Single Valued Neutrosophic Set Correlation Coefficient And Its Application In Fault Diagnosis

With the increasing automation of mechanical equipment, fault diagnosis becomes more and more important. However, the factors that cause mechanical failures are becoming more and more complex, and the uncertainty and coupling between the factors are getting higher and higher. In order to solve the given problem, this paper proposes a single-valued neutrosophic set ISVNS algorithm for processing of uncertain and inaccurate information in fault diagnosis, which generates neutrosophic set by triangular fuzzy number and introduces the formula of the improved weighted correlation coefficient. Since both the single-valued neutrosophic set data and the ideal neutrosophic set data are considered, the proposed method solves the fault diagnosis problem more eff ectively. Finally, experiments show that the algorithm can significantly improve the accuracy degree of fault diagnosis, and can better satisfy the diagnostic requirements in practice.

This volume presents state-of-the-art papers on new topics related to neutrosophic theories, such as neutrosophic algebraic structures, neutrosophic triplet algebraic structures, neutrosophic extended triplet algebraic structures, neutrosophic algebraic hyperstructures, neutrosophic triplet algebraic hyperstructures, neutrosophic n-ary algebraic structures, neutrosophic n-ary algebraic hyperstructures, refined neutrosophic algebraic structures, refined neutrosophic algebraic hyperstructures, quadruple neutrosophic algebraic structures, refined quadruple neutrosophic algebraic structures, neutrosophic image processing, neutrosophic image classification, neutrosophic computer vision, neutrosophic machine learning, neutrosophic artificial intelligence, neutrosophic data analytics, neutrosophic deep learning, and neutrosophic symmetry, as well as their applications in the real world.

Since linguistic neutrosophic numbers (LNNs) are depicted independently by the truth, indeterminacy, and falsity linguistic variables in indeterminate and inconsistent linguistic environment, they are very fit for human thinking and expressing habits to judgments of complex objects in real life world. Then the correlation coefficient is a critical mathematical tool in pattern recognition and decision making science, but the related research was rarely involved in LNN setting. Hence, this work first proposes two new correlation coefficients of LNNs based on the correlation and information energy of LNNs as the complement/extension of our previous work, and then develops a multiple criteria group decision making (MCGDM) method based on the proposed correlation coefficients in LNN setting. Lastly, a decision making example is provided to illustrate the applicability of the developed method. By comparison with the MCGDM methods regarding the existing correlation coefficients based on the maximum and minimum operations of LNNs, the decision results indicate the effectiveness of the developed MCGDM approach. Hence, the proposed approach provides another new way for linguistic neutrosophic decision making problems.

The single-valued neutrosophic set is a subclass of neutrosophic set, and has been proposed in recent years. An important application for single-valued neutrosophic sets is to solve multicriteria decision-making problems.

This book offers a comprehensive guide to the use of neutrosophic sets in multiple criteria decision making problems. It shows how neutrosophic sets, which have been developed as an extension of fuzzy and paraconsistent logic, can help in dealing with certain types of uncertainty that classical methods could not cope with. The chapters, written by well-known researchers, report on cutting-edge methodologies they have been developing and testing on a variety of engineering problems. The book is unique in its kind as it reports for the first time and in a comprehensive manner on the joint use of neutrosophic sets together with existing decision making methods to solve multi-criteria decision-making problems, as well as other engineering problems that are complex, hard to model and/or include incomplete and vague data. By providing new ideas, suggestions and directions for the solution of complex problems in engineering and decision making, it represents an excellent guide for researchers, lecturers and postgraduate students pursuing research on neutrosophic decision making, and more in general in the area of industrial and management engineering.

The aim of this paper is to propose the generalized version of the multipolar neutrosophic soft set with operations and basic properties. Here, we define the AND, OR, Truth-Favorite, and False-Favorite operators along with their properties. Also, we define the necessity and possibility of operations for them. Later on, to extend it to solve the decision-making problems, we define some information measures such as distance, similarity, and correlation coefficient for the generalized multipolar neutrosophic soft set. Several desirable properties and their relationship between them are derived. Finally, based on these information measures, a decision-making algorithm is stated under the neutrosophic environment to tackle the uncertain and vague information.

Single-valued neutrosophic sets (SVNSs) handling the uncertainties characterized by truth, indeterminacy, and falsity membership degrees, area more flexible way to capture uncertainty.

Fault diagnosis is an extensively applied issue to monitor condition and diagnose fault for safe and stable operation of the machine, which started to develop during the industrial revolution and applies various theories and technologies. Due to the growing complexity of contributing factors of a fault and the correlation of fault attributes which are often interrelated, traditional fault diagnosis methods fails to handle with this complex condition. To solve this problem, a new fault diagnosis method based on attributes weighted neutrosophic set is proposed in this paper. In the proposed approach, a attributes weighted model is developed to obtain the weights of attributes by the fault information. For a sample whose fault type is unknown, the neutrosophic set generated from the fault sample data are aggregated via the single valued neutrosophic power weighted averaging (SVNPWA) operator with the obtained attributes weights, then, the fault diagnosis results could be determined by the defuzzification method of fused neutrosophic set. This proposed method have capacity to differentiate the individual impact of attributes and handle the uncertain problems in the process of fault diagnosis. Finally, an illustrative example was provided to demonstrate the reasonableness and effectiveness of the proposed method.