Application of Artificial Intelligence to Gearbox Fault Diagnosis

Gearboxes are employed in a wide variety of applications, ranging from small domestic appliances to the rather gigantic power plants and marine propulsion systems. Gearbox failure may not only result in significant financial losses resulting from downtime of machinery but may also place human life at risk. Gearbox failure in transmission systems of warships and single engine aircraft, beside other military applications, is unacceptable. The criticality of the gearbox in rotary machines has resulted in enormous effort on the part of researchers to develop new and efficient methods of diagnosing faults in gearboxes so that timely rectification can be undertaken before catastrophic failure occurs. Artificial intelligence (AI) has been a significant milestone in automated gearbox fault diagnosis (GFD). This chapter reviews over a decade of research efforts on fault diagnosis of gearboxes with AI techniques. Some of areas of AI in GFD which still merit attention have been identified and discussed at the end of the chapter.

Uncertainty Analysis Using Fuzzy Random Set Theory

Uncertainty analysis of any physical model is always an essential task from the point of decision making analysis. Two kinds of uncertainties exist: (1) aleatory uncertainty which is due to randomness of the parameters of models of interest and (2) the epistemic uncertainty which is due to fuzziness of the parameters of the same models. So far both these uncertainties are addressed independently; however since in any practical problem both the types of uncertain variables present, it is required to address them jointly. In order to solve practical problems on uncertainty modeling, it is required to replace the abstract definition of hybrid set by fuzzy random set. Since uncertainty modeling using fuzzy random set has not been carried out so far, the present chapter will address the utility of fuzzy random set for uncertainty modeling on geotechnical and hydrological applications. This chapter will present the fundamentals of fuzzy random set and their application in uncertainty analysis.

Introduction to Intuitionistic Fuzzy Multisets and Its Applications

In this chapter a new concept named Intuitionistic Fuzzy Multiset is introduced, which is an attempt to combine the two concepts: Intuitionistic Fuzzy sets and Fuzzy Multisets. The basic operations and their various properties are discussed. The authors discussed two significant applications of Intuitionistic Fuzzy Multisets. Most of human reasoning involves the use of variables whose values are fuzzy sets. This is the basis for the concept of a linguistic variable. But in some situations like decision making problems, the description by a linguistic variable in terms of membership function only is not adequate. There is chance of existing a non-null complement. There are situations that each element has different membership values. In such situations Intuitionistic Fuzzy Multisets is more adequate. Here the authors present Intuitionistic Fuzzy Multisets as a tool for reasoning such a situation through a medical diagnosis problem. As the second application, accuracy of Collaborative Robots using the concept of Intuitionistic Fuzzy Multiset is discussed.

Creating Generalized and Hybrid Set and Library with Neutrosophy and Quad-Stage Method

Generalized and hybrid set can be created with neutrosophy and quad-stage method. Firstly the generalized and hybrid neutrosophic set is discussed. Secondly the combination or synthetical body of generalized and hybrid sets is named as “library” (various generalized and hybrid sets can be put into the related “library”); such as “mathematics library”, “physics library”, and the like. As for the constitution of “library”, the concept and methodology of a special “Four-library” are proposed. Neutrosophy and quad-stage method can also be used to solve many actual problems within the framework of “set” and “library”; for example, based on the analyses of one “Four-library”, jointly solving problem of advance of planet's perihelion with partial results of law of gravity and general relativity; and jointly expanding “uncertainty principle” to “certainty-uncertainty principle set”. Finally, we introduce the concepts of “variational principle of set” and “variational principle of library”, and establish a kind of “partial and temporary unified theory of mathematics so far”.

Multi-Attribute Decision Making Based on Interval Neutrosophic Trapezoid Linguistic Aggregation Operators

Multi-attribute decision making (MADM) play an important role in many applications, due to the efficiency to handle indeterminate and inconsistent information, interval neutrosophic sets is widely used to model indeterminate information. In this paper, a new MADM method based on interval neutrosophic trapezoid linguistic weighted arithmetic averaging aggregation (INTrLWAA) operator and interval neutrosophic trapezoid linguistic weighted geometric aggregation (INTrLWGA) operatoris presented. A numerical example is presented to demonstrate the application and efficiency of the proposed method.

Generalized Fuzzy Closed Sets in Smooth Bitopological Spaces

This chapter is devoted to the study of r-generalized fuzzy closed sets (briefly, gfc sets) in smooth bitopological spaces (briefly, smooth bts) in view definition of Šostak (1985). The chapter is divided into seven sections. The aim of Sections 1-2 is to introduce the fundamental concepts related to the work. In Section 3, the concept of r-(ti,tj)-gfc sets in the smooth bts's is introduce and investigate some notions of these sets, generalized fuzzy closure operator induced from these sets. In Section 4, (i,j)-GF-continuous (respectively, irresolute) mappings are introduced. In Section 5, the supra smooth topology which generated from a smooth bts is used to introduce and study the notion of r-t12-gfc sets for smooth bts's and supra generalized fuzzy closure operator . The present notion of gfc sets and the notion which introduced in section 3, are independent. In Section 6, two types of generalized supra fuzzy closure operators introduced by using two different approaches. Finally, Section 7 introduces and studies different types of fuzzy continuity which are related to closure.

Neutrosophic Soft Sets and Their Properties

Soft set plays an important role in the theory of approximations, as parameterized family of subsets in the universe of discourse. On the other hand, neutrosophic set is based on the neutrosophic philosophy, which states that: Every idea A has an opposite anti(A) and its neutral neut(A). This is the main theme of neutrosophic sets and logics. This chapter is about the hybrid structure called neutrosophic soft set, i.e. a soft set defined over a neutrosophic set. This chapter begins with the introduction of soft sets and neutrosophic sets. The notions of neutrosophic soft sets are defined and their properties studied. Then the algebraic structures associated with neutrosophic soft sets are debated. After that, the mappings on soft classes are studied with some of their properties. Finally, the notion of intuitionistic neutrosophic soft sets is taken into consideration.

Generalized Rough Sets

This chapter concerns construction of a new rough set structure for an ideal ordered topological spaces and ordered topological filters. The approximation space approached depend on general binary relation, partially order relation, ideal and filter concepts. Properties of lower and upper approximation are extended to an ideal order topological approximation spaces. The main aim of the rough set theory is reducing the bouwndary region by increasing the lower approximation and decreasing the upper approximation. So, in this chapter different methods are proposed to reduce the boundary region. Comparisons between the current approximations and the previous approximations (El-Shafei et al.,2013) are introduced. It's therefore shown that the current approximations are more generally and reduce the boundary region by increasing the lower approximation and decreasing the upper approximation. The lower and upper approximations satisfy some properties in analogue of Pawlak's spaces (Pawlak, 1982). Moreover, we give several examples for comparison between the current approach and (El-Shafei et al., 2013).

Sequences, Nets, and Filters of Fuzzy Soft Multi Sets in Fuzzy Soft Multi Topological Spaces

In this chapter, the authors introduce a new sequence of fuzzy soft multi sets in fuzzy soft multi topological spaces and their basic properties are studied. The concepts of subsequence, convergence sequence and cluster fuzzy soft multi sets of fuzzy soft multi sets are proposed. Actually Cluster analysis or clustering is the task of grouping a set of objects in such a way that objects in the same group (called a cluster) are more similar to each other than to those in other groups (clusters). It is a main task of exploratory data mining and a common technique for statistical data analysis used in many fields including machine learning, pattern recognition, image analysis, information retrieval and bioinformatics. Here the authors define the notions of net and filter and establish the correspondence between net convergence and filter convergence in fuzzy soft multi topological spaces.

Soft Sets and Its Applications

Uncertainty is an inherent characteristic of modern day databases. In order to handle such databases with uncertainty, several new models have been introduced in the literature. Some new models like fuzzy sets introduced by Zadeh (1965), rough sets invented by Z. Pawlak (1982) and intuitionistic fuzzy sets extended by K.T. Atanassov (1986). All these models have their own pros and cons. However, one of the major problems with these models is the lack of sufficient number of parameters to deal with uncertainty. In order to add adequate number of parameters, soft set theory was introduced by Molodtsov in 1999. Since then the theoretical developments on soft set theory has attracted the attention of researchers. However, the practical applications of any theory are of enough importance to make use of it. In this chapter, the basic definitions of soft set, operations and properties are discussed. Also, the aim in this chapter is to discuss on the different applications of soft sets; like decision making, parameter reduction, data clustering and data dealing with incompleteness.