A Dual Hesitant Fuzzy Multigranulation Rough Set over Two-Universe Model for Medical Diagnoses

In medical science, disease diagnosis is one of the difficult tasks for medical experts who are confronted with challenges in dealing with a lot of uncertain medical information. And different medical experts might express their own thought about the medical knowledge base which slightly differs from other medical experts. Thus, to solve the problems of uncertain data analysis and group decision making in disease diagnoses, we propose a new rough set model called dual hesitant fuzzy multigranulation rough set over two universes by combining the dual hesitant fuzzy set and multigranulation rough set theories. In the framework of our study, both the definition and some basic properties of the proposed model are presented. Finally, we give a general approach which is applied to a decision making problem in disease diagnoses, and the effectiveness of the approach is demonstrated by a numerical example

Multigranulation Super-Trust Model for Attribute Reduction

IEEE As big data often contains a significant amount of uncertain, unstructured and imprecise data that are structurally complex and incomplete, traditional attribute reduction methods are less effective when applied to large-scale incomplete information systems to extract knowledge. Multigranular computing provides a powerful tool for use in big data analysis conducted at different levels of information granularity. In this paper, we present a novel multigranulation super-trust fuzzy-rough set-based attribute reduction (MSFAR) algorithm to support the formation of hierarchies of information granules of higher types and higher orders, which addresses newly emerging data mining problems in big data analysis. First, a multigranulation super-trust model based on the valued tolerance relation is constructed to identify the fuzzy similarity of the changing knowledge granularity with multimodality attributes. Second, an ensemble consensus compensatory scheme is adopted to calculate the multigranular trust degree based on the reputation at different granularities to create reasonable subproblems with different granulation levels. Third, an equilibrium method of multigranular-coevolution is employed to ensure a wide range of balancing of exploration and exploitation and can classify super elitists’ preferences and detect noncooperative behaviors with a global convergence ability and high search accuracy. The experimental results demonstrate that the MSFAR algorithm achieves a high performance in addressing uncertain and fuzzy attribute reduction problems with a large number of multigranularity variables

New Challenges in Neutrosophic Theory and Applications

Neutrosophic theory has representatives on all continents and, therefore, it can be said to be a universal theory. On the other hand, according to the three volumes of “The Encyclopedia of Neutrosophic Researchers” (2016, 2018, 2019), plus numerous others not yet included in Encyclopedia book series, about 1200 researchers from 73 countries have applied both the neutrosophic theory and method. Neutrosophic theory was founded by Professor Florentin Smarandache in 1998; it constitutes further generalization of fuzzy and intuitionistic fuzzy theories. The key distinction between the neutrosophic set/logic and other types of sets/logics lies in the introduction of the degree of indeterminacy/neutrality (I) as an independent component in the neutrosophic set. Thus, neutrosophic theory involves the degree of membership-truth (T), the degree of indeterminacy (I), and the degree of non-membership-falsehood (F). In recent years, the field of neutrosophic set, logic, measure, probability and statistics, precalculus and calculus, etc., and their applications in multiple fields have been extended and applied in various fields, such as communication, management, and information technology. We believe that this book serves as useful guidance for learning about the current progress in neutrosophic theories. In total, 22 studies have been presented and reflect the call of the thematic vision. The contents of each study included in the volume are briefly described as follows. The first contribution, authored by Wadei Al-Omeri and Saeid Jafari, addresses the concept of generalized neutrosophic pre-closed sets and generalized neutrosophic pre-open sets in neutrosophic topological spaces. In the article “Design of Fuzzy Sampling Plan Using the Birnbaum-Saunders Distribution”, the authors Muhammad Zahir Khan, Muhammad Farid Khan, Muhammad Aslam, and Abdur Razzaque Mughal discuss the use of probability distribution function of Birnbaum–Saunders distribution as a proportion of defective items and the acceptance probability in a fuzzy environment. Further, the authors Derya Bakbak, Vakkas Uluc¸ay, and Memet S¸ahin present the “Neutrosophic Soft Expert Multiset and Their Application to Multiple Criteria Decision Making” together with several operations defined for them and their important algebraic properties. In “Neutrosophic Multigroups and Applications”, Vakkas Uluc¸ay and Memet S¸ahin propose an algebraic structure on neutrosophic multisets called neutrosophic multigroups, deriving their basic properties and giving some applications to group theory. Changxing Fan, Jun Ye, Sheng Feng, En Fan, and Keli Hu introduce the “Multi-Criteria Decision-Making Method Using Heronian Mean Operators under a Bipolar Neutrosophic Environment” and test the effectiveness of their new methods. Another decision-making study upon an everyday life issue which empowered us to organize the key objective of the industry developing is given in “Neutrosophic Cubic Einstein Hybrid Geometric Aggregation Operators with Application in Prioritization Using Multiple Attribute Decision-Making Method” written by Khaleed Alhazaymeh, Muhammad Gulistan, Majid Khan, and Seifedine Kadry

Shared Nearest-Neighbor Quantum Game-Based Attribute Reduction with Hierarchical Coevolutionary Spark and Its Application in Consistent Segmentation of Neonatal Cerebral Cortical Surfaces

© 2012 IEEE. The unprecedented increase in data volume has become a severe challenge for conventional patterns of data mining and learning systems tasked with handling big data. The recently introduced Spark platform is a new processing method for big data analysis and related learning systems, which has attracted increasing attention from both the scientific community and industry. In this paper, we propose a shared nearest-neighbor quantum game-based attribute reduction (SNNQGAR) algorithm that incorporates the hierarchical coevolutionary Spark model. We first present a shared coevolutionary nearest-neighbor hierarchy with self-evolving compensation that considers the features of nearest-neighborhood attribute subsets and calculates the similarity between attribute subsets according to the shared neighbor information of attribute sample points. We then present a novel attribute weight tensor model to generate ranking vectors of attributes and apply them to balance the relative contributions of different neighborhood attribute subsets. To optimize the model, we propose an embedded quantum equilibrium game paradigm (QEGP) to ensure that noisy attributes do not degrade the big data reduction results. A combination of the hierarchical coevolutionary Spark model and an improved MapReduce framework is then constructed that it can better parallelize the SNNQGAR to efficiently determine the preferred reduction solutions of the distributed attribute subsets. The experimental comparisons demonstrate the superior performance of the SNNQGAR, which outperforms most of the state-of-the-art attribute reduction algorithms. Moreover, the results indicate that the SNNQGAR can be successfully applied to segment overlapping and interdependent fuzzy cerebral tissues, and it exhibits a stable and consistent segmentation performance for neonatal cerebral cortical surfaces

Discrete Mathematics and Symmetry

Some of the most beautiful studies in Mathematics are related to Symmetry and Geometry. For this reason, we select here some contributions about such aspects and Discrete Geometry. As we know, Symmetry in a system means invariance of its elements under conditions of transformations. When we consider network structures, symmetry means invariance of adjacency of nodes under the permutations of node set. The graph isomorphism is an equivalence relation on the set of graphs. Therefore, it partitions the class of all graphs into equivalence classes. The underlying idea of isomorphism is that some objects have the same structure if we omit the individual character of their components. A set of graphs isomorphic to each other is denominated as an isomorphism class of graphs. The automorphism of a graph will be an isomorphism from G onto itself. The family of all automorphisms of a graph G is a permutation group

A Data-Driven Condition Monitoring of Product Quality Analysis System Based on RS and AHP

Mechanical and electrical products have complex structure and intelligent control system, their reliability plays an important role in the normal operation of security facilities. However, most manufacturers usually pay more attention to the product designing and manufacturing quality, with little interest in the intelligent fault diagnosis. The objective of this study is to develop the products quality intelligent analysis and management system based on Rough Set (RS) and Analytic Hierarchy Process (AHP). Firstly, this paper reviews the principle of hardware, software design, monitoring platform and quality analysis system to reduce the number of information transfer with computer technology. Secondly, the fault types and feature extractions of different faults of elevators are presented and simplified by using RS theory. Then, the objective weight of level index model can be obtained by AHP method, and the comprehensive analysis weight of each index is obtained by using the value of subjective and objective weight coefficients with the golden ratio. Finally, a comprehensive decision weight of the major index for quality control analysis system of many vertical elevators is presented. The results show that the data-driven condition monitoring and quality analysis system is a kind of important means to prevent a disaster of complex mechanical and electrical products