shortcomings and improve the classification performance, D-S evidence theory is applied to represent the evidence information support of other samples in the neighborhood, and the distance between samples in the neighborhood is taken into account. In this paper, a novel attribute reduction method of neighborhood rough set with a dynamic updating strategy is developed. Different from the traditional heuristic algorithm, the termination threshold of the proposed reduction algorithm is dynamically optimized. Therefore, when the attribute significance is not monotonic, this method can retrieve a better value, in contrast to the traditional method. Moreover, a new classification approach based on D-S evidence theory is proposed. Compared with the classical neighborhood classifier, this method considers the distribution of samples in the neighborhood, and evidence theory is applied to describe the closeness between samples. Finally, datasets from the UCI database are used to indicate that the improved reduction can achieve a lower neighborhood decision error rate than classical heuristic reduction. In addition, the improved classifier acquires higher classification performance in contrast to the traditional neighborhood classifier. This research provides a new direction for improving the accuracy of neighborhood classification.

A Fuzzy Rule-Based System for Classification of Diabetes

Diabetes is a fatal disease that currently has no treatment. However, early diagnosis of diabetes aids patients to start timely treatment and thus reduces or eliminates the risk of severe complications. The prevalence of diabetes has been rising rapidly worldwide. Several methods have been introduced to diagnose diabetes at an early stage, however, most of these methods lack interpretability, due to which the diagnostic process cannot be explained. In this paper, fuzzy logic has been employed to develop an interpretable model and to perform an early diagnosis of diabetes. Fuzzy logic has been combined with the cosine amplitude method, and two fuzzy classifiers have been constructed. Afterward, fuzzy rules have been designed based on these classifiers. Lastly, a publicly available diabetes dataset has been used to evaluate the performance of the proposed fuzzy rule-based model. The results show that the proposed model outperforms existing techniques by achieving an accuracy of 96.47%. The proposed model has demonstrated great prediction accuracy, suggesting that it can be utilized in the healthcare sector for the accurate diagnose of diabetes.

A topological reduction for predicting of a lung cancer disease based on generalized rough sets

The present work proposes new styles of rough sets by using different neighborhoods which are made from a general binary relation. The proposed approximations represent a generalization to Pawlak’s rough sets and some of its generalizations, where the accuracy of these approximations is enhanced significantly. Comparisons are obtained between the methods proposed and the previous ones. Moreover, we extend the notion of “nano-topology”, which have introduced by Thivagar and Richard [49], to any binary relation. Besides, to demonstrate the importance of the suggested approaches for deciding on an effective tool for diagnosing lung cancer diseases, we include a medical application of lung cancer disease to identify the most risk factors for this disease and help the doctor in decision-making. Finally, two algorithms are given for decision-making problems. These algorithms are tested on hypothetical data for comparison with already existing methods.

Different kinds of generalized rough sets based on neighborhoods with a medical application

Approximation space can be said to play a critical role in the accuracy of the set’s approximations. The idea of “approximation space” was introduced by Pawlak in 1982 as a core to describe information or knowledge induced from the relationships between objects of the universe. The main objective of this paper is to create new types of rough set models through the use of different neighborhoods generated by a binary relation. New approximations are proposed representing an extension of Pawlak’s rough sets and some of their generalizations, where the precision of these approximations is substantially improved. To elucidate the effectiveness of our approaches, we provide some comparisons between the proposed methods and the previous ones. Finally, we give a medical application of lung cancer disease as well as provide an algorithm which is tested on the basis of hypothetical data in order to compare it with current methods.

A novel stochastic group decision-making framework with dual hesitant fuzzy soft set for resilient supplier selection

Suppliers can be regarded as unavoidable sources of external risks in modern supply chains, which may cause disruption of supply chains. A resilient supplier usually has a high adaptive ability to reduce the vulnerability against disruptions and recover from disruption to keep continuity in operations. This paper develops an effective multi-attribute group decision-making (MAGDM) framework for resilient supplier selection. Because of the many uncertainties in resilient supplier selection, the dual hesitant fuzzy soft sets (DHFSSs), a very flexible tool to express uncertain and complex information of decision-makers, is utilized to cope with it. In order to obtain the resilient supplier’s partial order relationship and consider the psychological behavior of decision-makers, this paper proposes the MAGDM framework with DHFSSs based on the TOPSIS method and prospect theory for resilient supplier selection. Furthermore, we consider the consensus level among experts of different backgrounds and experiences and propose a consensus measure method based dual hesitant fuzzy soft numbers (DHFSNs) before selecting a resilient supplier. The expert weights are calculated by the group consensus level between the expert and the group opinions. Meanwhile, we define the entropy of DHFSSs to determine the attribute weights objectively in the decision-making process. Based on this, the proposed method is applied to a practical manufacturing enterprise with an international supply chain for a resilient supplier selection problem. Finally, by performing a sensitivity analysis and a comparative analysis, the results demonstrate the robustness and validity of the proposed method.

Possibility belief interval-valued soft set and its application in decision making

The aim of this article is to present the concept of restricted union and extended intersection of belief interval-valued soft sets, along with its properties. In addition, we propose the concept of possibility belief interval-valued soft set theory and investigate their properties. For suitability of possible applications, there are seven kinds of operations (e.g., union, intersection, restricted union, extended intersection, complement, soft max-AND, and soft min-OR) on the possibility belief interval-valued soft sets are defined and their basic theoretical are given. Then, we construct two algorithms by using soft max-AND and soft min-OR operations of possibility interval-valued soft sets for fuzzy decision-making problem. Lastly, we introduce an algorithm using a possibility interval-valued soft set to solve the decision-making problems and clarify its applicability by a numerical example.

Information structures in a fuzzy β-covering information system

This paper studies information structures in a fuzzy β-covering information system. We introduce the concepts of a fuzzy β-covering information system and homomorphism between them, and investigate related properties. The concept of information structure of a fuzzy β-covering information system is given. We discuss the relationships between information structures from the view of dependence and separation. Then granularity measures for a fuzzy β-covering information system are studied. Finally, we discuss invariance of fuzzy β-covering information systems under homomorphism and illustrate its application on data compression.

A new type of generalized picture fuzzy soft set and its application in decision making

 In this article, we propose a novel concept of the generalized picture fuzzy soft set by combining the picture fuzzy soft set and the fuzzy parameter set. For possible applications, we explain five kinds of operations (e.g., subset, equal, union, intersection, and complement) based on generalized picture fuzzy soft sets. Then, we establish several theoretical operations of generalized picture fuzzy soft sets. In addition, we present the new type by using the AND operation of the generalized picture fuzzy soft set for fuzzy decision-making and clarify its applicability with a numerical example. Finally, we give a comparison between the picture fuzzy soft set theory and the generalized picture fuzzy soft set theory. It is shown that our proposed (i.e., generalized picture fuzzy soft set theory) is viable and provide decision makers a more mathematical insight before making decisions on their options.

A decision-making framework for China’s rare earth industry security evaluation by neutrosophic soft CoCoSo method

The rare earth industry is a crucial strategic industry that is related to the national economy and national security. In the context of economic globalization, international competition is becoming increasingly fierce, and the rare earth industry is facing a more severe survival and development environment than ever before. Although China is the greatest world’s rare earth country in rare earth reserves, production, consumption and export volume, it is not a rare earth power. The rare earth industry has no right to speak in the international market. The comparative advantage is weakening and the security of rare earth industry appears. Therefore, studying the rare earth industry security has important theoretical and practical significance. When measuring the China’s rare earth industry security, the primary problem involves tremendous uncertainty. Neutrosophic soft set (NSS), depicted by the parameterized form of truth membership, falsity membership and indeterminacy membership, is a more serviceable pattern for capturing uncertainty. In this paper, five dimensions of rare earth industry security are identified and then prioritized against twelve different criteria relevant to structure, organization, layout, policy and ecological aspects of industry security. Then, the objective weight is computed by CRITIC (Criteria Importance Through Inter-criteria Correlation) method while the integrated weight is determined by concurrently revealing subjective weight and objective weight. Later, neutrosophic soft decision making method based CoCoSo (Combined Compromise Solution) is explored for settling the issue of low discrimination. Lastly, the feasibility and validity of the developed algorithm is verified by the issue of China’s rare earth industry security evaluation.

Medical applications via minimal topological structure

It is known that mathematical statics, mathematical modeling, and differential equations are used to give an in-depth understanding of many medical problems. On the edge of the information revolution, minimal structures show some qualitative properties issues that are difficult to deal with it, such as quality of education, nutrition, etc. The aim of this paper is to discuss two medical applications and show that a minimal structure space is suitable for analyzing several real-life problems. Then, the accuracy of the decision-making and attributes reduction of the medical information system are explained and obtained. Furthermore, we introduce a comparison between our approach and Pawlak’s approach to find accuracy for decision-making. Finally, the accuracy of decision-making via a variable precision model is improved.

Comparison of six types of rough approximations based on j-neighborhood space and j-adhesion neighborhood space

In this paper, we generalize three types of rough set models based on j-neighborhood space (i.e, type 1 j-neighborhood rough set, type 2 j-neighborhood rough set, and type 3 j-neighborhood rough set), and investigate some of their basic properties. Also, we present another three types of rough set models based on j-adhesion neighborhood space (i.e, type 4 j-adhesion neighborhood rough set, type 5 j-adhesion neighborhood rough set, and type 6 j-adhesion neighborhood rough set). The fundamental properties of approximation operators based on j-adhesion neighborhood space are established. The relationship between the properties of these types is explained. Finally, according to j-adhesion neighborhood space, we give a comparison between the Yao’s approach and our approach.

Combination of the Single-Valued Neutrosophic Fuzzy Set and the Soft Set with Applications in Decision-Making

In this article, we propose a novel concept of the single-valued neutrosophic fuzzy soft set by combining the single-valued neutrosophic fuzzy set and the soft set. For possible applications, five kinds of operations (e.g., subset, equal, union, intersection, and complement) on single-valued neutrosophic fuzzy soft sets are presented. Then, several theoretical operations of single-valued neutrosophic fuzzy soft sets are given. In addition, the first type for the fuzzy decision-making based on single-valued neutrosophic fuzzy soft set matrix is constructed. Finally, we present the second type by using the AND operation of the single-valued neutrosophic fuzzy soft set for fuzzy decision-making and clarify its applicability with a numerical example.