Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

There is an increasing demand for dynamic systems to become safer and more reliable This requirement extends beyond the normally accepted safety-critical systems such as nuclear reactors and aircraft, where safety is of paramount importance, to systems such as autonomous vehicles and process control systems where the system availability is vital It is clear that fault diagnosis is becoming an important subject in modern control theory and practice Robust Model-Based Fault Diagnosis for Dynamic Systems presents the subject of model-based fault diagnosis in a unified framework It contains many important topics and methods; however, total coverage and completeness is not the primary concern The book focuses on fundamental issues such as basic definitions, residual generation methods and the importance of robustness in model-based fault diagnosis approaches In this book, fault diagnosis concepts and methods are illustrated by either simple academic examples or practical applications The first two chapters are of tutorial value and provide a starting point for newcomers to this field The rest of the book presents the state of the art in model-based fault diagnosis by discussing many important robust approaches and their applications This will certainly appeal to experts in this field Robust Model-Based Fault Diagnosis for Dynamic Systems targets both newcomers who want to get into this subject, and experts who are concerned with fundamental issues and are also looking for inspiration for future research The book is useful for both researchers in academia and professional engineers in industry because both theory and applications are discussed Although this is a research monograph, it will be an important text for postgraduate research students world-wide The largest market, however, will be academics, libraries and practicing engineers and scientists throughout the world

Robust Model-Based Fault Diagnosis for Dynamic Systems

From the Publisher:
A comprehensive treatment of model-based fuzzy control systems
This volume offers full coverage of the systematic framework for the stability and design of nonlinear fuzzy control systems. Building on the Takagi-Sugeno fuzzy model, authors Tanaka and Wang address a number of important issues in fuzzy control systems, including stability analysis, systematic design procedures, incorporation of performance specifications, numerical implementations, and practical applications.
Issues that have not been fully treated in existing texts, such as stability analysis, systematic design, and performance analysis, are crucial to the validity and applicability of fuzzy control methodology. Fuzzy Control Systems Design and Analysis addresses these issues in the framework of parallel distributed compensation, a controller structure devised in accordance with the fuzzy model.
This balanced treatment features an overview of fuzzy control, modeling, and stability analysis, as well as a section on the use of linear matrix inequalities (LMI) as an approach to fuzzy design and control. It also covers advanced topics in model-based fuzzy control systems, including modeling and control of chaotic systems. Later sections offer practical examples in the form of detailed theoretical and experimental studies of fuzzy control in robotic systems and a discussion of future directions in the field.
Fuzzy Control Systems Design and Analysis offers an advanced treatment of fuzzy control that makes a useful reference for researchers and a reliable text for advanced graduate students in the field.

Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach

http://omreza.persiangig.com/Topsis2000.pdf

Extensions of the TOPSIS for group decision-making under fuzzy environment

We present a new method of finding the fuzzy weights in fuzzy hierarchical analysis which is the direct fuzzification of the original method used by Saaty (1980) in the analytic hierarchy process. We test our new procedure in two cases where there are formulas for the crisp weights. An example is presented where there are five criteria and three alternatives.

Fuzzy hierarchical analysis

This chapter continues the previous chapter but now we can have two or more independent (predictor, explanatory) variables, the \(\overline{X}_i\). Another change from Chapter 12 is now we will work with fuzzy trapezoidal (shaped) fuzzy numbers instead of fuzzy triangular (shaped) fuzzy numbers. As in Chapter 12 we usually assume our fuzzy numbers are non-negative so that in the evaluation of fuzzy expressions the extension principle and the α-cut and interval arithmetic method produce the same results. However, in Section 13.5.4 we allow fuzzy numbers in an interval I = [ − a,a], a > 0. This chapter is based on [1].

Multivariate Nonlinear Regression

In this chapter we apply our fuzzy Monte Carlo method to determine approximate solutions to a fuzzy transportation problem. The next section presents the standard definition of the transportation model. Then in Section 23.3 we fuzzify it and apply our fuzzy Monte Carlo method to generate approximate solutions. An example is given which is to show the results of our fuzzy Monte Carlo method.

Fuzzy Transportation Problem

By “long tailed distributions” ([2], Chapter 10) we mean that we have different classes of customers, with one class of customer taking a long time in a server. We will consider only two classes of customer: (1) normal, or those who take a regular, or normal, time in a server; and (2) long, or those who usually take a much longer time in a server. The long tailed distribution relates to the fact that there is a positive probability that a customer will take a long time in the server. We will model this situation as having two different arrival rates, one for the “normal” customers and another for those who take a long time in the servers. Also, there will be two different service rates. The results will depend on whether we are using fuzzy probabilities or fuzzy arrival/service rates.

Long Tailed Distributions

Resolving Contradictions: Possibility and Necessity

We first argue that a very important class of fuzzy functions in multivariate non-linear fuzzy regression is the multivariate fuzzy polynomials. Given some data, generated by a multivariate fuzzy function, our evolutionary algorithm searches our library of multivariate fuzzy polynomials for the one that best fits this data. Tests of our multivariate non-linear fuzzy regression package are given when the multivariate fuzzy function is a multivariate fuzzy polynomial.

James J. Buckley

Papers

Multivariate Nonlinear Regression

Fuzzy Transportation Problem

Long Tailed Distributions

Resolving Contradictions: Possibility and Necessity

Multivariate non-linear fuzzy regression