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.

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 contains 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 fail 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 defuzzication 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.

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.

In this paper, a neutrosophic set based fault diagnosis method based on multi-stage fault template data is proposed to solve this problem. For an unknown fault sample whose fault type is unknown and needs to be diagnosed, the neutrosophic set based on multi-stage fault template data is generated, and then the generated neutrosophic set is fused via the simplified neutrosophic weighted averaging (SNWA) operator.

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.

Neutrosophic set, initiated by Smarandache, is a novel tool to deal with vagueness considering the truth-membership T, indeterminacy-membership I and falsity-membership F satisfying the condition 0 ≤ T + I + F ≤ 3. It can be used to characterize the uncertain information more sufficiently and accurately than intuitionistic fuzzy set. Neutrosophic set has attracted great attention of many scholars that have been extended to new types and these extensions have been used in many areas such as aggregation operators, decision making, image processing, information measures, graph and algebraic structures.

Zadeh's fuzzy set theory incorporates the impreciseness of data and evaluations, by imputting the degrees by which each object belongs to a set. Its success fostered theories that codify the subjectivity, uncertainty, imprecision, or roughness of the evaluations. Their rationale is to produce new flexible methodologies in order to model a variety of concrete decision problems more realistically. This Special Issue garners contributions addressing novel tools, techniques and methodologies for decision making (inclusive of both individual and group, single- or multi-criteria decision making) in the context of these theories. It contains 38 research articles that contribute to a variety of setups that combine fuzziness, hesitancy, roughness, covering sets, and linguistic approaches. Their ranges vary from fundamental or technical to applied approaches.