Erich Peter Klement

Bio: Erich Peter Klement is an academic researcher from Johannes Kepler University of Linz. The author has contributed to research in topics: Fuzzy logic & Fuzzy set. The author has an hindex of 44, co-authored 184 publications receiving 6183 citations. Previous affiliations of Erich Peter Klement include University of Mainz & University of California, Berkeley.

Limit Theorems for Fuzzy Random Variables

Abstract: A strong law of large numbers and a central limit theorem are proved for independent and identically distributed fuzzy random variables, whose values are fuzzy sets with compact levels. The proofs are based on embedding theorems as well as on probability techniques in Banach space.

A Universal Integral as Common Frame for Choquet and Sugeno Integral

Abstract: The Choquet and the Sugeno integral provide a useful tool in many problems in engineering and social choice where the aggregation of data is required. However, their applicability is restricted because of the special operations used in the construction of these integrals. Therefore, we provide a concept of integrals generalizing both the Choquet and the Sugeno case. For functions with values in the nonnegative real numbers, universal integrals are introduced and investigated, which can be defined on arbitrary measurable spaces and for arbitrary monotone measures. For a fixed pseudo-multiplication on the nonnegative real numbers, the smallest and the greatest universal integrals are given. Finally, another construction method for obtaining universal integrals is introduced, and the restriction to the unit interval, i.e., to fuzzy integrals, is considered.

Triangular Norm-Based Measures and Games with Fuzzy Coalitions

Abstract: Introduction. I. Triangular Norm-Based Tribes. II. Triangular Norm-Based Measures. III. Too-Measures. IV. Games with Fuzzy Coalitions. V. Extensions of the Diagonal Value. VI. Related Topics and Applications. Bibliography. Index.

Machine learning

Abstract: 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.).

Fuzzy Set Theory - and Its Applications

Abstract: Fuzzy Set Theory - And Its Applications, Third Edition is a textbook for courses in fuzzy set theory. It can also be used as an introduction to the subject. The character of a textbook is balanced with the dynamic nature of the research in the field by including many useful references to develop a deeper understanding among interested readers. The book updates the research agenda (which has witnessed profound and startling advances since its inception some 30 years ago) with chapters on possibility theory, fuzzy logic and approximate reasoning, expert systems, fuzzy control, fuzzy data analysis, decision making and fuzzy set models in operations research. All chapters have been updated. Exercises are included.

On ordered weighted averaging aggregation operators in multicriteria decisionmaking

Abstract: The author is primarily concerned with the problem of aggregating multicriteria to form an overall decision function. He introduces a type of operator for aggregation called an ordered weighted aggregation (OWA) operator and investigates the properties of this operator. The OWA's performance is found to be between those obtained using the AND operator, which requires all criteria to be satisfied, and the OR operator, which requires at least one criteria to be satisfied. >

Convergence of Probability Measures

Abstract: Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.