What is fuzzy logic?--a system of concepts and methods for exploring modes of reasoning that are approximate rather than exact. While the engineering community has appreciated the advances in ...understanding using fuzzy logic for quite some time, fuzzy logic's impact in non-engineering disciplines is only now being recognized. The authors of Fuzzy Logic in Geology attend to this growing interest in the subject and introduce the use of fuzzy set theory in a style geoscientists can understand. This is followed by individual chapters on topics relevant to earth scientists: sediment modeling, fracture detection, reservoir characterization, clustering in geophysical data analysis, ground water movement, and time series analysis. George Klir is the Distinguished Professor of Systems Science and Director of the Center for Intelligent Systems, Fellow of the IEEE and IFSA, editor of nine volumes, editorial board member of 18 journals, and author or co-author of 16 booksForeword by the inventor of fuzzy logic-- Professor Lotfi Zadeh
The aim of this paper is to formalize, within a broad range of theories of imprecise probabilities, the notion of a total, aggregate measure of uncertainty and its various disaggregations into ...measures of nonspecificity and conflict. As a framework for facilitating this aim, we introduce a system of well-justified axiomatic requirements for such measures. It is shown that these requirements can be equivalently defined for belief functions and credal sets. Some important consequences are then derived within this framework, which clarify the role of various uncertainty measures proposed in the literature. Moreover, some well-defined new open problems for future research also emerge from the introduced framework.
The paper gives an overview of applying fuzzy measures and relevant nonlinear integrals in data mining, discussed in five application areas: set function identification, nonlinear multiregression, ...nonlinear classification, networks, and fuzzy data analysis. In these areas, fuzzy measures allow us to describe interactions among feature attributes towards a certain target (objective attribute), while nonlinear integrals serve as aggregation tools to combine information from feature attributes. Values of fuzzy measures in these applications are unknown and are optimally determined via a soft computing technique based on given data.
The aim of this paper is to provide a survey of issues regarding the problem of solving generalized fuzzy relational equations that are defined within a recently introduced framework of ...sup-preserving aggregation structures. Generalized fuzzy relational equations subsume the previously studied types of fuzzy relational equations, that is those based on either sup-t-norm or inf-residuum classes of compositions.
The principal purpose of this paper is to present a comprehensive overview of generalized information theory (GIT): a research program whose objective is to develop a broad treatment of ...uncertainty-based information, not restricted to classical notions of uncertainty. After a brief overview of classical information theories, a broad framework for formalizing uncertainty and the associated uncertainty-based information of a great spectrum of conceivable types is sketched. The various theories of imprecise probabilities that have already been developed within this framework are then surveyed, focusing primarily on some important unifying principles applying to all these theories. This is followed by introducing two higher levels of the theories of imprecise probabilities: (i) the level of measuring the amount of relevant uncertainty (predictive, retrodictive, prescriptive, diagnostic, etc.) in any situation formalizable in each given theory, and (ii) the level of some methodological principles of uncertainty, which are contingent upon the capability to measure uncertainty and the associated uncertainty-based information. Various issues regarding both the measurement of uncertainty and the uncertainty principles are discussed. Again, the focus is on unifying principles applicable to all the theories. Finally, the current status of GIT is assessed and future research in the area is discussed.
It is shown in this paper how the emergence of fuzzy set theory and the theory of monotone measures considerably expanded the framework for formalizing uncertainty and suggested many new types of ...uncertainty theories. The paper focuses on issues regarding the measurement of the amount of relevant uncertainty (predictive, prescriptive, diagnostic, etc.) in nondeterministic systems formalized in terms of the various uncertainty theories. It is explained how information produced by an action can be measured by the reduction of uncertainty produced by the action. Results regarding measures of uncertainty (and uncertainty-based information) in possibility theory, Dempster–Shafer theory, and the various theories of imprecise probabilities are surveyed. The significance of these results in developing sound methodological principles of uncertainty and uncertainty-based information is discussed.
The principal aim of this paper is to bring the relatively little-known Hartley-like measure of uncertainty to the attention of readers of this journal. First, the reader is introduced to the ...classical Hartley measure of uncertainty, applicable to finite sets, and to the complementary Hartley-like measure of uncertainty, applicable to infinite sets. This is followed by an overview of some well-known applications of these measures to classical sets as well as standard fuzzy sets of possible alternatives. Applications of the Hartley-like measure to two types of non-standard fuzzy sets are then explored. This paper concludes with a discussion of two open research problems regarding the Hartley-like measure, solutions of which are essential for overcoming some practical limitations of this measure.
A revised fuzzy-set interpretation of possibility theory is introduced in this paper. Contrary to the standard fuzzy-set interpretation of possibility theory, which is coherent only for normal fuzzy ...sets, the revised interpretation is shown to be coherent for all fuzzy sets. It is also argued that the revised interpretation, which coincides with the standard one for normal fuzzy sets, is more meaningful on intuitive grounds. Prior to the introduction of the revised interpretation, previous efforts to overcome the well-known difficulties of the standard interpretation are critically examined, and it is demonstrated that none of them results in a coherent and meaningful interpretation of possibility theory.
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