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

Data Mining - Concepts and Techniques.

Theory of fuzzy integrals and its applications

We describe the idea of Pythagorean membership grades and the related idea of Pythagorean fuzzy subsets. We focus on the negation and its relationship to the Pythagorean theorem. We look at the basic set operations for the case of Pythagorean fuzzy subsets. A relationship is shown between Pythagorean membership grades and complex numbers. We specifically show that Pythagorean membership grades are a subclass of complex numbers called Π-i numbers. We investigate operations that are closed under Π-i numbers. We consider the problem of multicriteria decision making with satisfactions expressed as Pythagorean membership grades, Π-i numbers. We look at the use of the geometric mean and ordered weighted geometric operator for aggregating criteria satisfaction.

Pythagorean Membership Grades, Complex Numbers, and Decision Making

Some patients, especially patients with chronic diseases such as heart disease, require continuous monitoring of their condition. Wearable devices for patient monitoring were introduced many years ago – for instance, wearable ambulatory ECG (electrocardiogram) recorders commonly known as Holter monitors (Figure 1) are used for monitoring cardiac patients. However, these monitors are quite bulky and can only record the signal for a limited time. Patients are often asked to wear a Holter monitor for a few days and then return to the clinic for diagnosis. This often overlooks transient but life-threatening events. In addition, we don’t know under what condition the signals are acquired, and this often leads to false alarms. For example, a sudden rise in heart rate may be caused by emotion, such as watching a horror movie, or by exercise, rather than by a heart condition. Body sensing To address these issues, the concept of Body Sensor Networks (BSN) was first proposed in 2002 by Prof. Guang-Zhong Yang from Imperial College London. The aim of the BSN is to provide a truly personalised monitoring platform that is pervasive, intelligent, and Figure 1 A patient wearing a Holter monitor

Body sensor networks

The objective of this paper is to investigate the innovative concept of complex fuzzy sets. The novelty of the complex fuzzy set lies in the range of values its membership function may attain. In contrast to a traditional fuzzy membership function, this range is not limited to [0, 1], but extended to the unit circle in the complex plane. Thus, the complex fuzzy set provides a mathematical framework for describing membership in a set in terms of a complex number. The inherent difficulty in acquiring intuition for the concept of complex-valued membership presents a significant obstacle to the realization of its full potential. Consequently, a major part of this work is dedicated to a discussion of the intuitive interpretation of complex-valued grades of membership. Examples of possible applications, which demonstrate the new concept, include a complex fuzzy representation of solar activity (via measurements of the sunspot number), and a signal processing application. A comprehensive study of the mathematical properties of the complex fuzzy set is presented. Basic set theoretic operations on complex fuzzy sets, such as complex fuzzy complement, union, and intersection, are discussed at length. Two novel operations, namely set rotation and set reflection, are introduced. Complex fuzzy relations are also considered. Index Terms-Complex fuzzy intersection, complex fuzzy relations, complex fuzzy sets, complex fuzzy union, complex-valued grades of membership, fuzzy complex numbers.

Menahem Friedman

Papers

Complex fuzzy sets

Fuzzy linear systems

Numerical solutions of fuzzy differential and integral equations

Numerical solutions of fuzzy differential equations

A new fuzzy arithmetic